Dick Bond

Inflation Then k=(1+q)(a) ~r/16 0<= multi-parameter expansion in (lnHa ~ lnk)

Dynamics ~ Resolution ~ 10 good e-folds (~10-4Mpc-1 to ~ 1 Mpc-1 LSS) ~10+ parameters? Bond, Contaldi, Kofman, Vaudrevange 07

r(kp) i.e. k is prior dependent now, not then. Large (uniform ), Small

(uniform ln). Tiny (roulette inflation of moduli; almost all string-inspired models)

KKLMMT etc, Quevedo etal, Bond, Kofman, Prokushkin, Vaudrevange 07, Kallosh and Linde 07

General argument: if the inflaton < the Planck mass, then r < .007 (Lyth96 bound)

Cosmic Probes CMB, CMBpol (E,B modes of polarization)

B from tensor: Bicep, Planck, Spider, Spud, Ebex, Quiet, Pappa, Clover, …, Bpol

CFHTLS SN(192),WL(Apr07), JDEM/DUNE BAO,LSS,Ly

Inflation & its Cosmic Probes, now & then

Inflation & its Cosmic Probes, now & then

Dick Bond

Inflation Now1+w(a)= sf(a/aeq;as/aeq;s) goes to ax3/2 = 3(1+q)/2 ~1

good e-fold. only ~2params

Cosmic Probes NowCFHTLS SN(192),WL(Apr07),CMB,BAO,LSS,Ly

Zhiqi Huang, Bond & Kofman 07 s=0.0+-0.25 now, late-inflaton (potential gradient)2

to +-0.07 then Planck1+JDEM SN+DUNE WL, weak as < 0.3 now <0.21 then

(late-inflaton mass is < Planck mass, but not by a lot)

Cosmic Probes Then JDEM-SN + DUNE-WL + Planck1

NOW

Inflation & its Cosmic Probes, now & then

–Dick Bond

Inflation now

Dynamical background late-inflaton-field trajectories imprint luminosity distance, angular diameter distance, volume growth, growth rate of density fluctuations

Prior late-inflaton primordial fluctuation information is largely lost because tiny mass

(field sound speed=c?)

late-inflaton may have an imprint on other fields?

New late-inflaton fluctuating field power is tiny

w-trajectories for V(): pNGB example e.g.sorbo et07

For a given quintessence potential V(), we set the “initial conditions” at z=0 and evolve backward in time.

w-trajectories for Ωm (z=0) = 0.27 and (V’/V)2/(16πG) (z=0) = 0.25, the 1-sigma limit, varying the initial

kinetic energy w0 = w(z=0)

Dashed lines are our first 2-param approximation using an a-averaged

s= (V’/V)2/(16πG) and 2 -fitted as.Wild rise solutions

Slow-to-medium-roll solutions

Complicated scenarios: roll-up then roll-down

Approximating Quintessence for Phenomenology

+ Friedmann Equations + DM+B

1+w=2sin2

Zhiqi Huang, Bond & Kofman 07

1+w=-2sinh2

Include a w<-1 phantom field, via a negative kinetic energy term

slow-to-moderate roll conditions

1+w< 0.2 (for 0<z<10) and gives a 1-parameter model (as<<1):

Early-Exit Scenario: scaling regime info is lost by Hubble damping, i.e.small as

1+w< 0.3 (for 0<z<10) gives a 2-parameter model (as and s):

CMB+SN+LSS+WL+Lya

w(a)=w0+wa(1-a)

effective constraint eq.

Some ModelsCosmological Constant (w=-1)

Quintessence

(-1≤w≤1)

Phantom field (w≤-1)

Tachyon fields (-1 ≤ w ≤ 0)

K-essence

(no prior on w)

Uses latest April’07

SNe, BAO, WL, LSS, CMB, Lya data

w(a)=w0+wa(1-a) models

45 low-z SN + ESSENCE SN + SNLS 1st year SN+ Riess high-z SN, 192 “gold”SN all fit with MLCS

illustrates the near-degeneracies of the contour plotillustrates the near-degeneracies of the contour plot

piecewise parameterization 4,9,40

z-modes of w(z)

