Paul Frampton Rencontres du Vietnam August 2004
Dark Energy - A Pedagogic Review
Paul Frampton
University of North Carolina at Chapel Hill
Paul Frampton Rencontres du Vietnam August 2004
Plan of the talk
 What observations and theoretical assumptions underly dark energy?
 If General Relativity hold at all scales, the most conservative assumption,
then DE follows from SNe1A or independently from CMB combined with LSS.
 What is the equation of state for DE?
 Should we seriously query general relativity at large distance scales?
Paul Frampton Rencontres du Vietnam August 2004
Einstein - Friedmann Equation
The Einstein field equations relate geometry (LHS) to distribution of mass-energy
(RHS)
We hesitate to change this?
Addition to luminous + dark matter
- But checked accurately only at SS scales.
- Cosmological constant, L?
– higher-dimensional gravity?
– More generally, DARK ENERGY
Paul Frampton Rencontres du Vietnam August 2004
Observational issues
 How can we constrain dark energy?
– expansion history H(t)
– time-dependence of w(t) – SNe1A
– does DE cluster – no evidence for it?
– How does DE couple to gravity or to DM? Related to clustering.
Paul Frampton Rencontres du Vietnam August 2004
The issues
 What can we measure observationally?
– Time evolution of H(z)
– Temporal evolution and spatial distribution of structure
– Local tests of general relativity and the equivalence principle tho
extrapolation from Solar System to Universe is some 13-15
orders of magnitude comparable to extrapolation from weak scale to
GUT scale. Usual prior is a desert hypothesis.
Paul Frampton Rencontres du Vietnam August 2004
L as dark energy : Why 10^{-121} (Planck mass)^4?
 Lamb shift and Casimir effect proved that vacuum fluctuations exist
 UV divergences are the source of the problem
=?
a) ∞?
b) regularized at the Planck scale
c) regularized at the QCD scale
d) 0 until SUSY breaking then
e) all of the above
f) none of the above
g) none of the above
= 1076 GeV4?
= 10-3 GeV4 ?
=1
GeV4?
= 10 -47 GeV4?
= 10 -47 GeV4?
=0
?
p+
p-
Paul Frampton Rencontres du Vietnam August 2004
Coincidence problem
 Coincidence problem
– DE much earlier interferes with structure formation
-- DE much later L still negligible and we would not
be aware of it.
 Try to avoid anthropic arguments, however tempting!
,
Paul Frampton Rencontres du Vietnam August 2004
The Quintessence possibility
 Dynamical scalar field
– now called Quintessence generically
 E.g. Scaling potentials
V~e-Q
V~((Q-a)b+c) e-Q
Wetterich 1988,
Ferreira & Joyce 1998
Albrecht & Skordis 2000
 E.g. Tracker potentials
V~Q-
V~exp(M/Q-1)
Ratra & Peebles 1988
Wang, Steinhardt,
Zlatev 1999
.
Paul Frampton Rencontres du Vietnam August 2004
Approaches to the coincidence problem
 We’re not special: universe sees periodic epochs
of acceleration
V~M4e-Q(1+Asin Q)
Dodelson , Kaplinghat,
Stewart 2000
 We’re special: the key is our proximity to the
matter/ radiation equality
–Non-minimal coupling to matter
e.g. Bean & Magueijo 2001
–Non-minimal coupling to gravity
e.g. Perrotta & Bacciagalupi 2002
–k-essence : A dynamical push after zeq with
non-trivial kinetic Lagrangian term
Armendariz-Picon, et al 2000
Paul Frampton Rencontres du Vietnam August 2004
Modifications to gravity
 Quintessential inflation (e.g. Copeland et al 2000)
– Randall Sundrum scenario
– r2 term increases the damping of  as rolls down
potential at early (inflationary) times
–inflation possible with V () usually too steep to
produce slow-roll
 Cardassian expansion (e.g. Frith 2003)
–Adjustment to FRW, n<0, affects late time evolution
 Curvature on the brane (Dvali ,Gabadadze Porrati 2000)
–Gravity 5-D on large scales l>lc i.e. modified at late
times – OF ALL PRESENT GRAVITY
MODIFICATIONS MAY BE BEST MOTIVATED?
Paul Frampton Rencontres du Vietnam August 2004
Combining the dark matter and dark energy problems?
 ‘Unified’ dark matter/ dark energy
–at early times like CDM w~0, cs2~0
–at late times like L
w <0
 E.g. Chaplygin gases
–an adiabatic fluid, parameters w0, 
cs2=  |w|
–An example is an effective tachyonic action
(Gibbons astro-ph/0204008 )
Paul Frampton Rencontres du Vietnam August 2004
Phantom dark energy : w<-1
Present data are consistent with w = 1 as for
a cosmological constant
 e.g. Scalar field lagrangian with the ‘wrong’
sign in the kinetic term (Carroll, Hoffman,
Trodden 2003)
--But quantum instabilities require cut off scale
~3MeV (Cline, Jeon & Moore 2003)
 Brane world models can predict temporary w<1 (Alam & Sanhi 2002)
Paul Frampton Rencontres du Vietnam August 2004
W < -1 case continued
I shall spend more time on this exotic
case because it is where the need
for new physics is most dramatic.
One interpretation of dark energy comes
from string theory – closed strings in
a toroidal cosmology.
(Bastero-Gil, Frampton and
Mersini,Phys.Rev D65, 106002
(2002). hep-th/0110167.


