isapp september 2010 rocky kolb the university of chicago dark matter and energy rocky i: dark...

ISAPP September 2010

Rocky Kolb The University of Chicago

Dark Matter and EnergyDark Matter and Energy

Rocky I: Dark Matter

Rocky II: Dark Energy

Cold Dark Matter: (CDM) 25%

Dark Energy (): 70%

Stars:0.8%

H & He:gas 4%

Chemical Elements: (other than H & He)0.025%

Neutrinos: 0.17%

CDMCDMCDMCDM

Radiation: 0.005%

Cosmological Constant (Dark Energy)Cosmological Constant (Dark Energy)Cosmological Constant (Dark Energy)Cosmological Constant (Dark Energy)

1917 Einstein proposedcosmological constant, .

1929 Hubble discoveredexpansion of the Universe.

1934 Einstein called it“my biggest blunder.”

1998 Astronomers foundevidence for it, and renamed it “Dark Energy.”

Cosmological Constant (Dark Energy)Cosmological Constant (Dark Energy)Cosmological Constant (Dark Energy)Cosmological Constant (Dark Energy)

Einstein’s Equations: 1 82R g R g GT

T g p p U U Equation of State:

Conservation of stress-energy: 3 1; 0 wT a p w

1. If p (w)then Tgand G Cosmological constant behaves like fluid with w

2. Vacuum energy unchanged in expansion 0a

Vacuum energy behaves like fluid with w

The Unbearable Lightness of Nothing

10–30 g cm

The Cosmoillogical ConstantThe Cosmoillogical ConstantThe Cosmoillogical ConstantThe Cosmoillogical Constant

So small, and yet not zero!

The Cosmological ConstantThe Cosmological ConstantThe Cosmological ConstantThe Cosmological Constant

Dark (and Useless) Energy

1 MeV liter


4 430 -3 4 310 g cm 10 eV 10 cm

Illogical magnitude (what’s it related to?):

2 229 338 10 cm 10 eVG


classical

0E quantum

12E

All fields: harmonic oscillators with zero-point energy


All fields: harmonic oscillators with zero-point energy

3 2 2 3C

all particles all particles

d k k m dk k

4

4 90 3

4 30 3

4 30 3

: bad prediction

: 10 g cm

: 10 g cm

10 eV: Observed 10 g cm

C

C Pl Pl

C SUSY SUSY

C

M M

M M

Gravitons: Vacuum energy

e+

e-

g

Photons: Lamb shift

e+

e-


high-temperature

low-temperature

V

V

GUT: g cm SUSY: g cm

EWK: g cm CHIRAL: g cm

OBSERVED: g cm


4 430 -3 4 310 g cm 10 eV 10 cm

Illogical magnitude (what’s it related to?):

2 229 338 10 cm 10 eVG

Illogical timing (cosmic coincidence?):

BBNEWKGUT

M R

REC


TODAY


Global warming, but universal cooling:

The Universe is cold and dark….and getting colder and darker!

(Dark Energy is now ppm and will only increase!)

All evidence for dark energy/acceleration comesfrom measuring the expansion history of the Universe

We infer acceleration/dark energy by comparing observations

with the predictions of a model

Do not directly observe• acceleration of the universe• dark energy

Cosmoillogical Constant (Dark Energy)Cosmoillogical Constant (Dark Energy)Cosmoillogical Constant (Dark Energy)Cosmoillogical Constant (Dark Energy)

University of Chicago 1909 National ChampionsUniversity of Chicago 1909 National Champions

EdwinHubble

Hubble’s Discovery Paper - 1929Hubble’s Discovery Paper - 1929Hubble’s Discovery Paper - 1929Hubble’s Discovery Paper - 1929s

constant sHubble'

v

0

0

H

dH

Riess et al.

velocity: H (Hubble’s constanta

scal

e fa

cto

r a

time

deceleration0a

3 0p

03 0

ap

scal

e fa

cto

r a

time

acceleration

: p

Expansion History of the UniverseExpansion History of the UniverseExpansion History of the UniverseExpansion History of the Universe

acceleration: G ( p) (acceleration)a

distance: D a (cosmic scale factor)

Hubble DiagramHubble DiagramHubble DiagramHubble Diagram

redshift of spectral lines

app

aren

t b

rig

htn

ess

of

stan

dar

d c

and

le

nearby universepresent velocityH

distant universepast velocityacceleration

1929–1998

1998–today

Friedmann equation (G GT)


2

23 3 8

a kG

a a

Friedmann-Robertson-Walker metric

2

2 2 2 2 2 2 2 22

sin 1

drds dt a t r d r d

kr

a(t) = cosmic scale factor

k spatial curvature constant: R k/a(t)



22

8

3

k GH

a

0ii

C

t

203

8C

H

G

01

az

a t redshift:

critical density:


Hubble constant curvature matter radiation


• “All of observational cosmology is a search for two numbers.” (H and M) — Sandage, Physics Today, 1970

2 3 42 20 1 1 1k M RH z H z z z

• radiation contribution (R) small for z 2 32 2

0 1 1 1M MH z H z z

• kMR 2 3 42 2

0 1 1 1 1M R M RH z H z z z

• Age of the universe

Many observables based on H(z) [ or dz H(z) ]

• Luminosity distance Flux = (Luminosity / dL)

• Angular diameter distance Physical size / dA

• Volume (number counts) N / V (z)

• Distances


"How helpful to us is astronomy's pedantic accuracy, which I used to secretly ridicule!"

Precision CosmologyPrecision CosmologyPrecision CosmologyPrecision Cosmology

Einstein’s statement to Arnold Sommerfeld on December 9, 1915 (regarding measurements of the advance of the perihelion of Mercury)

ClosedFlatOpen

Accelerating

Decelerating

M

1. Find standard candle (SNe Ia)2. Observe magnitude & redshift 3. Assume a cosmological model

4. Compare observations & model

Astier et al. (2006)SNLS

Einstein–de Sitter model

Hubble DiagramHubble DiagramHubble DiagramHubble Diagram2.0

1.5

1.0

0.5

00 0.5 1.0

• radiation contribution (R) small for z


2 3 42 20

0 1 1 11 k M RH z zH z z z

Hubble cosmological constant constant curvature matter radiation


• [Could add walls ( z )]

• kMR

• k well determined (close to zero) from CMB

• M reasonably well determined


Equation of state parameter: w p wfor

if w w(z): 3 1

0

1 exp 3 1z

w dzz w z

z

2 312 3 420 1 11 1

w

w k M RH z zH z z z

dark energy curvature matter radiation


parameterize: w(z) w wa z (z)

Cosmology is a search for two numbers (w and wa).

Ast

ier

et a

l. (

2006

)S

NL

SE

instein

-de S

itter: sp

atially flat, k

,m

atter-do

min

ated m

od

el(m

aximu

m th

eoretical b

liss)

CDM

con

fusi

ng

ast

ron

om

ical

no

tati

on

re

late

d t

o s

up

ern

ova

bri

gh

tnes

s

supernova redshift z

3) Baryon acoustic oscillations4) Weak lensing

1) Hubble diagram (SNe)2) Cosmic Subtraction

The case for :5) Galaxy clusters6) Age of the universe7) Structure formation


cmb

dynamics x-ray gaslensing

simulations

power spectrum

TOTAL M

CMB many methods


How We “Know” Dark Energy ExistsHow We “Know” Dark Energy ExistsHow We “Know” Dark Energy ExistsHow We “Know” Dark Energy Exists• Assume model cosmology:

– Friedmann-Lemaître-Robertson-Walker (FLRW) model Friedmann equation: H2 G/ k/a2

– Energy (and pressure) content: M R +

– Input or integrate over cosmological parameters: H, B, etc.