1=0.12 2=0.32 3=0.63

Higher Chebyshev expansion is not useful:

data cannot determine >2 EOS

parameters 9 & 40 into Parameter

eigenmodes DETF Albrecht etal06, Crittenden etal06,

hbk07

Data used 07.04:

CMB+SN+WL

+LSS+Lya

49

40

Measuring constant w (SNe+CMB+WL+LSS)1+w = 0.02 +/- 0.05

Measuring s

(SNe+CMB+WL+LSS+Lya)Modified CosmoMC with Weak Lensing and time-varying w models

3-parameter parameterizationnext order corrections:

m (a) (depends on s redefines aeq)

vs (a) (adds new s parameter)

enforce asymptotic kinetic-dominance w=1 (add as power suppression)

perfect moderate-to-slow roll fits ... & even the baroque …

correction on w only ~ 0.01

fits the baroque wild-rising trajectories

Measuring the 3 parameters with current data• Use 3-parameter formula over 0<z<4 &

w(z>4)=wh (irrelevant parameter unless large).

as <0.3

Comparing 1-2-3-parameter results

Conclusion: for current data, the multi-parameter complications are largely irrelevant (as <0.3):

we cannot reconstruct the quintessence potential

we can only measure the slope s

CMB + SN + WL + LSS +Lyastrajectories are slowly

varying: why the fits are good

Thawing, freezing or non-monotonic?

• Thawing: 1+w monotonic up as z decreases

• Freezing: 1+w monotonic down to 0 as z decreases• ~15% thaw, 8% freeze, most non-monotonic with flat priors

With freezing prior:

With thawing prior:

the quintessence field is below the reduced Planck mass

Forecast: JDEM-SN (2500 hi-z + 500 low-z)

+ DUNE-WL (50% sky, gals @z = 0.1-1.1, 35/min2 ) +

Planck1yr

s=0.02+0.07-0.06

as<0.21 (95%CL)

Beyond Einstein panel: LISA+JDEM

ESA

• the data cannot determine more than 2 w-parameters (+ csound?). general higher order Chebyshev expansion in 1+w as for “inflation-then” =(1+q) is not that useful. Parameter eigenmodes show what is probed

• The w(a)=w0+wa(1-a) phenomenology requires baroque potentials• Philosophy of HBK07: backtrack from now (z=0) all w-trajectories arising from

quintessence (s >0) and the phantom equivalent (s <0); use a 3-parameter model to well-approximate even rather baroque w-trajectories.

• We ignore constraints on Q-density from photon-decoupling and BBN because further trajectory extrapolation is needed. Can include via a prior on Q (a) at z_dec and z_bbn

• For general slow-to-moderate rolling one needs 2 “dynamical parameters” (as, s) & Q to describe w to a few % for the not-too-baroque w-trajectories.

• as is < 0.3 current data (zs >2.3) to <0.21 (zs >3.7) in Planck1yr-CMB+JDEM-SN+DUNE-WL future

In the early-exit scenario, the information stored in as is erased by Hubble friction over the observable range & w can be described by a single parameter s.

• a 3rd param s, (~ds /dlna) is ill-determined now & in a Planck1yr-CMB+JDEM-SN+DUNE-WL future

• To use: given V, compute trajectories, do a-averaged s & test (or simpler s -estimate)• for each given Q-potential, velocity, amp, shape parameters are needed to define a w-trajectory

• current observations are well-centered around the cosmological constant s=0.0+-0.25 • in Planck1yr-CMB+JDEM-SN+DUNE-WL future s to +-0.07• but cannot reconstruct the quintessence potential, just the slope s & hubble drag info• late-inflaton mass is < Planck mass, but not by a lot

• Aside: detailed results depend upon the SN data set used. Best available used here (192 SN), soon CFHT SNLS ~300 SN + ~100 non-CFHTLS. will put all on the same analysis/calibration footing – very important.

