dark energy and the preposterous universe

Dr. Sean C

arroll, Enrico F

ermi Institute (IT

P C

olloquium 3-21-02) D

ark Energy and the P

reposterous Universe

Dark Energy andThe Preposterous Universe

Sean Carroll, University of Chicagohttp://pancake.uchicago.edu/~carroll/

Executive Summary: We finally have a good idea of

what the universe is made of. But it makes no sense. The next step is to move from

inventory to understanding.

c

With: Jennie Chen, Mark Hoffman, Manoj Kaplinghat, Laura Mersini, Mark Trodden

The universe: uniform (homogeneous and isotropic) space expanding with time.Time

Relative size at different times is measured by the scale factor a(t).

a

t> Big Bang <

Dr. Sean C

arroll, Enrico F

ermi Institute (IT

P C




Einstein’s General Relativity relates the expansionrate H (the "Hubble constant") to the energy density ρ (ergs/cm3) and the spatial curvature κ :

H 2 =8 πG

3ρ B

κ

a2

H is related to the scale factor by H = a/a. You can figure out the history of the universe if you know how ρ scales as a function of a.

.

So cosmologists want to know: what kind of stuff makes up the universe, and how does it evolve with a?

Stars and gas are slowly−moving (compared to c, the speed of light). Most of their energy is rest energy, from their mass (E = mc2).

Anything which is mostly rest energy, cosmologists call "matter". The energy density in matter is its rest energy times its number density n

M:

ρM = n M m c 2

Hence: ρM ∝ aB3 ,

since the number density gets diluted as the volume expands.

What makes up the universe?

Dr. Sean C

arroll, Enrico F

ermi Institute (IT

P C




In contrast to matter, consider "radiation" (particlesmoving at speeds close to c). Radiation redshifts asthe universe expands, as wavelengths get stretched;each particle loses energy as 1/a.

Particles redshift and number density dilutes,so the energy density in radiation goes as

ρR ∝ aB4 .

Today, there is much more matter than radiation.

First surprise: Most matter in the universe is not comprised of ordinary stuff (atoms etc.), but some completely different kind of particle. It’s invisible and transparent, and is given the name Dark Matter.

There is about five times as much dark matter as ordinary matter.How do we know? We can detect its gravitational pull, through dynamics of galaxies, gravitational lensing, etc.

Dr. Sean C

arroll, Enrico F

ermi Institute (IT

P C




Even with dark matter, there is still not as much matterin the universe as we might expect.

Define the density parameter, Ω : Ω =8πG

3 H 2ρ

Then, from the Friedmann equation,

Ω > 1 → κ > 0

Ω = 1 → κ = 0

Ω < 1 → κ < 0

Observed matter content (ordinary plus dark): ΩM = 0.3 .

positive curvature

flat

negative curvature

Second surprise: Most of the universe isn’t even matter! It’s something called Dark Energy, which:

is smoothly distributed through space varies slowly (if at all) with time.

Paradigmatic candidate: vacuum energy (a/k/a the cosmological constant, Λ). An immutable energy inherent in every cubic centimeter of space.

(artist’s impressionof vacuum energy)

Dr. Sean C

arroll, Enrico F

ermi Institute (IT

P C




If there were dark energy, how would we know?

Contributes to density (ΩTot = ΩM + ΩDE), and hence to curvature κ.

Redshifts away slowly, so makes the universe accelerate: a ∝ a √ρ (from Friedmann eq.).

Fortunately, these are things we can go look for.

Fluctuations in the Cosmic Microwave Background peak at acharacteristic length scale of 300,000 light years; observing thecorresponding angular scale measures the geometry of space.

Result: the universe is flat! ΩTot = 1.

[TOCO;Boomerang;Maxima; DASI]

Dr. Sean C

arroll, Enrico F

ermi Institute (IT

P C




Type Ia supernovae arestandardizable candles;observations of many athigh redshift test thetime evolution of theexpansion rate.

Result: the universe isaccelerating!

There must be some sortof energy density whichdoesn’t redshift away.

[Riess et al.; Perlmutter et al.]

[Jaffe et al.]

Concordance: ΩΜ = 0.3, ΩΛ = 0.7 .

Dr. Sean C

arroll, Enrico F

ermi Institute (IT

P C




Dark Energy

Dark Matter

Ordinary Matter

5% Ordinary Matter25% Dark Matter70% Dark Energy

The final accounting seems to be:

This is a preposterous universe.

Why is the dark energy density small, but not quite zero? Naive expectation: ρ

DE(theory)/ρ

DE(obs) = 10120.

Why now? Remember ρDE

/ρM ~ a3. So why are

they approximately equal today?

For that matter: Why are the amounts of "ordinary" and "dark" matter comparable? (And why isn’t there as much antimatter as matter?)