• Calculate observables dL(z), dA(z), H(z),

• Compare to observations

• Model cosmology fits with , but not without

• All evidence for dark energy is indirect : observed H(z) is not described by H(z) calculated from the Einstein-de Sitter model [spatially flat (from CMB) ; matter dominated (M)]

Taking Sides!Taking Sides!Taking Sides!Taking Sides!

• Can’t hide from the data – CDM too good to ignore– SNe– Subtraction: – Baryon acoustic oscillations– Galaxy clusters– Weak lensing– …

H(z) not given by

Einstein–de Sitter

G(FLRW) G T(matter)

• Modify left-hand side of Einstein equations (G)

3. Beyond Einstein (non-GR)

4. (Just) Einstein (back reaction of inhomogeneities)

• Modify right-hand side of Einstein equations (T)

1. Constant (“just” a cosmoillogical constant)

2. Not constant (dynamics described by a scalar field)

1964 Austin-Healey Sprite

1974 Fiat 128

Tools to Modify the Right-Hand SideTools to Modify the Right-Hand SideTools to Modify the Right-Hand SideTools to Modify the Right-Hand Side

anthropic principle(the landscape)

scalar fields(quintessence)

Tools to Modify the Right-Hand SideTools to Modify the Right-Hand SideTools to Modify the Right-Hand SideTools to Modify the Right-Hand Side

Duct Tape

Anthropic/Landscape/DUCTtapeAnthropic/Landscape/DUCTtapeAnthropic/Landscape/DUCTtapeAnthropic/Landscape/DUCTtape

• Many sources of vacuum energy

• String theory has many (?) vacua

• Some of them correspond to cancellations that yield a small

• Although exponentially uncommon, they are preferred because …

• More common values of results in an inhospitable universe

Quintessence/Quintessence/WDWD––4040Quintessence/Quintessence/WDWD––4040

• Many possible contributions. • Why then is total so small?• Perhaps unknown dynamics sets global vacuum energy equal to zero……but we’re not there yet!

V()

0

Requires m eV

Tools to Modify the Left-Hand SideTools to Modify the Left-Hand SideTools to Modify the Left-Hand SideTools to Modify the Left-Hand Side

• Braneworld modifies Friedmann equation

• Gravitational force law modified at large distance

• Tired gravitons

• Gravity repulsive at distance R Gpc

• n = 1 KK graviton mode very light, m (Gpc)

• Einstein & Hilbert got it wrong f (R)

• “Backreaction” of inhomogeneities

Five-dimensional at cosmic distances

Deffayet, Dvali& Gabadadze

Gravitons metastable - leak into bulkGregory, Rubakov & Sibiryakov;

Dvali, Gabadadze & Porrati

Kogan, Mouslopoulos,Papazoglou, Ross & Santiago

Csaki, Erlich, Hollowood & Terning

Räsänen; Kolb, Matarrese, Notari & Riotto;Notari; Kolb, Matarrese & Riotto

Binetruy, Deffayet, Langlois

1 4 416S G d x g R R Carroll, Duvvuri, Turner, Trodden

Backreaction of InhomogeneitiesBackreaction of InhomogeneitiesBackreaction of InhomogeneitiesBackreaction of Inhomogeneities

Homogeneous model Inhomogeneous model

3

h

h h

h h h

a V

H a a

3

i

i i

i i i

x

a V

H a a

h i x

We think not!

?h iH H

(Buchert & Ellis)


G (g) G ( g)

Inhomogeneities–ExampleInhomogeneities–ExampleInhomogeneities–ExampleInhomogeneities–Example

FLRW

FLRW00 00 00

2

00

, ,

, 8 ,

8 3

3 8

G x t G t G x t

G t G x t GT x t

a GG

a G

• (aa) is not G

• Perturbed Friedmann–Lemaître–Robertson–Walker model:

Kolb, Matarrese, Notari & Riotto

• (aa is not even the expansion rate)

• Could G be large, or is it ?

• Could G play the role of dark energy?

• The expansion rate of an inhomogeneous universe of average

density need NOT be! the same as the expansion rate of a homogeneous universe of average density !

• Difference is a new term that enters an effective Friedmann equation — the new term need not satisfy energy conditions!

• We deduce dark energy because we are comparing to the wrong model universe.

Ellis, Barausse, Buchert


Célérier; Räsänen; Kolb, Matarrese, Notari & Riotto; Schwarz, …

• Most conservative approach — nothing new – no new fields (like eV mass scalars)– no extra long-range forces– no modification of general relativity– no modification of gravity at large distances– no Lorentz violation– no extra dimensions, bulks, branes, etc.– no anthropic/landscape/faith-based reasoning

• Magnitude?: calculable from observables related to

• Why now?: acceleration triggered by era of non-linear structure

• Possible attractor for effective


CDM is the correct phenomenological model, but …

… there is no dark energy, gravity is not modified,and the universe is not accelerating (in the usual sense).


Backreaction Causes Allergic ReactionBackreaction Causes Allergic Reaction

Acceleration From InhomogeneitiesAcceleration From InhomogeneitiesAcceleration From InhomogeneitiesAcceleration From Inhomogeneities• View scale factor as zero-momentum mode of gravitational field

• In homogeneous/isotropic model it is the only degree of freedom

• Inhomogeneities: non-zero modes of gravitational field

• Non-zero modes interact with and modify zero-momentum mode

cosmology scalar-field theory

zero-mode a (vev of a scalar field)

non-zero modes inhomogeneities thermal/finite-density bkgd.

modify a(t) modify (t) e.g., acceleration e.g., phase transitions

Cosmology scalar field theory analogue

physical effect

• Expansion rate of

inhomogeneous Universe expansion rate of homogeneous

Universe with • Inhomogeneities modify zeromode [effective scale

factor is aD VD]

• Effective scale factor has a (global) effect on observables

• Potentially can account for acceleration without dark energy or modified GR

• Model an inhomogeneous Universe as a homogeneous

Universe model with

• a(t) / V is the zeromode of a homogeneous model with

• Inhomogeneities only have a local effect on observables

• Cannot account for observed acceleration

Standard approach Our approach

Acceleration From InhomogeneitiesAcceleration From InhomogeneitiesAcceleration From InhomogeneitiesAcceleration From Inhomogeneities

cmb

dynamics x-ray gaslensing

i iC C H G

power spectrum

simulations

TOTAL (CMB) M

SubtractionSubtractionSubtractionSubtraction

TOTALM

SubtractionSubtractionSubtractionSubtraction How can 1.0 = 0.3?

