Dark EnergySean Carroll, Caltech

SSI 2009

1.Evidence for Dark Energy2.Vacuum Energy and the Cosmological Constant3.Dynamical Dark Energy and Quintessence4.Was Einstein Right?

25% DarkMatter

5% OrdinaryMatter

70% Dark Energy

Dec. 1997: Something was in the air!

- age of the universe- absence of power on small scales- measurements of matter density

Theorists had a favorite model: a flat universe,full of matter (ordinary + cold dark), with primordialscale-free perturbations.

That model couldn’t be right! Something had to give --“flat,” “cold,” “scale-free,” or perhaps even “matter.”

1. Evidence for Dark Energy

The Friedmann equation with matter and radiation:

Multiply by a2 to get:

If a is increasing, each termon the right is decreasing;we therefore predict theuniverse should bedecelerating (a decreasing).

.

a

t> Big Bang <

To

Two groups went out to look for the ‘deceleration’of the universe, using type Ia supernovae asstandardizable candles.

SN 1994d

Result: supernovae aredimmer than expected.

The universe is notdecelerating at all, it’s accelerating.

Can’t be explained bymatter and radiation.

[Riess et al.; Perlmutter et al.; Knop et al.]

size

time> Big Bang <

decelerating

accelerating

What could make the universe accelerate? From theFriedmann equation, we need something that doesn’t dilute away as the universe expands.

Call it dark energy.

If the dark energy density evolves as

then a DE-dominated universe obeys

which implies acceleration for

But people usually use the “equation-of-state parameter”

so that acceleration happens for

Fun non-Euclidean fact: “constant expansion rate” = “acceleration.”

The expansion rate is described bythe Hubble constant, H, relating thedistance of a galaxy to its velocity.

Einstein tells us that the Hubbleconstant (squared) is proportionalto the energy density .

If is constant (vacuum energy),H will be constant. But the distanced to some particular galaxy will beincreasing, so from v = Hd itsapparent velocity will go up:it will accelerate away from us.

Density parameter, :

Then, if we know we can instantly infer the geometryof space:

Matter (ordinary + dark) only accounts for ≈0.3, implyingnegative curvature. Triangles should add up to < 180o.

How can we check this idea?

CMB temperature anisotropies provide a standard ruler.

They were produced about 400,000 years after the Big Bang,and should be most prominent at a physical size of 400,000 light years across.

Tot

= [peak

(deg)]-1/2.

Observation: peak

= 1o.

The universe is flat:

Tot

= 1 .

flat

positivelycurved

negativelycurved

[Miller et al.; de Bernardis et al; WMAP]

Concordance:

= 0.3,

= 0.7 .

smoothly distributed through space varies slowly (if at all) with time ≈ (constant w ≈-1)

Dark energy could be exactly constant through space and time: vacuum energy (i.e. the cosmological constant ). Energy of empty space.

(artist's impressionof vacuum energy)

2. Vacuum Energy (the Cosmological Constant)

What we know about dark energy:

People sometimes pretend there is a difference between a cosmological constant,

and a vacuum energy,

There’s not; just set .

Problem One:Why is the vacuumenergy so small?

We know that virtual particlescouple to photons (e.g. Lambshift); why not to gravity?

Naively:vac

= ∞, or at least vac

= EPl/L

Pl3 = 10120

vac(obs).

e-

e+

e-

e+

photon graviton

Youarehere

Problem Two:Why is the vacuum

energy important now?

We seem to be living in aspecial time. Copernicuswould not be pleased.

The Gravitational Physics Data Book:

Newton's constant: G = (6.67 ± 0.01) x 10-8 cm3 g-1 sec-2

Cosmological constant: = (1.2 ± 0.2) x 10-55 cm-2

If we set h = c = 1, we can write G = E

Planck-2 and vac = E

vac4 , and

EPlanck = 1027 eV , vac = 10

-3 eV .

Different by 1030.

Could we just be lucky?

Supersymmetry can squelch the vacuum energy; unfortunately,in the real world it must be broken at E

SUSY ~ 1012 eV.

Typically we would then expect

which is off by 1015. But if instead we were able to predict

it would agree with experiment. (All we need is a theorythat predicts this relation!)

energy

EPlanck Esusy Evac

1027 eV 1012 eV 10-3 eV

String theory has extra dimensions, with a vast“landscape” of ways to hidethem. Perhaps 10500 or more.

The “constants of nature”we observe depend on theshape and size of thecompact manifold.Everything changes fromone compactification tothe next, including thevalue of the vacuum energy.

Is environmental selection at work?

[Bousso & Polchinski; Kachru et al.]

Maybe each compactification actually exists somewhere. Regions outside our observable universe, where the lawsof physics and constants of nature appear to be different.

In that case, vacuumenergy would be like the weather; not a fundamental parameter, but something that depends on where you are in the universe.