• Newest CFHTLS Lensing data is important to narrow the range over just CMB and SN

Inflation now summary

THEN THEN

Inflation & its Cosmic Probes, now & then

Dick Bond

Inflation then

Amplitude As, average slope <ns>, slope fluctuations ns = ns -< ns > (running,

running of running, …)

for scalar (low L to high L CMB ACT/SPT; Epol Quad, SPTpol, Quiet2, Planck)

& tensor At, <nt>, nt = nt-< nt >

(low L <100 Planck, Bicep, EBEX, Spider, SPUD, Clover, Bpol)

& isocurvature Ais, <nis>, nis= nis-< nis> power spectra (subdominant)

Blind search for structure (not really blind because of prior probabilities/measures)

Fluctuation field power spectra related to dynamical background field trajectories

Defines a tensor/scalar functional relation between; both to Hubble & inflaton potential

Standard Parameters of Cosmic Structure Formation

Òk

What is the Background curvature of the universe?

Òk > 0Òk = 0Òk < 0

closed

flatopen

Òbh2 ÒË nsÒdmh2

Density of Baryonic Matter

Density of non-interacting Dark

Matter

Cosmological Constant

Spectral index of primordial scalar (compressional)

perturbations

PÐ(k) / knsà1

nt

Spectral index of primordial tensor (Gravity Waves)

perturbations

Ph(k) / knt

lnAs ø lnû8

Scalar Amplitude

r = A t=As

Tensor Amplitude

Period of inflationary expansion, quantum noise metric perturbations

üc

Optical Depth to Last Scattering

SurfaceWhen did stars

reionize the universe?

òø `à1s ; cf :ÒË r < 0.6 or < 0.28 95% CL

ns = .958 +- .015

.93 +- .03 @0.05/Mpc run&tensor

r=At / As < 0.28 95% CL

<.36 CMB+LSS run&tensor

dns /dln k = -.060 +- .022

-.038 +- .024 CMB+LSS run&tensor

As = 22 +- 2 x 10-10

The Parameters of Cosmic Structure FormationThe Parameters of Cosmic Structure FormationCosmic Numerology: aph/0611198 – our Acbar paper on the basic 7+; bckv07

WMAP3modified+B03+CBIcombined+Acbar06+LSS (SDSS+2dF) + DASI (incl polarization and CMB weak lensing and tSZ)

bh2 = .0226 +- .0006

ch2 = .114 +- .005

= .73 +.02 - .03

h = .707 +- .021

m= .27 + .03 -.02

zreh = 11.4 +- 2.5

CMBology

ForegroundsCBI, Planck

ForegroundsCBI, Planck

SecondaryAnisotropies (CBI,ACT)

(tSZ, kSZ, reion)

SecondaryAnisotropies (CBI,ACT)

(tSZ, kSZ, reion)

Non-Gaussianity(Boom, CBI, WMAP)

Non-Gaussianity(Boom, CBI, WMAP)

Polarization ofthe CMB, Gravity Waves

(CBI, Boom, Planck, Spider)

Polarization ofthe CMB, Gravity Waves

(CBI, Boom, Planck, Spider)

Dark Energy Histories(& CFHTLS-SN+WL)

Dark Energy Histories(& CFHTLS-SN+WL)

subdominant phenomena

(isocurvature, BSI)

subdominant phenomena

(isocurvature, BSI)

Inflation Histories(CMBall+LSS)

Inflation Histories(CMBall+LSS)

Probing the linear & nonlinear cosmic web

Probing the linear & nonlinear cosmic web

wide open braking

approach to preheating

Kahler modulus potential T=+i

2004

2005

2006

2007

2008

2009

Polarbear(300 bolometers)@Cal

SZA(Interferometer) @Cal

APEX(~400 bolometers) @Chile

SPT(1000 bolometers) @South Pole

ACT(3000 bolometers) @Chile

Planck08.8

(84 bolometers)

HEMTs @L2

Bpol@L2

ALMA(Interferometer) @Chile

(12000 bolometers)SCUBA2

Quiet1

Quiet2Bicep @SP

QUaD @SP

CBI pol to Apr’05 @Chile

Acbar to Jan’06, 07f @SP

WMAP @L2 to 2009-2013?

2017

(1000 HEMTs) @Chile

Spider

Clover @Chile

Boom03@LDB

DASI @SP

CAPMAP

AMI

GBT

2312 bolometer @LDB

JCMT @Hawaii

CBI2 to early’08

EBEX@LDB

LMT@Mexico

LHC

ACT@5170m

CBI2@5040m

why Atacama? driest desert in the world. thus: cbi, toco, apex,

asti, act, alma, quiet, clover

WMAP3 sees 3rd pk, B03 sees 4th

Current high L state

November 07

Current high L state

November 07

CBI sees 4th 5th pk

CBI excess 07

WMAP3 sees 3rd pk, B03 sees 4th

PRIMARY END @ 2012? PRIMARY END @ 2012?