For a spatially flat FLRW universe H G

This is another way of stating

This expression is not valid if FLRW is not valid

e.g., 200

8 3

3 8

GH G

G

CélérierIguchi, Nakamura, NakaoMoffat Nambu and Tanimoto Mansouri Chang, Gu, Hwang Alnes, Amarzguioui, Grøn Mansouri Apostolopoulos, Brouzakis, Tetradis, TzavaraGarfinkle Kai, Kozaki, Nakao, Nambu, YooMarra, Kolb, Matarrese, RiottoMustapha, Hellaby, EllisIguchi, Nakamura, NakaoVanderveld, Flanagan, WassermanEnqvist and MattssonBiswas, Mansouri, NotariMarra, Kolb, MatarreseMarraBrouzakis, Tetradis, TzavaraBiswas and NotariBrouzakis and TetradisAlnes and AmarzguiouiGarcia-Bellido and Haugboelle

LemLemaîaître–Tolmantre–Tolman––BondiBondiLemLemaîaître–Tolmantre–Tolman––BondiBondi

• Advantages:– Solvable inhomogeneous model– Can describe wide variety of dynamics

• Disadvantages:– Can’t encompass strong (volume) backreaction (spherical symmetry)– Generically have small dynamical range before shell crossing


22 2 2 2 2,

,1

R r tds dt dr R r t d

r

2 2 2 2 rH R R H R R

2

,8 ,

, ,

r tG r t

R r t R r t

Spherically symmetric metric

Spherically symmetric density

d dt d dr

Expansion rates

2

2 30

,

,

M

R r t ra t

R r t a t

r kr

r H r

FRW

• Spherical model

• Overall Einstein–de Sitter

• Inner underdense Gpc region

• Calculate dL(z)

• Compare to SNe data

• Fit with !• No local acceleration

(counterexample to no-go theorems)


Alnes at al.

LemLemaîaître–Tolmantre–Tolman––BondiBondiLemLemaîaître–Tolmantre–Tolman––BondiBondi• Possible to produce model with EXACT dL(z) and (z) of LCDM

Célérier, et al. 2009

• Slight local overdensity.

Backgrounds and BackreactionsBackgrounds and BackreactionsBackgrounds and BackreactionsBackgrounds and BackreactionsCan write ds () dt a (t) () dx

, but not with a(t)

from the underlying EdS model, but a(t) from a CDM model.

How?

Give some thought to what is meant by a background solution.Kolb, Marra, Matarrese

Backgrounds and BackreactionsBackgrounds and BackreactionsBackgrounds and BackreactionsBackgrounds and BackreactionsSome thoughts on cosmological background solutions

Global Background Solution: FLRW solution generated using H, H (sub-H Hubble volume average),

and the local equation of state (e.o.s.).

Average Background Solution: FLRW solution that describes volume expansion of our past light cone. Energy content, curvature, and e.o.s. that generates the ABS need not be , , nor local e.o.s. (Buchert formalism)

Phenomenological Background Solution: FLRW model that best describes the observations on our light cone. Energy content, curvature, and e.o.s. that generates the PBS need not be H, H, and local e.o.s. (Swiss-cheese example)

Kolb, Marra, Matarrese

Backgrounds and BackreactionsBackgrounds and BackreactionsBackgrounds and BackreactionsBackgrounds and BackreactionsBackreaction: the three backgrounds do not coincide


Strong Backreaction: Global Background Solution does not describe expansion history (hence does not describe observations) (Buchert formalism)

Weak Backreaction: Global Background Solution describes global expansion, but Phenomenological Background Solution differs (Swiss Cheese)

““Backreaction” Causes Allergic ReactionBackreaction” Causes Allergic Reaction““Backreaction” Causes Allergic ReactionBackreaction” Causes Allergic Reaction• We have been driven to consider some remarkable possibilities

– ground states in the landscape– Modification of GR in the infrared– Lorentz violation– eV scalar fields– Extra dimensions

• There should be some effort in rethinking some basic old things

– Is there a global background solution?– Is CDM just a phenomenological background solution?– Could it revolutionize something in the early universe?

• Backreactions can potentially do three remarkable things

– Explain “why now”– Express dark energy parameters in terms of observables– Potentially predict

Taking SidesTaking SidesTaking SidesTaking Sides

1. Right-Hand Side: Dark energy• Constant vacuum energy, i.e., a cosmoillogical constant• Time varying vacuum energy, i.e., quintessence

2. Left-Hand Side • Modification of GR • Standard cosmological model (FLRW) not applicable

The expansion history of the universe is not described by the Einstein-de Sitter model:

Explanations:

1. Well established: Supernova Ia

2. Circumstantial: subtraction, age, structure formation, …

3. Emergent techniques: baryon acoustic oscillations, clusters, weak lensing

Phenomenology:1. Measure evolution of expansion rate: is w ?2. Order of magnitude improvement feasible

Backgrounds and BackreactionsBackgrounds and BackreactionsBackgrounds and BackreactionsBackgrounds and Backreactions


FLRW Assumption: global background solution follows from the cosmological principle

Specify H, H,& local e.o.s. Global Background Solution describes a(t), H(t), and all other observables

GBS PBS if large peculiar velocities



Averaged Peculiar Velocities: velocities obtained after subtracting the Hubble flow of the Averaged Background Solution

Global Peculiar Velocities: velocities obtained after subtracting the Hubble flow of the Global Background Solution

Background peculiar velocity not measured as a local effect

Phenomenological Peculiar Velocities: obtained after subtracting the Hubble flow of the Phenomenological Background Solution



Bare Cosmological Principle: universe is homo/iso on sufficiently large scales can describe observable universe by a mean-field description Average Background Solution exists.

Bare Copernican Principle: no special place in the universe every observer can describe the universe by a mean-field description a Phenomenological Background Solution exists for every observer (but not necessarily unique).



• Average Background Solution follows from the Bare Cosmological Principle.

• Phenomenological Background Solution follows from the Bare Copernican Principle (the success of CDM).

• Global Background Solution follows from the FLRW assumption.

"Nothing more can be done by the theorists. In this matter it is only you, the astronomers, who can perform a simply invaluable service to theoretical physics."

Einstein in August 1913 to Berlin astronomer Erwin Freundlich encouraging him to mount an expedition to measure the deflection of light by the sun.

Dark EnergyDark EnergyDark EnergyDark Energy

H(z)

dL(z) dA(z) V(z)

baryonosc.

stronglensing

weaklensing

supernova clusters clustersstronglensing

Growth of structure

clustersweak

lensing P(k,z)

Observational ProgramObservational ProgramObservational ProgramObservational Program

Test gravity

solarsystem

millimeterscale

accelerators P(k,z)

2 4 0k k kH G

source?

DETF* Experimental Strategy: DETF* Experimental Strategy: DETF* Experimental Strategy: DETF* Experimental Strategy:

• Determine as well as possible whether the accelerating expansion is consistent with being due to a cosmological constant. (Is w ?)

• If the acceleration is not due to a cosmological constant, probe the underlying dynamics by measuring as well as possible the time evolution of the dark energy. (Determine w(z).)

• Search for a possible failure of general relativity through

comparison of the effect of dark energy on cosmic expansion with the effect of dark energy on the growth of cosmological structures like galaxies or galaxy clusters. (Hard to quantify.)

