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									                                     70% Dark Energy

Dark Energy
       Sean Carroll, Caltech

             SSI 2009                              5% Ordinary
                                 25% Dark            Matter

 1.   Evidence for Dark Energy
 2.   Vacuum Energy and the Cosmological Constant
 3.   Dynamical Dark Energy and Quintessence
 4.   Was Einstein Right?
              1. Evidence for 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 primordial
scale-free perturbations.

That model couldn’t be right! Something had to give --
“flat,” “cold,” “scale-free,” or perhaps even “matter.”
The Friedmann equation with matter and radiation:

Multiply by a2 to get:

 If a is increasing, each term    a
 on the right is decreasing;
 we therefore predict the
 universe should be
 decelerating (a decreasing).
                                 > Big Bang <       t
  Two groups went out to look for the ‘deceleration’
o of the universe, using type Ia supernovae as
  standardizable candles.

    SN 1994d
Result: supernovae are
dimmer than expected.

The universe is not
decelerating at all,
it’s accelerating.

Can’t be explained by
matter and radiation.

[Riess et al.; Perlmutter et al.; Knop et al.]
       What could make the universe accelerate? From the
       Friedmann equation, we need something that
       doesn’t dilute away as the universe expands.

       Call it dark energy.

size                  accelerating


       > Big Bang <                  time
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 by
 the Hubble constant, H, relating the
 distance of a galaxy to its velocity.

                                Einstein tells us that the Hubble
                                constant (squared) is proportional
                                to the energy density .

  If  is constant (vacuum energy),
  H will be constant. But the distance
  d to some particular galaxy will be
  increasing, so from v = Hd its
  apparent velocity will go up:
  it will accelerate away from us.
               How can we check this idea?

Density parameter, :

Then, if we know  we can instantly infer the geometry
of space:

  Matter (ordinary + dark) only accounts for ≈ 0.3, implying
  negative curvature. Triangles should add up to < 180o.
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 .
             positively          negatively
                curved           curved
                                              [Miller et al.; de Bernardis et al; WMAP]

 M = 0.3,
 L = 0.7 .
     2. Vacuum Energy (the Cosmological Constant)

What we know about dark energy:
   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 L).
     (artist's impression
     of vacuum energy)
                            Energy of empty space.
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 vacuum
    energy so small?

We know that virtual particles
couple to photons (e.g. Lamb
shift); why not to gravity?

                         e-                                     e-

photon                               graviton
                              e+                                        e+

   Naively:vac = ∞, or at least vac = EPl/LPl3 = 10120 vac(obs).
    Problem Two:
  Why is the vacuum     You
energy important now?   here

                          We seem to be living in a
                          special time. Copernicus
                          would not be pleased.
            Could we just be lucky?

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

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

                      If we set h = c = 1, we can write
                      G = EPlanck-2 and vac = Evac4 , and

                         EPlanck = 1027 eV ,   Evac = 10-3 eV .

                      Different by 1030.
  Supersymmetry can squelch the vacuum energy; unfortunately,
  in the real world it must be broken at ESUSY ~ 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 theory
  that predicts this relation!)

         1027 eV                1012 eV               10-3 eV
          EPlanck               Esusy                    Evac
      Is environmental selection at work?

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

The “constants of nature”
we observe depend on the
shape and size of the
compact manifold.
Everything changes from
one compactification to
the next, including the
value of the vacuum energy.
                                  [Bousso & Polchinski; Kachru et al.]
Maybe each compactification actually exists somewhere.
Regions outside our observable universe, where the laws
of physics and constants of nature appear to be different.

In that case, vacuum
energy 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 surprising
 that we find such a tiny value of the vacuum energy –
 regions where it is large are simply inhospitable.
        3. Dynamical Dark Energy (Quintessence)
Dark energy doesn’t vary quickly, but maybe slowly.


     kinetic   gradient   potential
     energy     energy     energy

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

 This is an observationally interesting possibility.

 Might be relevant to the cosmological constant problem
    or the coincidence scandal -- somehow.
A problem: mass.

An excitation of the quintessence field is
a 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 drive
the mass up! Unless there is a symmetry or other
physics that cuts it off.


Every particle we have observed has a symmetry
keeping its mass low. (The Higgs is a mystery.)
A field with a large mass rolls    V()
quickly down its potential.



Quintessence requires                     .

That’s very small. A new fine-tuning.
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.
                                         torsion-balance experiment

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

                                                          [Adelberger et al.]

Also: gradual evolution
of physical constants as the
field evolves.

Limit: couplings must be
suppressed by ~ 105 MP.
                                                                [Webb et al.]
   Both fine-tunings -- mass and interactions -- can be
   addressed in one fell swoop, by imagining a
   slightly broken symmetry

    V()                           Then the quintessence
                                   is a pseudo-Nambu-
                                   Goldstone boson,
                                   with a cosine potential
                                 and naturally small
                                   mass and interactions.
[Frieman et al; Carroll]
But one interaction is allowed -- a parity-violating
term of the form           , coupling quintessence to
the electromagnetic fields.

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

WMAP 5-year data:             .

Radio galaxies also provide
interesting constraints.

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

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

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

Simplest possibility: replace

                                               [Carroll, Duvvuri,
                                                Trodden & Turner 2003]

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.
                      Scalar-Tensor Gravity
  Introduce a scalar field (x) that determines the
I strength of gravity. Einstein's equation

    is replaced by

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

    The new field (x) is an extra degree of freedom;
    an independently-propagating scalar particle.
The new scalar doesn’t
interact directly with
matter, because we say
so. But it does influence
the metric.

A natural value for the
Brans-Dicke parameter
 would be
where  = 1 is GR.
                    [Chiba 2003]

Experiments imply
      > 40,000 .
                     Loophole: the Chameleon Effect.

Curvature contributes to                                 n
the effective potential
for . With the right
bare potential, the field
can be pinned (with
large mass) in dense                               V0
regions, e.g. the galaxy.

Deviations from GR can be                   [Khoury & Weltman;
hidden on sub-galactic scales.               Hu & Sawicki]
Dvali, Gabadadze, & Porrati (DGP) gravity: an infinite
extra dimension, with gravity stronger in the bulk;
5-d kicks in at large distances.

                     4-d gravity       5-d gravity suppressed by rc ~ H0-1

5-d GR          5-d 0-1
               rc ~ Hgravity term
           suppressed by rc ~ H0-1
                    r* = (rS rc2)1/3

                      rS = 2GM

                4-d GR

                                                   [Dvali, Gabadadze & Porrati 2000]
          Self-acceleration in DGP cosmology

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

This exhibits self-acceleration: for  = 0, there is a
de Sitter solution with H = 1/rc = 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.

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

2. f(R) gravity can fit the data, but only through
   various 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 has
   issues with negative-energy ghosts.
                   Bottom line:

 Dark energy is probably a cosmological constant.

Gravity is probably described by GR on large scales.

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