CMB ~2009+ Planck1+WMAP8+SPT/ACT/Quiet+Bicep/QuAD/Quiet +Spider+Clover

http://www.astro.caltech.edu/~lgg/spider_front.htmhttp://www.astro.caltech.edu/~lgg/spider_front.htm

No Tensor

SPIDER Tensor Signal

Tensor

• Simulation of large scale polarization signal

forecast Planck2.5

100&143

Spider10d

95&150

Synchrotron pol’n

Dust pol’n

are higher in B

Foreground Template removals

from multi-frequency data

is crucial

Latham Boyle 07Latham Boyle 07

GW/scalar curvature: current from CMB+LSS: r < 0.6 or < 0.25 (.28) 95%; good shot at 0.02 95% CL with BB polarization (+- .02 PL2.5+Spider), .01 target

BUT foregrounds/systematics?? But r-spectrum. But low energy inflation

Very very difficult to get at with direct gravity wave detectors – even in our dreams (Big Bang Observer ~ 2030)

Inflation in the context of ever changing fundamental theory

1980

2000

1990

-inflation Old Inflation

New Inflation Chaotic inflation

Double InflationExtended inflation

DBI inflation

Super-natural Inflation

Hybrid inflation

SUGRA inflation

SUSY F-term inflation SUSY D-term

inflation

SUSY P-term inflation

Brane inflation

K-flationN-flation

Warped Brane inflation

inflation

Power-law inflation

Tachyon inflationRacetrack inflation

Assisted inflation

Roulette inflation Kahler moduli/axion

Natural inflation

Power law (chaotic) potentials

V/MP4 ~ 2 MP

-1/2

NI(k) +/3

ns-1+1NI(k) -/6

ntNI(k) -/6

=1, NI

rnsnt

=2, NI

rnsnt

Power law (chaotic) potentials

V/MP4 ~ 2 MP

-1/2

NI(k) +/3

ns-1+1NI(k) -/6

ntNI(k) -/6

=1, NI

rnsnt

=2, NI

rnsnt

MP-2= 8G

PNGB:V/MP4 ~red

4sin2fred -1/2

nsfred-2

1-nsexp[1-nsNI (k)] (1+1-ns -1

exponentially suppressed; higher r if lowerNI & 1-ns

to match ns.96, fred~ 5, r~0.032

to match ns.97, fred~ 5.8, r~0.048

cf. =1, rnsnt

PNGB:V/MP4 ~red

4sin2fred -1/2

nsfred-2

1-nsexp[1-nsNI (k)] (1+1-ns -1

exponentially suppressed; higher r if lowerNI & 1-ns

to match ns.96, fred~ 5, r~0.032

to match ns.97, fred~ 5.8, r~0.048

cf. =1, rnsnt

ABFFO93ABFFO93

Moduli/brane distance limitation in stringy inflation. Normalized canonical inflaton

over e.g. 2/nbrane1/2

BM06

= (dd ln a)2 so r < .007, <<?

ns.97, fred~ 5.8, r~0.048,

cf. =1, rns

cf. =2, rns

ns.97, fred~ 5.8, r~0.048,

cf. =1, rns

cf. =2, rns

roulette inflation examples r ~ 10-10 roulette inflation examples r ~ 10-10 possible way out with many fields assisting: N-flationpossible way out with many fields assisting: N-flation

energy scale of inflation & r

V/MP4 ~ Ps r (1-3) 3/2

V~ (1016 Gev)4 r/0.1 (1-3)

energy scale of inflation & r

V/MP4 ~ Ps r (1-3) 3/2

V~ (1016 Gev)4 r/0.1 (1-3)

roulette inflation examples V~ (few x1013

Gev)4

roulette inflation examples V~ (few x1013

Gev)4

H/MP ~ 10-5 (r/.1)1/2 H/MP ~ 10-5 (r/.1)1/2 inflation energy scale cf. the gravitino mass (Kallosh &