* Dark Energy Task Force

w: the present value of the dark-energy eos parameter

wa : the rate of change of the dark-energy eos parameter

DE : the present dark-energy density

M : the present matter density

B : the present baryon density

H : the Hubble constant : amplitude of rms primordial curvature fluctuations

nS : the spectral index of primordial perturbations.

DETF Cosmological ModelDETF Cosmological ModelDETF Cosmological ModelDETF Cosmological Model

0( ) (1 )aw a w w a Parameterize dark-energy equation of state parameter w as:

• Today (a ) w() w

• In the far past (a → ) w() w wa

Standard eight-dimensional cosmological model:

w

wa

ww((aa)) ww + + wwaa((aa))ww((aa)) ww + + wwaa((aa))

DETF figure of merit:(area) of the error ellipse

wpresent valuewa early value

Supernova Type IaSupernova Type IaSupernova Type IaSupernova Type Ia

• Measure redshift and intensity as function of time (light curve)

• Systematics (dust, evolution, intrinsic luminosity dispersion, etc.)

• A lot of information per supernova

• Well developed and practiced

• Present procedure:

– Discover SNe by wide-area survey (the “easy” part)

– Follow up with spectroscopy (the “hard” part) (requires a lot of time on 8m-class telescopes)

– Photometric redshifts?

Photometric RedshiftsPhotometric RedshiftsPhotometric RedshiftsPhotometric Redshifts

Traditional redshiftfrom spectroscopy

Photometric redshiftfrom multicolor

photometry

Baryon Acoustic OscillationsBaryon Acoustic OscillationsBaryon Acoustic OscillationsBaryon Acoustic OscillationsB

ig B

ang T

od

ay

Time

ionized neutral

recombination

z » t » yrT K

Pre-recombination• universe ionized• photons provide enormous pressure and restoring force• perturbations oscillate (acoustic waves)

Post-recombination• universe neutral• photons travel freely (decoupled from baryons)• perturbations grow (structure formation)

Eisenstein

• Each overdense region is an overpressure that launches a spherical sound wave

• Wave travels outward at c / 3

• Photons decouple, travel to us and observable as CMB acoustic peaks

• Sound speed plummets, wave stalls

• Total distance traveled 150 Mpc imprinted on power spectrum

WMAP

SDSS

Baryon Acoustic OscillationsBaryon Acoustic OscillationsBaryon Acoustic OscillationsBaryon Acoustic Oscillations

Mpc

dA

Mpc Hz

Baryon Acoustic OscillationsBaryon Acoustic OscillationsBaryon Acoustic OscillationsBaryon Acoustic Oscillations• Acoustic oscillation scale depends on M h and B h(set by CMB acoustic oscillations)

• It is a small effect (B h >> M h)

• Dark energy enters through dA and H

• Virtues

– Pure geometry.

– Systematic effects should be small.

• Problems:

– Amplitude small, require large scales, huge volumes

– Photometric redshifts?

– Nonlinear effects at small z, cleaner at large z , but … dark energy is not expected to be important at large z

Baryon Acoustic OscillationsBaryon Acoustic OscillationsBaryon Acoustic OscillationsBaryon Acoustic Oscillations

Weak LensingWeak LensingWeak LensingWeak Lensing

dark energyaffects growth

rate of M

4 LS

OS

DGM

b D

dark energyaffects geometricdistance factors

observedeflection

angle

DOS

DLS

b

Weak LensingWeak LensingWeak LensingWeak Lensing

Space vs. Ground:• Space: no atmosphere PSF

• Space: Near IR for photo-z’s

• Ground: larger aperture

• Ground: less expensive

The signal from any single galaxy is very small,but there are a lot of galaxies! Require photo-z’s?

• DES (2012)– 1000’s of sq. degs. deep multicolor data

• LSST (2015)– full hemisphere, very deep 6 colors

• JDEM/Euclid (???)

Galaxy ClustersGalaxy ClustersGalaxy ClustersGalaxy Clusters

Cluster redshift surveys measure• cluster mass, redshift, and spatial clustering

Sensitivity to dark energy• volume-redshift relation• angular-diameter distance–redshift relation• growth rate of structure• amplitude of clustering

Problems:• cluster selection must be well understood• proxy for mass?• need photo-z’s

Systematics Are The KeySystematics Are The KeySystematics Are The KeySystematics Are The Key

none

optimistic

pessimistic

Technique ZFigure of merit

The Power of Two (or 3, or 4)The Power of Two (or 3, or 4)The Power of Two (or 3, or 4)The Power of Two (or 3, or 4)

Combined

CombinedFigure of merit

Technique AFigure of merit

My guess offutureprogress

OngoingFOM ongoing

Next step UltimateFOM ongoing

95% C.L.

CMB WMAP 2/3 WMAP 5 yr

Planck Planck 4yr

Clusters AMI

SZA

APEX

AMIBA

SPT

ACT

DES

SNe

Pan-STARRS

DES LSST

JDEMSDSS CFHTLS

CSP

ATLAS

SKAFMOS WFMOS

SDSS

Lensing CFHTLS

ATLAS KIDS

DES, VISTA

JDEM

LSST SKA

Pan-STARRS

SUBARU

20202008

ESSENCE

XCS

DUNE

2010

BAO LSST

SDSSDLS

LAMOST

Hyper suprime

DES, VISTA,VIRUS

Pan-STARRSHyper suprime JDEM

What’s AheadWhat’s AheadWhat’s AheadWhat’s Ahead2015

Roger Davies

– Walt Whitman

“To me every hour of the light and dark is a miracle. Every cubic inch of space is a miracle.”

Every cubic inch of space is a miracle!• cosmic radiation• virtual particles• Higgs potential• extra dimensions• dark matter• dark energy

Cold Dark Matter: (CDM) 25%

Dark Energy (): 70%

Stars:0.8%

H & He:gas 4%

Chemical Elements: (other than H & He)0.025%

Neutrinos: 0.17%

CDMCDMCDMCDM

Radiation: 0.005%

I must reject fluids and ethers of all kinds, magnetical, electrical, and universal, to whatever quintessential thinness they may be treble-distilled and (as it were) super-substantiated.

Samuel Taylor Coleridge Theory of Life

(1816)

ISAPP September 2010

Rocky Kolb The University of Chicago

Dark Matter and EnergyDark Matter and Energy

Rocky I: Dark Matter

Rocky II: Dark Energy

Dark Energy Task Force ChargeDark Energy Task Force ChargeDark Energy Task Force ChargeDark Energy Task Force Charge

1. Summarize existing program of funded projects

2. Summarize proposed and emergent approaches

3. Identify important steps, precursors, R&D, …

4. Identify areas of dark energy parameter space existing or

proposed projects fail to address

5. Prioritize approaches (not projects)

“The DETF is asked to advise the agencies on the optimum† near and intermediate-term programs to investigate dark energy and, in cooperation with agency efforts, to advance the justification, specification and optimization of LST# and JDEM‡.”