Dr. Sean C

arroll, Enrico F

ermi Institute (IT

P C




Vacuum energy is the most natural thing in the world.

φ

V(φ)

Consider a single scalar field: ρφ = 1

2φ 2+ 1

2∇ φ 2+V φ

φ = const ρφ = V φ = const .

Crucial point: no known (unbroken) symmetry would prefer V(φ) = 0.

Why is the vacuum energy so small?

E 0= 0 E 0=1

2ħ ω

Another contributor to vacuum energy: quantum fluctuations.

Every Fourier mode of any quantum field acts like an harmonicoscillator, with a corresponding zero−point energy.

Classical: Quantum:

Integrating over these modes gives an infinite vacuum energy;imposing a Planck−scale cutoff yields ρ

vac

(theory) = (MPl = 1027 eV)4 = 10120 ρvac(obs)

Obtaining agreement would require neglecting all modes smaller than (10−3 eV)−1 = 1 mm.

Dr. Sean C

arroll, Enrico F

ermi Institute (IT

P C




On the other hand, maybe an infinite answer is just wrong.Supersymmetry does better. (In a manner of speaking.)

Good news: In a perfectly supersymmetric state, bosonic and fermionic contributions to ρ

vac exactly cancel.

Bad news: We don’t live in a perfectly supersymmetric universe; SUSY is (likely) broken around

Good news: This makes the cosmological constant problem not so bad: ρ

vac

(theory) = (MSUSY = 1012 eV)4 = 1060 ρvac(obs).

Bad news: This is a much more reliable calculation!

M SUSY≈1012 eV.

Youare

here

Why are vacuum and matter comparable?

The "best−fit universe"withis an unstable point, caught in the process ofevolving from purelymatter to purely vacuum.

ΩM= 0 .3 , Ω Λ= 0 . 7

Dr. Sean C

arroll, Enrico F

ermi Institute (IT

P C




And it’s movingquickly:

Ω Λ

ΩM

∼a3

ΩR+Ω

M

Ω Λ

What might be going on?

Possibilities include:

The true vacuum energy is small, but nonzero.

We live in a false vacuum; the true vacuum has zero energy.

A slowly−varying dynamical component is mimicking a vacuum energy.

Einstein was wrong.

Dr. Sean C

arroll, Enrico F

ermi Institute (IT

P C




1) Might the true vacuum energy be nonzero?

Some numerology: M S U S Y = M Pl an c k M v a c

M vac4 = eB2 ⁄α M Planck

4

There are no very good reasons why any suchformula ought to be true. But the idea is toderive the vacuum energy from other parameters,and attribute the coincidence problem to justbeing lucky.

By the way: String theorists find it very hard to get ρ v a c> 0 .

Perfectly reasonable people are driven to invoke theanthropic principle.

What if:

The vacuum energy ρΛ takes on different values, with

uniform probability, in different "parts of the universe" (in space, time, or branches of the wavefunction).

Everything else remains the same from place to place: constants of nature, initial conditions, galaxy formation, etc.

Then the most likely thing for observers in such an ensemble tofind is that |ρΛ| = (1−10) ρΜ (just as we do).

[Garriga & Vilenkin; Martel, Shapiro & Weinberg]

Dr. Sean C

arroll, Enrico F

ermi Institute (IT

P C




2) Do we live in a false vacuum?

φ

V(φ)

Good: compatible with ultimately.Bad: why would the splitting be so tiny?

ρ v a c= 0

Keep in mind:

No observational signature.

Stability not really an issue.

3) Is the dark energy a slowly−varying dynamical component?

φ

V(φ)e.g. a slowly−rolling scalar field: "quintessence"

Good: Consistent with ρvac = 0 ultimately. Observationally interesting. Consistent with string theory? Solve the coincidence problem?

Bad: Unnatural particle physics. (mφ ~ 10−33 eV) Should have been detected already.

Dr. Sean C

arroll, Enrico F

ermi Institute (IT

P C




Characterize using an effective equation of staterelating pressure to energy density:

For matter, w = 0; for actual vacuum energy, w = −1.

p = w ρ

Limits from supernovae and large−scale structure arealready pretty good:

[Perlmutter, Turner& White]

Should we consider w < −1?

Against: Violates "null dominant energy condition" (|ρ| <= |p|; ρ +p >= 0).

For: Nevertheless possible to find apparently−stable

models [e.g. L = -φ 2 − exp(-φ2)].

[Caldwell]

.

φ

V(φ)

Dr. Sean C

arroll, Enrico F

ermi Institute (IT

P C




Could dark−energy dynamics solve the coincidence problem?