Linde 07) if a KKLT/largeVCY-like generation mechanism

1013 Gev (r/.01)1/2 ~ H < m3/2 cf. ~Tev

String Theory Landscape & Inflation++ Phenomenology for CMB+LSS

Hybrid D3/D7 Potential

KKLT, KKLMMT

f||

fperp

•D3/anti-D3 branes in a warped geometry

•D3/D7 branes

•axion/moduli fields ... shrinking holesBB04, CQ05, S05, BKPV06

large volume 6D cct Calabi Yau

endend

Roulette Inflation: Ensemble of Kahler Moduli/Axion InflationsBond, Kofman, Prokushkin & Vaudrevange 06

Roulette: which minimum

for the rolling ball depends upon the throw; but which roulette wheel we

play is chance too.

The ‘house’ does not just play dice with

the world. Very small r’s may arise from string-inspired low-energy inflation models

“quantum eternal

inflation” regime

stochastic kick >

classical drift

Ps (ln Ha) Kahler trajectoriesPs (ln Ha) Kahler trajectories

observable rangeobservable range

But it is much easier

to get models

which do not agree with

observationsi.e. data

selectsthe few that

‘work’ from the vast

cases that do not

But it is much easier

to get models

which do not agree with

observationsi.e. data

selectsthe few that

‘work’ from the vast

cases that do not

(ln a) (ln a)H (ln a)H (ln a)

10-1010-10

New Parameters of Cosmic Structure FormationÒk

Òbh2

lnP s(k)Òdmh2

scalar spectrumuse order N Chebyshev

expansion in ln k, N-1 parameters

amplitude(1), tilt(2), running(3), …

(or N-1 nodal point k-localized values)

òø `à1s ; cf :ÒË

tensor (GW) spectrumuse order M Chebyshev

expansion in ln k, M-1 parameters amplitude(1), tilt(2),

running(3),...Dual Chebyshev expansion in ln k:

Standard 6 is Cheb=2

Standard 7 is Cheb=2, Cheb=1

Run is Cheb=3

Run & tensor is Cheb=3, Cheb=1

Low order N,M power law but high order Chebyshev is Fourier-like

üc

lnP t(k)

lnPs Pt (nodal 2 and 1) + 4 params cf Ps Pt (nodal 5 and 5) + 4 params

reconstructed from CMB+LSS data using Chebyshev nodal point expansion & MCMC

lnPs Pt (nodal 2 and 1) + 4 params cf Ps Pt (nodal 5 and 5) + 4 params

reconstructed from CMB+LSS data using Chebyshev nodal point expansion & MCMC

no self consistency: order 5 in scalar and tensor power

r = .21+- .17 (<.53)

Power law scalar and constant tensor + 4 params

effective r-prior makes the limit stringent

r = .082+- .08 (<.22)

run+tensor r = .13+- .10 (<.33)

lnPs lnPt (nodal 5 and 5) + 4 params. Uniform in exp(nodal bandpowers) cf. uniform

in nodal bandpowers reconstructed from April07 CMB+LSS data using Chebyshev nodal point expansion & MCMC: shows prior dependence with current data

lnPs lnPt (nodal 5 and 5) + 4 params. Uniform in exp(nodal bandpowers) cf. uniform

in nodal bandpowers reconstructed from April07 CMB+LSS data using Chebyshev nodal point expansion & MCMC: shows prior dependence with current data

logarithmic prior

r < 0.075

uniform prior

r < 0.42

New Parameters of Cosmic Structure FormationÒk

Òbh2lnH(kp)

ï (k); k ù HaÒdmh2

=1+q, the deceleration parameter history

order N Chebyshev expansion, N-1 parameters

(e.g. nodal point values)

P s(k) / H 2=ï ;P t(k) / H 2

òø `à1s ; cf :ÒË

Hubble parameter at inflation at a pivot pt

Fluctuations are from stochastic kicks ~ H/2 superposed on the downward drift at lnk=1.