† Optimum minimum (agencies); Optimum maximal (community)# LST Large Survey Telescope‡ JDEM Joint Dark Energy Mission

Dark Energy Task Force ReportDark Energy Task Force ReportDark Energy Task Force ReportDark Energy Task Force ReportContext

The issue: acceleration of the UniversePossibilities: dark energy ( or not), non-GRMotivation for future investigations

Goals and MethodologyGoal of dark energy investigationsMethodology to analyze techniques/implementations

FindingsTechniques & implementations (largely from White Papers)Systematic uncertaintiesWhat we learned from analysis

RecommendationsA Dark Energy PrimerDETF Fiducial Model and Figure of MeritStaging Stage IV from the Ground and/or SpaceDETF Technique Performance Projections Dark Energy Projects (Present and Future)Technical Appendix

ContextContextContextContext

1. Conclusive evidence for acceleration of the Universe.Standard cosmological framework dark energy (70% of mass-energy).

2. Possibility: Dark Energy constant in space & time (Einstein’s ).

3. Possibility: Dark Energy varies with time (or redshift z or a (z)).

4. Impact of dark energy can be expressed in terms of “equation of state” w(a) p(a) / (a) with w(a) for

5. Possibility: GR or standard cosmological model incorrect.

6. Not presently possible to determine the nature of dark energy.

ContextContextContextContext7. Dark energy appears to be the dominant component of the

physical Universe, yet there is no persuasive theoretical

explanation. The acceleration of the Universe is, along with

dark matter, the observed phenomenon which most directly

demonstrates that our fundamental theories of particles and

gravity are either incorrect or incomplete. Most experts

believe that nothing short of a revolution in our understanding

of fundamental physics will be required to achieve a full

understanding of the cosmic acceleration. For these reasons,

the nature of dark energy ranks among the very most

compelling of all outstanding problems in physical science.

These circumstances demand an ambitious observational

program to determine the dark energy properties as well as

possible.

Goals and MethodologyGoals and MethodologyGoals and MethodologyGoals and Methodology

1. The goal of dark-energy science is to determine the very nature of the darkenergy .Toward this goal, our observational program must:a. Determine whether the accelerated expansion is due to a

cosmological constant.b. If it is not due to a constant, probe the underlying dynamics

bymeasuring as well as possible the time evolution of dark energy, for example by measuring w(a).

c. Search for a possible failure of GR through comparison of cosmicexpansion with growth of structure.

2. w(a) is a continuous function; must parameterize; no parameterization can represent all possibilities; we choose w(a) w + (a)wa ; assumes dark energy insignificant at early

times.

Because the field is so new, it has suffered from a lack of standardization which has made it very difficult to compare directly different approaches.

To address this problem we have done our own modeling of the different techniques so that they could be compared in a consistent manner.

These quantitative calculations form the basis of our extensive factual findings, on which our recommendations are based

Goals and MethodologyGoals and MethodologyGoals and MethodologyGoals and Methodology4. Goals of dark-energy observational program through

measurement of expansion history of Universe [dL(z) , dA(z) , V(z)], and through measurement of growth rate of structure. All described by

w(a). If failure of GR, possible difference in w(a) inferred from different types of

data.

5. To quantify progress in measuring properties of dark energy we definedark energy figure-of-merit from combination of uncertainties in w and wa.

The DETF figure-of-merit is the reciprocal of the area of the error ellipse enclosing the 95% confidence limit in the w–wa plane. Larger figure-of-merit indicates greater

accuracy.

6. Figure of merit serves as a quantitative guide to constrain a large, but not exhaustive, set of dark-energy models. The nature of dark energy is poorly understood; no single figure of merit is appropriate for every eventuality. Potential shortcomings of the choice of any figure of merit must be evaluated in the larger context, which includes the critical need to make side-by-side comparisons. In our judgment there is no better choice of a figure of merit available at this time.

Goals and MethodologyGoals and MethodologyGoals and MethodologyGoals and Methodology

7. We made extensive use of statistical (Fisher-matrix) techniques

incorporating CMB and H information to predict future performance

(75 models).

8. Our considerations follow developments in Stages: I. What is known now (1/1/06).II. Anticipated state upon completion of ongoing projects.III. Near-term, medium-cost, currently proposed projects.IV. Large-Survey Telescope (LST) and/or Square Kilometer

Array (SKA),and/or Joint Dark Energy (Space) Mission (JDEM).

Eighteen FindingsEighteen FindingsEighteen FindingsEighteen Findings1. Four observational techniques dominate White Papers:

a. Baryon Acoustic Oscillations (BAO) large-scale surveys measure features in distribution of galaxies. BAO: dA(z)

and H(z). b. Cluster (CL) surveys measure spatial distribution of galaxy

clusters. CL: dA(z), H(z), growth of structure.

c. Supernovae (SN) surveys measure flux and redshift of Type Ia SNe. SN: dL(z).

d. Weak Lensing (WL) surveys measure distortion of background images due to gravitational lensing. WL: dA(z), growth of structure.

2. Different techniques have different strengths and weaknesses and sensitive in different ways to dark energy and other cosmo. parameters.

3. Each of the four techniques can be pursued by multiple observational approaches (radio, visible, NIR, x-ray observations), and a single experiment can study dark energy with multiple techniques. Not all missions necessarily cover all techniques; in principle different combinations of projects can accomplish the same overall goals.

4. Four techniques at different levels of maturity:a. BAO only recently established. Less affected by

astrophysical uncertainties than other techniques. b. CL least developed. Eventual accuracy very difficult to

predict. Application to the study of dark energy would have to be built upon a strong case that systematics due to non-linear astrophysical processes are under control.

c. SN presently most powerful and best proven technique. If photo-z’s are used, the power of the supernova technique depends critically on accuracy achieved for photo-z’s. If spectroscopically measured redshifts are used, the power as reflected in the figure-of-merit is much better known, with the outcome depending on the ultimate systematic uncertainties.

d. WL also emerging technique. Eventual accuracy will be limited by systematic errors that are difficult to predict. If the systematic errors are at or below the level proposed by the proponents, it is likely to be the most powerful individual technique and also the most powerful component in a multi-technique program.

Eighteen FindingsEighteen FindingsEighteen FindingsEighteen Findings

Systematics: none, optimistic, pessimistic

5. A program that includes multiple techniques at Stage IV can provide more than an order-of-magnitude increase in our figure-of-merit. This would be a major advance in our understanding of dark energy.

6. No single technique is sufficiently powerful and well established that it is guaranteed to address the order-of-magnitude increase in our figure-of-merit alone. Combinations of the principal techniques have substantially more statistical power, much more ability to discriminate among dark energy models, and more robustness to systematic errors than any single technique. Also, the case for multiple techniques is supported by the critical need for confirmation of results from any single method.


Combination

Technique #2

Technique #1

8. In our modeling we assume constraints on H from current

data and constraints on other cosmological parameters expected to come from measurement of CMB temperature and polarization anisotropies.

a. These data, though insensitive to w(a) on their own, contribute to our knowledge of w(a) when combined with any of the dark energy techniques we have considered.

b. Increased precision in a particular cosmological parameter may improve dark energy constraints from a single technique, valuable for comparing independent methods.

7. Results on structure growth, obtainable from weak lensing or cluster observations, are essential program components in order to check for a possible failure of general relativity.

9. Improvements in cosmological parameters tend not to improve knowledge of dark energy from a multi-technique program10. Setting spatial curvature to zero greatly helps SN, but modest impact on other techniques. Little difference when in combination.