Therefore (so the reasoning goes), it's hardly surprisingthat we find such a tiny value of the vacuum energy – regions where it is large are simply inhospitable.

[Weinberg]

V()

kineticenergy

gradientenergy

potentialenergy

[Wetterich; Peebles & Ratra; Caldwell, Dave & Steinhardt; etc.]

This is an observationally interesting possibility.

Might be relevant to the cosmological constant problemor the coincidence scandal -- somehow.

3. Dynamical Dark Energy (Quintessence)

Dark energy doesn’t vary quickly, but maybe slowly.

A problem: mass.

An excitation of the quintessence field isa quintessence particle:

In quantum field theory, we don’t see the “bare”particle; we see the collective effect of the sum over fluctuating (virtual) quantum fields.

The effect of these virtual particles is to drivethe mass up! Unless there is a symmetry or otherphysics that cuts it off.

Every particle we have observed has a symmetrykeeping its mass low. (The Higgs is a mystery.)

A field with a large mass rolls quickly down its potential.

Quintessence requires .

That’s very small. A new fine-tuning.

V()

A related problem: interactions.

If A couples to B, and B to C, A should couple to C.

It’s hard to keep a new field completely isolated; it should couple to Standard Model particles.

Coupling to a low-mass (long-range)field implies a fifth force of nature,which can be searched for inlaboratory experiments.

Also: gradual evolutionof physical constants as the field evolves.

Limit: couplings must be suppressed by ~ 105 M

P.

torsion-balance experiment

[Webb et al.]

[Adelberger et al.]

Both fine-tunings -- mass and interactions -- can beaddressed in one fell swoop, by imagining a slightly broken symmetry

V()

[Frieman et al; Carroll]

Then the quintessenceis a pseudo-Nambu-Goldstone boson,with a cosine potential and naturally smallmass and interactions.

But one interaction is allowed -- a parity-violatingterm of the form , coupling quintessence tothe electromagnetic fields.

This interaction produces cosmological birefringence:polarization vectors rotate as they travel throughthe evolving scalar field.

WMAP 5-year data: .

Radio galaxies also provide interesting constraints.

So:

1.A cosmological constant fits the data, at theexpense of a dramatic fine-tuning.

2.Dynamical models introduce new fine-tunings,in the form of the small mass and couplings ofthe new scalar field.

3.Dynamical models have not yet shed any light on the cosmological constant problem or the coincidence scandal.

Simplest possibility: replace

with

The vacuum in this theory is not flat space, but an accelerating universe! But: the modified action brings a new tachyonic scalar degree of freedom to life. A scalar-tensor theory of gravity.

[Carroll, Duvvuri, Trodden & Turner 2003]

4. Modified Gravity

Introduce a scalar field (x) that determines thestrength of gravity. Einstein's equation

is replaced by

Scalar-Tensor Gravity

Int

The new field (x) is an extra degree of freedom;an independently-propagating scalar particle.

variable “Newton's constant”extra energy-momentum from

The new scalar doesn’tinteract directly withmatter, because we sayso. But it does influencethe metric.

A natural value for the Brans-Dicke parameter would be ~ 1 ,where = 1 is GR.

Experiments imply

> 40,000 .

[Chiba 2003]

Cassini

[Khoury & Weltman; Hu & Sawicki]

V

V 0

n

Loophole: the Chameleon Effect.

Curvature contributes tothe effective potentialfor . With the rightbare potential, the fieldcan be pinned (with large mass) in denseregions, e.g. the galaxy.

Deviations from GR can be hidden on sub-galactic scales.

Dvali, Gabadadze, & Porrati (DGP) gravity: an infiniteextra dimension, with gravity stronger in the bulk;5-d kicks in at large distances.

[Dvali, Gabadadze & Porrati 2000]

5-d gravity suppressed by rc ~ H

0-14-d gravity

5-d gravity term suppressed by r

c ~ H

0-1

rS = 2GM

rc ~ H

0-1

r* = (r

S r

c2)1/3

4-d GR

crossover

5-d GR

This exhibits self-acceleration: for = 0, there is ade Sitter solution with H = 1/r

c = constant. However:

The acceleration is somewhat mild; think weff

~ -0.7.

Inconsistent with present data at about 5.

Fluctuations of the brane have negative energies(ghosts). Hard to fix this problem.

Self-acceleration in DGP cosmology

The DGP version of the Friedmann equation is (naturally):

So:

1.We would expect GR to be modified on shortscales, not on long scales, but it could happen.

2. f(R) gravity can fit the data, but only throughvarious fine-tunings (over and above the cosmological constant and coincidence problems)and the chameleon mechanism.

3.DGP gravity doesn’t really fit the data , and hasissues with negative-energy ghosts.

Gravity is probably described by GR on large scales.

Bottom line:

Dark energy is probably a cosmological constant.