Potential trajectory from HJ (SB 90,91):

üc

à ï = d lnH =d lna

1à ïà ï = d lnk

d lnH

d lnkd inf = 1à ï

æ ïp

V / H 2(1à 3ï );

ï = (d lnH =d inf)2

H(kp)

lns (nodal 5) + 4 params. Uniform in exp(nodal bandpowers) cf. uniform in

nodal bandpowers reconstructed from April07 CMB+LSS data using Chebyshev nodal point expansion & MCMC: shows prior dependence with current data

lns (nodal 5) + 4 params. Uniform in exp(nodal bandpowers) cf. uniform in

nodal bandpowers reconstructed from April07 CMB+LSS data using Chebyshev nodal point expansion & MCMC: shows prior dependence with current data

log prior

r (<0.34; .<03 at 1-sigma!)

s self consistency: order 5 uniform prior

r = (<0.64)

1à ïà ï = d lnk

d lnH

V / H 2(1à 3ï ); d lnk

d inf = 1à ïæ ï

pP s(k) / H 2=ï ;P t(k) / H 2

ï = (d lnH =d inf)2

lns (nodal 5) + 4 params. Uniform in exp(nodal bandpowers) cf. uniform in nodal

bandpowers reconstructed from April07 CMB+LSS data using Chebyshev nodal point expansion & MCMC: shows prior dependence with current data

lns (nodal 5) + 4 params. Uniform in exp(nodal bandpowers) cf. uniform in nodal

bandpowers reconstructed from April07 CMB+LSS data using Chebyshev nodal point expansion & MCMC: shows prior dependence with current data

logarithmic prior

r < 0.33, but .03 1-sigma

uniform prior

r < 0.64

CL BB for lns (nodal 5) + 4 params inflation trajectories reconstructed from

CMB+LSS data using Chebyshev nodal point expansion & MCMC

CL BB for lns (nodal 5) + 4 params inflation trajectories reconstructed from

CMB+LSS data using Chebyshev nodal point expansion & MCMC

Planck satellite 2008.6 Spider

balloon 2009.9

Spider balloon 2009.9

uniform prior

log prior

Spider+Planck broad-band

error

CL BB for lnPs lnPt (nodal 5 and 5) + 4 params inflation trajectories reconstructed

from CMB+LSS data using Chebyshev nodal point expansion & MCMC

CL BB for lnPs lnPt (nodal 5 and 5) + 4 params inflation trajectories reconstructed

from CMB+LSS data using Chebyshev nodal point expansion & MCMC

Planck satellite 2008.6 Spider

balloon 2009.9

Spider balloon 2009.9

Spider+Planck broad-band

error

uniform prior

log prior

B-pol simulation: input LCDM (Acbar)+run+uniform tensor

r (.002 /Mpc) reconstructed cf. rin

s order 5 uniform prior s order 5 log prior

a very stringent test of the -trajectory methods: A+

Planck1yr simulation: input LCDM (Acbar)+run+uniform tensor

r (.002 /Mpc) reconstructed cf. rin

s order 5 uniform prior s order 5 log prior

Planck1 simulation: input LCDM (Acbar)+run+uniform tensor

Ps Pt reconstructed cf. input of LCDM with scalar running & r=0.1

s order 5 uniform prior

s order 5 log prior

lnPs lnPt (nodal 5 and 5)

Inflation then summarythe basic 6 parameter model with no GW allowed fits all of the data OK

Usual GW limits come from adding r with a fixed GW spectrum and no consistency criterion (7 params). Adding minimal consistency does not make that

much difference (7 params)

r (<.28 95%) limit comes from relating high k region of 8 to low k region of GW CL

Uniform priors in (k) ~ r(k): with current data, the scalar power downturns ((k) goes up) at low k if there is freedom in the mode expansion to do this. Adds GW

to compensate, breaks old r limit. T/S (k) can cross unity. But log prior in drives to low r. a B-pol could break this prior dependence, maybe Planck+Spider.

Complexity of trajectories arises in many-moduli string models. Roulette example: 4-cycle complex Kahler moduli in large compact volume Type IIB string theory

TINY r ~ 10-10 if the normalized inflaton < 1 over ~50 e-folds then r < .007

~10 for power law & PNGB inflaton potentials

Prior probabilities on the inflation trajectories are crucial and cannot be decided at this time. Philosophy: be as wide open and least prejudiced as possible

Even with low energy inflation, the prospects are good with Spider and even Planck to either detect the GW-induced B-mode of polarization or set a powerful

upper limit against nearly uniform acceleration. Both have strong Cdn roles. CMBpol

End End