(H ): km s Mpc km s Mpc k prior


12. Our inability to forecast reliably systematic error levels is the biggest impediment to judging the future capabilities of the techniques. We need

a. BAO– Theoretical investigations of how far into the non-linear regime the data can be modeled with sufficient reliability and further understanding of galaxy bias on the galaxy power spectrum.

b. CL– Combined lensing and Sunyaev-Zeldovich and/or X-ray observations of large numbers of galaxy clusters to constrain the relationship between galaxy cluster mass and observables.

c. SN– Detailed spectroscopic and photometric observations of about 500 nearby supernovae to study the variety of peak explosion magnitudes and any associated observational signatures of effects of evolution, metallicity, or reddening, as well as improvements in the system of photometric calibrations.

d. WL– Spectroscopic observations and multi-band imaging of tens to hundreds of thousands of galaxies out to high redshifts and faint magnitudes in order to calibrate the photometric redshift technique and understand its limitations. It is also necessary to establish how well corrections can be made for the intrinsic shapes and alignments of galaxies, removal of the effects of optics (and from the ground) the atmosphere and to characterize the anisotropies in

the point-spread function.


13. Six types of Stage III projects have been considered:a. a BAO survey on an 8-m class telescope using

spectroscopyb. a BAO survey on an 4-m class telescope using photo-z’sc. a CL survey on an 4-m class telescope using photo-z’s for

clusters detected in ground-based SZ surveysd. a SN survey on a 4-m class telescope using spectroscopy

from a 8-m class telescope e. a SN survey on a 4-m class telescope using photo-z’sf. A WL survey on a 4-m class telescope using photo-z’s

a. These projects are typically projected by proponents to cost in the range of 10s of $M.


14. Our findings regarding Stage-III projects are1. Only an incremental increase in knowledge of dark-energy

parameters is likely to result from a Stage-III BAO project using photo-z’s. The primary benefit would be in exploring photo-z uncertainties.

2. A modest increase in knowledge of dark-energy parameters is likely to result from Stage-III SN project using photo-z’s. Such a survey would be valuable if it were to establish the viability of photometric determination of supernova redshifts, types, and evolutionary effects.

3. A modest increase in knowledge of dark-energy parameters is likely to result from any single Stage-III CL, WL, spectroscopic BAO, or spectroscopic SN survey.

4. The SN, CL, or WL techniques could, individually, produce factor-of-two improvements in the DETF figure-of-merit, if the systematic errors are close to what the proponents claim.

5. If executed in combination, Stage-III projects would increase the DETF figure-of-merit by a factor in the range of approximately three to five, with the large degree of uncertainty due to uncertain forecasts of systematic errors.


DETF Projections

Stage II

Stage III-p

Stage III-o

Combination of all techniques from a Stage-III photometric survey

15. Four types of next-generation (Stage IV) projects have been considered:

a. an optical Large Survey Telescope (LST), using one or more of the four techniques

b. an optical/NIR JDEM satellite, using one or more of four techniques

c. an x-ray JDEM satellite, which would study dark energy by the cluster technique

d. a Square Kilometer Array, which could probe dark energy by weak lensing and/or the BAO technique through a hemisphere-scale survey of 21-cm emission

Each of these projects is in the $0.3-1B range, but dark energy is not the only (in some cases not even the primary) science that would be done by these projects. According to the White Papers received by the Task Force, the technical capabilities needed to execute LST and JDEM are largely in hand. The Task Force is not constituted to undertake a study of the technical issues.

16. Each of the Stage IV projects considered (LST, JDEM, and SKA) offers compelling potential for advancing our knowledge of dark energy as part of a multi-technique program.


17. The Stage IV experiments have different risk profiles: a. SKA would likely have very low systematic errors, but

needs technical advances to reduce its cost. The performance of SKA would depend on the number of galaxies it could detect, which is uncertain.

b. Optical/NIR JDEM can mitigate systematics because it will likely obtain a wider spectrum of diagnostic data for SN, CL, and WL than possible from ground, incurring the usual risks of a space mission.

c. LST would have higher systematic-error risk, but can in many respects match the statistical power of JDEM if systematic errors, especially those due to photo-z measurements, are small. An LST Stage IV program can be effective only if photo-z uncertainties on very large samples of galaxies can be made smaller than what has been achieved to date.


18. A mix of techniques is essential for a fully effective Stage IV program. The technique mix may be comprised of elements of a ground-based program, or elements of a space-based program, or a combination of elements from ground- and space-based programs. No unique mix of techniques is optimal (aside from doing them all), but the absence of weak lensing would be the most damaging provided this technique proves as effective as projections suggest.


DETF Projections

Stage II

Stage IV-p

Stage IV-o

Combination of all techniques from Stage-IV ground-based survey

DETF Projections

Stage II

Stage IV-p

Stage IV-o

Combination of all techniques from Stage-IV space-based survey

DETF Projections

I. We strongly recommend that there be an aggressive program to explore dark energy as fully as possible, since it challenges our understanding of fundamental physical laws and the nature of the cosmos.

II. We recommend that the dark energy program have multiple techniques at every stage, at least one of which is a probe sensitive to the growth of cosmological structure in the form of galaxies and clusters of galaxies.

III. We recommend that the dark energy program include a combination of techniques from one or more Stage III projects designed to achieve, in combination, at least a factor of three gain over Stage II in the DETF figure-of-merit, based on critical appraisals of likely statistical and systematic uncertainties.

Six RecommendationsSix RecommendationsSix RecommendationsSix Recommendations

IV. We recommend that the dark energy program include a combination of techniques from one or more Stage IV projects designed to achieve, in combination, at least a factor of ten gain over Stage II in the DETF figure-of-merit, based on critical appraisals of likely statistical and systematic uncertainties. Because JDEM, LST, and SKA all offer promising avenues to greatly improved understanding of dark energy, we recommend continued research and development investments to optimize the programs and to address remaining technical questions and systematic-error risks.

V. We recommend that high priority for near-term funding should be given as well to projects that will improve our understanding of the dominant systematic effects in dark energy measurements and, wherever possible, reduce them, even if they do not immediately increase the DETF figure-of-merit.


VI. We recommend that the community and the funding agencies develop a coherent program of experiments designed to meet the goals and criteria set out in these recommendations.


I. Standardization1. Parameterize dark energy as w– wa

2. Eight-parameter cosmological model3. Priors4. Figure of merit

II. Importance of combinations We have a website with library of Fisher matrices &

combiner programs (All power to the people!)

III. DETF Technique Performance Projections1. Thirty-two (count ‘em, 32!) data models2. Optimistic & pessimistic projections3. Four techniques, two stages, five platforms

IV. Use DETF Technique Performance Projections as a guideline!!!

1. We may be off-base (proposers must justify systematic-error budget!)

2. People get smarter

DETF LegacyDETF LegacyDETF LegacyDETF Legacy

The purpose of this SWG is to continue the work of the Dark Energy Task Force in developing a quantitative measure of the power of any given experiment to advance our knowledge about the nature of dark energy. The measure may be in the form of a “Figure of Merit” (FoM) or an alternative formulation.

