dark energy - a pedagogic review

Paul Frampton Rencontres du Vietnam August 2004

Dark Energy - A Pedagogic Review

Paul Frampton

University of North Carolina at Chapel Hill


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?


Einstein - Friedmann Equation

The Einstein field equations relate geometry (LHS) to distribution of mass-energy (RHS)

We hesitate to change this?

- But checked accurately only at SS scales.

– higher-dimensional gravity?

Addition to luminous + dark matter

- Cosmological constant,

– More generally, DARK ENERGY


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.


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.


Lamb shift and Casimir effect proved that vacuum fluctuations exist

UV divergences are the source of the problem

as dark energy : Why 10^{-121} (Planck mass)^4?

p +

p -

p+

p-

e+

e-

π+π

-

e+

e-

= ?

a) ∞?b) regularized at the Planck scale = 1076 GeV4?c) regularized at the QCD scale = 10-3 GeV4 ?d) 0 until SUSY breaking then = 1 GeV4?e) all of the above = 10 -47 GeV4?f) none of the above = 10 -47 GeV4?g) none of the above = 0 ?


Coincidence problem

– DE much earlier interferes with structure formation

-- DE much later still negligible and we would not be aware of it.

Try to avoid anthropic arguments, however tempting!

Coincidence problem

,


Dynamical scalar field

– now called Quintessence generically

E.g. Scaling potentials

E.g. Tracker potentials

V~e-Q

V~Q-

V~((Q-a)b+c) e-

Q

Wetterich 1988, Ferreira & Joyce 1998

Albrecht & Skordis 2000

.

The Quintessence possibility

Ratra & Peebles 1988

V~exp(M/Q-1) Wang, Steinhardt, Zlatev 1999


Approaches to the coincidence problem

We’re not special: universe sees periodic epochs of acceleration

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

V~M4e-Q(1+Asin Q) Dodelson , Kaplinghat, Stewart 2000


Quintessential inflation (e.g. Copeland et al 2000)

– Randall Sundrum scenario

– 2 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?

Modifications to gravity


‘Unified’ dark matter/ dark energy

–at early times like CDM w~0, cs2~0

–at late times like w <0

E.g. Chaplygin gases

–an adiabatic fluid, parameters w0,

–An example is an effective tachyonic action Gibbons astro-ph/0204008 )

Combining the dark matter and dark energy problems?

cs2= |w|


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)


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


Future fate of the dark energy

Without dark energy, the destiny of the universe was tied to the geometry ina simple manner: the universe will expand forever if it is open or flat. It will stop expandingand contract to a Big Crunch if it is closed.

With Dark Energy, this connection between geometry and destiny is lost and the futurefate depends entirely on how the presently-dominant dark energy will evolve.


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.


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.


Stability issues for w < -1

In this model of DE, because the energy

density of DE is so small compared to

e.g. the energy density in a common

magnetic field of say 10T, the 1st order

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.

Of course, this is merely a toy model but the general conclusion is probably correct – that there can be no microscopic or macroscopic effect of the dark energy.

This makes the DE even more difficult to investigate except through astronomical observations.


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


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

Therefore, there is a missing 0.7 of dark energy,

A conclusion completely independent of the SNe1a data which precipitated the discovery in 1998.

WMAP analyses have produced an impressive list of cosmic parameters with unprecedent high accuracy.

The dawn of Precision Cosmology

A reminder that one prior is that general relativity holds at all length scales.


VERY preliminary evidence for w < -1?

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

ElgarØy and Multimäki 2004

WMAP TT + SN1a

WMAP TT


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.

-


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.

dark energy - a pedagogic review

Documents