This leads generically to w < -1
Frampton Phys. Lett. B555, 139
(2003). astro-ph/0209037
Paul Frampton Rencontres du Vietnam August 2004
Future fate of the dark energy
Without dark energy, the destiny of the universe was tied to the geometry in
a simple manner: the universe will expand forever if it is open or flat. It will stop expanding
and contract to a Big Crunch if it is closed.
With Dark Energy, this connection between geometry and destiny is lost and the future
fate depends entirely on how the presently-dominant dark energy will evolve.
Paul Frampton Rencontres du Vietnam August 2004
Future Fate (continued)


This question is studied in
Kallosh et al. astro-ph/0307185. Frampton and Takahashi,
Phys. Lett. B557, 135 (2003). astro-ph/0211544.


If w < -1 is time independent, the scale factor diverges at a finite future time – the Big Rip.
Generally, this is at least as far in the future as the Big Bang is in the past.

Such a cosmology has a philosophical appeal? More symmetry between past and future.
With a time dependence to w(t) there are two other possible fates:
(i)An infinite lifetime universe where dark energy is dominant at all future times.
(ii)A disappearing dark energy where the universe becomes (again) matter dominated.
Paul Frampton Rencontres du Vietnam August 2004
Stability Issues for the case w < -1
 The case w < -1 gives rise to some
exceptionally interesting puzzles for
theoretical physics.
 There is the question of violating the
energy conditions of GR. There exist
inertial frames where the energy
density is negative signaling vacuum
instability. Frampton, Mod. Phys. Lett.
A19, 801 (2004) hep-th/0302007.
 S.M. Carroll, M. Hoffman and M.
Trodden. astro-ph/0301273.
Paul Frampton Rencontres du Vietnam August 2004
Stability (continued)
 Let us make two assumptions as
illustrative: that there exists a stable
ground state and that the dark energy
decays to it by 1st order PT.
 We can then use old arguments from
e.g. P.H. Frampton, Phys, Rev. Lett. 37,
1378 (1976) to investigate nucleation.
If there is even the tiniest interaction
between DE and other interactions,
nucleation would have occurred long
ago unless the appropriate radius is at
least galactic in size or bigger.
Paul Frampton Rencontres du Vietnam August 2004
Stability issues for w < -1
 In this model of DE, because the energy  Of course, this is merely a toy model
density of DE is so small compared to
e.g. the energy density in a common
magnetic field of say 10T, the 1st order
but the general conclusion is probably
correct – that there can be no
microscopic or macroscopic effect of
the dark energy.
PT can be adequately suppressed only
by decoupling DE completely from all
but gravitational forces OR by arguing
that a collision would need to be between
galaxies or larger objects to be effected.
Certainly no terrestrial experiment can be
effected by DE background.
 This makes the DE even more difficult
to investigate except through
astronomical observations.
Paul Frampton Rencontres du Vietnam August 2004
SN1a: first evidence for dark energy


Perlmutter at al
Riess et al.

Over 100 SNe1a out to Z of 1.7
Advantages:
–single objects (simpler than galaxies)
–observable over wide z range
Challenges
–Extinction from dust
– chemical composition/ evolution
– understanding mechanism behind
Phillips relation for light curves
Paul Frampton Rencontres du Vietnam August 2004
Further evidence for Dark Energy
 CMB data from WMAP, combined with LSS
of galaxy surveys 2dF and SDSS, tell us
the Universe is very close to flat and that
matter contribute only about 0.3
 WMAP analyses have produced an
impressive list of cosmic parameters with
unprecedent high accuracy.
 The dawn of Precision Cosmology
Therefore, there is a missing 0.7 of dark
energy,
A conclusion completely independent of the
SNe1a data which precipitated the
discovery in 1998.
 A reminder that one prior is that general
relativity holds at all length scales.
Paul Frampton Rencontres du Vietnam August 2004
VERY preliminary evidence for w < -1?
L
WMAP TT
+ SN1a
WMAP TT
ElgarØy and Multimäki 2004
QuickTime™ and a
Paul Frampton Rencontres du Vietnam August 2004
Solar system test of DGP Gravity

Anomalous perihelion precession in modified
gravity theories (Dvali et al 2002)
-

Lunar laser ranging

Unfortunately solar system tests are only known
ways for testing general relativity.
One would like a systematic study of this question
instead at cosmological scales.

Paul Frampton Rencontres du Vietnam August 2004
Conclusions: Theory and Observation
 The theoretical community is yet to come up with a definitive proposal to explain the
observations. String theory has been disappointing regarding this opportunity.
 The nature of dark energy is so profound for cosmology and particle physics we need the SN1a
results improved on (SNAP, JDEM, -- NASA needs the resources!), as well as complemented by
a range of observational constraints on CMB (WMAP2, Planck).
 The equation of state will be decisive. If w = -1 it’s a cosmological constant with its fine-tuning
and coincidence problems. If w > -1 quintessence will have a shot in the arm.
 If the data would settle down to a value w < -1, we could be at the dawn of a revolution in theory
with general relativity at the largest length scales called into question.