JOINT DARK ENERGY MISSIONSCIENCE WORKING GROUP

STATEMENT OF TASKJune 2008

FoMSWGFoMSWGFoMSWGFoMSWG

DETF FoMDETF FoMDETF FoMDETF FoM

Marginalize over all other parameters and find uncertainties in w and wa

w

w a

DETF FoM (area of ellipse)

CDM value

errors in w and wa

are correlated

w(a) = w wa( a) w w today & w w wa in the far past

DE DE (today) exp {[ w (a) ] d ln a} CDM: w (a)


From DETF:The figure of merit is a quantitative guide; since the nature of dark energy is poorly understood, no single figure of merit is appropriate for every eventuality.

FoMSWG emphasis!

FoMSWGFoMSWGFoMSWGFoMSWGFoMSWG (like DETF) adopted a Fisher (Information) Matrix approach toward assessing advances in dark energy science.

2

1 b bij i j

b b

f f

p p

observe b quantities

observable b function of parameter pi : f (pi)

FoMSWGFoMSWGFoMSWGFoMSWG1. Pick a fiducial cosmological model.

Not much controversy: CDM [assumes Einstein gravity (GR)].

1. ns scalar spectral index

2. M present matter density M h

3. B present baryon density

4. k present curvature density

5. DE present dark energy density

6. departure of growth from GR prediction caused by dark energy

7. SNe absolute magnitude8. G departure of growth during linear era (unity if GR)

9. ln S(k*) primordial curvature perturbation amplitude

FoMSWGFoMSWGFoMSWGFoMSWG2. Specify cosmological parameters of fiducial cosmological

model (including parameterization of dark energy).

Not much controversy in non-dark energy parameters (we use WMAP5).

Parameterize dark energy as a function of redshift or scale factor



Issue #1: parameterization of w(a) (want to know a function—but can only measure parameters)

• DETF: w(a) w wa( a) w w today & w w wa in the far past – advantage: (only) two parameters– disadvantages: can’t capture more complicated behaviors of w

– FoM based on excluding w (either w or wa )

• FoMSWG: w(a) described by piecewise constant values wi defined in bins between a and a –advantage: can capture more complicated behaviors–disadvantage: 36 parameters (issue for presentation, not computation)

–merit based on excluding w (any wi )



Issue #2: parameterization of growth of structure (testing gravity)

• DETF discussed importance of growth of structure, but offered no measure

• Many (bad) ideas on how to go beyond Einstein gravity—no community consensus on clean universal parameter to test for modification of gravity

• FoMSWG made a choice, intended to be representative of the trends Growth of Structure Growth of Structure (GR) + ln M(z)

: one-parameter measure of departure from Einstein gravity

FoMSWGFoMSWGFoMSWGFoMSWG3. For pre-JDEM and for a JDEM, produce “data models”

including systematic errors, priors, nuisance parameters, etc.• Most time-consuming, uncertain, controversial, and critical

aspect

• Have to predict* “pre-JDEM” (circa 2016) knowledge of cosmological parameters, dark energy parameters, prior information, and nuisance parameters

• Have to predict how a JDEM mission will perform

• Depends on systematics that are not yet understood or completely quantified

* Predictions are difficult, particularly about the future

We made “best guess” for pre-JDEMStrongly recommend don’t reopen this can of worms

FoMSWGFoMSWGFoMSWGFoMSWG4. Predict how well JDEM will do in constraining dark energy.

This is what a Fisher matrix was designed to do:

• can easily combine techniques

• tool (blunt instrument?) for optimization and comparison

Technical issues, but fairly straightforward

FoMSWGFoMSWGFoMSWGFoMSWG5. Quantify this information into a “figure of merit”

Discuss DETF figure of merit

Discuss where FoMSWG differs

DETF FoMDETF FoMDETF FoMDETF FoM

z

wp) w

w

w

zp

excluded

excluded

DETF FoM (area of ellipse)

[(wp)(wa)]

w a

w p

errors in wp and wa

are uncorrelated

(w wa ) (wp, wa)

FoMSWGFoMSWGFoMSWGFoMSWG“… no single figure of merit is appropriate …”

I. Determine the effect of dark energy on the expansion history of the universe by determining w(a), parametrized as described above (higher priority)

… but a couple of graphs and a few numbers can convey a lot!

II. Determine the departure of the growth of structure from the result of the fiducial model to probe dark energy and test gravity

III. A proposal should be free to argue for their own figure of merit

FoMSWGFoMSWGFoMSWGFoMSWGI. Determine the effect of dark energy on the expansion history of the universe by determining w(a), parametrized as described above (higher priority)

1. Assume growth of structure described by GR

2. Marginalize over all non-w “nuisance” parameters

3. Perform “Principal Component Analysis” of w(a)

4. Then assume simple parameterization w(a) = w wa ( a) and calculate (wp), (wa), and zp


• Generally, errors in different wi are correlated (like errors in w and wa)

w

w a

35

0

1 ( ) i ii

w a e a

• Expand w(a) in a complete set of orthogonal eigenvectors ei(a) with eigenvalues ai (like wp and wa)

w a

w p

• Have 36 principal components– Errors ( i) are uncorrelated– Rank how well principal components are measured

• Can do this for each technique individually & in combination


• Graph of principal components as function of z informs on redshift sensitivity of technique [analogous to z p] (may want first few PCs)

• Desirable to have reasonable redshift coverage

• Can visualize techniques independently and in combination


• Graph of for various principal components informs on

sensitivity to w [analogous to (wa) and (wp)]

• If normalize to pre-JDEM, informs on JDEM improvement over pre-JDEM

• Again, can visualize techniques independently and in combination


1. Assume growth of structure described by GR

2. Marginalize over all non-w parameters

3. Perform “Principal Component Analysis” of w(a)

4. Then assume simple parameterization w(a) = w wa ( a)

5. Calculate (wp), (wa), and zp

DETFanalysis

FoMSWGFoMSWGFoMSWGFoMSWGII. Determine the departure of the growth of structure from the result of the fiducial model to probe dark energy and test gravity

Calculate fully marginalized ()

FoMSWGFoMSWGFoMSWGFoMSWGIII. A proposal should be free to argue for their own figure of merit

Different proposals will emphasize different methods, redshift ranges, and aspects of complementarity with external data. There is no unique weighting of these differences. Proposers should have the opportunity to frame their approach quantitatively in a manner that they think is most compelling for the study of dark energy. Ultimately, the selection committee or project office will have to judge these science differences, along with all of the other factors (cost, risk, etc). The FoMSWG method will supply one consistent point of comparison for the proposals.