"Tracker" potentials like and lead to a dark−energy density which remains proportional to the dominant source; of course, this doesn’t make the universe accelerate!At issue: we need something special about today in order to make today special.

eBφ1 ⁄φ

Two possibilities:

Today is not so far (on a log scale) from matter/radiation equality (zeq ~ 104).

Perhaps acceleration is something that just happens from time to time.

L= f φ g ∇ φ 2

[Armendariz−Picon, Mukhanov & Steinhardt]

"k−essence": energy density evolves differently during matter− & radiation−dominated eras

Mechanism: Novel kinetic energy:

ρ

a

R

M k

"Tracks" duringradiation era, then"sticks" duringmatter era.

Dr. Sean C

arroll, Enrico F

ermi Institute (IT

P C




V φ =eBφ 1+α sin φ[Dodelson, Kaplinghat & Stewart]

Oscillating dark energy: just something that happens from time to time.

Mechanism: Perturbed tracker:

Dark energy has no right to be completely "dark"; it should couple weakly to standard−model fields.

Slowly−rolling, nearly−massless fields lead to long−range "5th forces", in addition to gradual evolution of the "constants" of nature.

To avoid detection in experiments to date, we need to introduce dimensionless couplings of order 10−4−10−5 or less.

on the other hand...

ϕ γ

γquantum gravity

L ∼β

M Pl

φ F µ ν F µ ν

(β is a dimensionless constant)

Dr. Sean C

arroll, Enrico F

ermi Institute (IT

P C




... maybe α is changing slowly with time?

[Webb et al.]

But there’s a competing limit: the Oklo Natural Reactor.

1.8 billion years ago, a naturalwater−moderated fission reactoroperated in Gabon, West Africa.

Isotopic abundances constrainthe 149Sm neutron−capture cross−section, and thus α.

Result: |∆α/α| < 1.2 × 10−7 (95% CL) at redshift z ≈ 0.13.

[Damour and Dyson]

Issues: initial abundances, variation of other constants.

Dr. Sean C

arroll, Enrico F

ermi Institute (IT

P C




Can the Oklo and absorption line results be reconciled?

∆α/α

z

Oklo

If a scalar field ϕ is responsible, we need the evolution of ϕto have slowed down signficantly. This can happen in somemodels, but usually not by so much.

Sensible particle physics models?

Pseudo−Goldstone bosons: approx symmetry φ→ φ+const.

Naturally small masses; naturally small couplings.

φ

V(φ)

V φ = µ4 1+cos φ

No tracking behavior; any effective w possible.Possible signature: cosmological birefringence.

[Hill, Freiman, et al; Carroll]

Dr. Sean C

arroll, Enrico F

ermi Institute (IT

P C




Dynamical dark energy doesn’t have to be a rolling scalar field.

Some alternatives:

A web of tangled topological defects (i.e. a "solid")

Dark−matter particles with gradually increasing masses

Ultra−short wavelength (transplanckian) modes

Curved−spacetime renormalization effects

[Vilenkin, Bucher, Pen, Spergel]

[Anderson & Carroll]

[Bastero−Gill, Mersini]

[Parker & Raval]

4) Was Einstein wrong?

Extra dimensions, scalar fields, holography...

Test using Big Bang Nucleosynthesis. Usual story:

T > 1 MeV: Weak interactions rapidly interconvert protons and neutrons.

1 MeV > T > 80 keV: Weak interactions frozen out; n/p decays from 1/6 to 1/7.

T = 80 keV: Deuterium can survive; neutrons rapidly converted to 4He, plus trace amounts of 2D, 3He, 7Li.

Generally: Increasing H increases 4He, and vice−versa.

Dr. Sean C

arroll, Enrico F

ermi Institute (IT

P C




[Carroll & Kaplinghat]

Notice: there is a coincidence problem!

Result: a range of allowed histories, but all withinthe vicinity of the conventional model.

BBN tests GR on length scales of the Hubble radius at z ~ 109

(solar system scales). Alternatively, GR could break down at afixed length scale corresponding to the current Hubble radius.

Even better: perhaps this breakdown explains away both dark matter and dark energy.

Milgrom (infamously) points out: galactic dark matter isonly required for accelerations

a ⁄c < 10B18 sB1

Meanwhile, the universe starts accelerating when theHubble constant reaches

H 0 ≈ 10B18 sB1

Coincidence? Probably. [see e.g. Kaplinghat & Turner]

Dr. Sean C

arroll, Enrico F

ermi Institute (IT

P C




Something dark and mysterious is going on.

An ordinary cosmological constant is a perfectfit, even if we can’t explain it.

Dynamical mechanisms are interesting and testable; they also raise additional problems.

Answering these questions will tell us something extremely profound: either about particle physics or about gravity, and certainly about cosmology.

Conclusions

dark energy and the preposterous universe

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