FoMSWGFoMSWGFoMSWGFoMSWGJudgment on ability of mission to determine departure of Dark Energy from :

1. Graph of first few principal components for individual techniques and combination

• Redshift coverage• Complementarity of techniques

2. Graph of how well can measure modes

• Can easily compare to pre-JDEM (as good as data models)

• Relative importance of techniques (trade offs)

3. Three numbers: (wp), (wa), and zp

• Consistency check

4. One number, ()

FoMSWGFoMSWGFoMSWGFoMSWGConclusions:1. Figure(s) of Merit should not be the sole (or even most

important) criterion1. Systematics2. Redshift coverage3. Departure from w must be convincing!4. Ability to differentiate “true” dark energy from modified

gravity is important5. Multiple techniques important6. Robustness

2. Crucial to have common fiducial model and priors

3. Fisher matrix is the tool of choice1. FoMSWG (and DETF) put enormous time & effort into data

models2. Data models can not be constructed with high degree of

certainty3. Fisher matrix good for comparing and optimizing

techniques4. Principal component analysis yields a lot of information5. We find a prescription for analysis and presentation

4. No one FoM gives complete picture

““Backreaction” Causes Allergic ReactionBackreaction” Causes Allergic Reaction““Backreaction” Causes Allergic ReactionBackreaction” Causes Allergic Reaction

• No compelling argument that backreactions are the answer

– We don’t know necessary or sufficient conditions– Just because some unrealistic model seems to give SNe dL(z) doesn’t mean that backreactions are the answer

• No proof that backreactions are not the answer

– Physics is littered with discarded no-go theorems– Just because some unrealistic model doesn’t give SNe dL(z) doesn’t mean that backreactions are not the answer

• Why take spatial average at fixed time ?

• If this is a large effect one would expect to see large velocities.

• Don’t see it in Newtonian limit.

• Even with large non-linear perturbations, can write metric in perturbed Newtonian form ds () dt + a(t) () dx

with

Strong Allergic ReactionStrong Allergic ReactionStrong Allergic ReactionStrong Allergic Reaction

• Don’t see it in perturbation theory.

• No-go theorem: local deceleration parameter positive. irrelevant

light-cone average

not Newtonian

not perturbative

red herring

with respect to which background?

Inhomogeneities–CosmologyInhomogeneities–CosmologyInhomogeneities–CosmologyInhomogeneities–Cosmology

• For a general fluid, four velocity u (,) (local observer comoving with energy flow)

• For irrotational dust, work in synchronous and comoving gauge

• Velocity gradient tensor

• is the volume-expansion factor and ij is the shear tensor

(shear will have to be small)

• For flat FLRW, hij(t) a(t)ij

H and ij =

2 2 ( , ) i jijds dt h x t dx dx

1; 2 ( is traceless)i i ik i i i

j j kj j j ju h h

2

22

36 2 0q G

• No-go theorem: Local deceleration parameter positive:

• However must coarse-grain over some finite domain:

3

3D

D

D

h d x

h d x

• Evolution and smoothing do not commute:

22

D DD D D

What Accelerates?What Accelerates?What Accelerates?What Accelerates?

Buchert & Ellis;Kolb, Matarrese & Riotto

•

Hirata & Seljak; Flanagan; Giovannini;Ishibashi & Wald

D D

Can have q but qD 0 (“no-go” goes)

D D

1/3 30 D D D D

D

a V V V d x h

• Define a coarse-grained scale factor:

• Coarse-grained Hubble rate:

13

DD D

D

aH

a

eff eff

2

eff

43

3

8

3

D

D

D

D

a Gp

a

a G

a

• Effective evolution equations:3

eff

3

eff

16 16

33

16 16

D DD

D D

RQ

G G

RQp

G G

notdescribedby a simplep w

Inhomogeneities and SmoothingInhomogeneities and SmoothingInhomogeneities and SmoothingInhomogeneities and Smoothing

• Kinematical back reaction: 22 223 2D DD D

Q

Kolb, Matarrese & Riottoastro-ph/0506534;Buchert & Ellis

eff eff3 04

DD

Qp

G

Inhomogeneities and SmoothingInhomogeneities and SmoothingInhomogeneities and SmoothingInhomogeneities and Smoothing

• Kinematical back reaction: 22 223 2D DD D

Q

• For acceleration:

• Integrability condition (GR): 6 4 2 3 0D D D D Da Q a a R

• Acceleration is a pure GR effect:– curvature vanishes in Newtonian limit

– QD will be exactly a pure boundary term, and small

• Particular solution: QD hRiD const. – i.e., eff QD (so QD acts as a cosmological constant)

• 2nd-order perturbation theory in x)(Newtonian potential):

Kolb, Notari, Matarrese & Riotto (KNMR)

2 42 2 2

2 4, 2 2 ,

, ,

20 23

9 54

130 4

27 27i ij

i ij

H

H

– Each derivative accompanied by conformal time = /aH

– Each factor of accompanied by factor of c.

– Highest derivative is highest power of / c : “Newtonian” – Lower derivative terms / cn : “Post-Newtonian”

– and its derivatives can be expressed in terms of /

Any Indication in Perturbation Theory?Any Indication in Perturbation Theory?Any Indication in Perturbation Theory?Any Indication in Perturbation Theory?

Post-Newtonian Newtonian

mean of 2 0

• 2 2 2 52 2

00

110

Hka

A dk k T ka H a

– Individual Newtonian terms large, i.e., hr2r2i

– But total Newtonian term vanishes hr2r2i h,,ij,iji

– Post-Newtonian: hr¢ r i ) huge! (large k/aH)

•

Räsänen

2

4 2 2 2 3 2 04 4

00

110

Hka

A dk k T ka H a


KNMR

H / a()n () a(k/aH)n n

• H hMpc

• (k/aH)2n n » (£)n (k/hMpc)n (£)n

– n : £(k/h Mpc)2 (aa) : curvature

– n : £ (k/h Mpc)(aa)1 : ?

– n : 9£10 (k/h Mpc)6 (aa):

• Of course have to include transfer function, integrate over k, etc.

• (aH)2n anHn (aa)n

• A £


• First term in gradient expansion (2 spatial derivatives):3 2 0D DDR a Q

• In general, gradient expansion gives

• Dominant term is combination: ()n () (k/aH)2n n+1

no acceleration

23 3

1

23

2

2 derivatives

2 derivatives

nn m

n nDn m n

nn m

D n nn m n

R r a r n

Q q a q n

• Newtonian terms, ()n » (k/aH)nn, individually are large, butonly appear as surface terms, hence small in total

Notari; Kolb, Matarrese, & Riotto

• Post-Newtonian terms, ()n (k/aH)2n n, individually are small, but do not appear as surface terms


• Notice n contributes to QD and hRiD terms / a, i.e., expansion as if driven by a cosmological constant !!!

• Lowest-order term to make big contribution is n ( derivatives)

• But why stop at n = 3 ?????

• We have developed a RG-improved calculation (still inadequate)


Many issues:• non-perturbative nature• how are averaged quantities related to observables?• comparison to observed LSS• gauge/frame choices• physical meaning of coarse graining?

Program:

• can inhomogeneities change effective zero mode?• how does it affect observables?• can one design an inhomogeneous universe that “accelerates”?• could it lead to an apparent dark energy?• can it be reached via evolution from usual initial conditions?• does it at all resemble our universe?• large perturbative terms resum to something harmless?• is perturbation theory relevant?

Thinking Forward about BackreactionsThinking Forward about Backreactions

• Can the effect be large for many smaller (H) voids?

• Can one large void be compatible with observations?

• Is the spherical symmetry of LTB a bug or a feature?

• Must be able to express backreactions in terms of w(a).

– eventually we must make a prediction!

• If backreactions are important, i.m.o., it must be an effect that is– non-Newtonian– non-perturbative

• Voids caustics, walls, coherent structures not in P(k)!

• Someone please solve the “cosmological constant problem.”

isapp september 2010 rocky kolb the university of chicago dark matter and energy rocky i: dark...

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