Dark Energy - A Pedagogic Review

1. Paul Frampton Rencontres du Vietnam August 2004 Dark Energy - A Pedagogic Review Paul Frampton University of North Carolina at Chapel Hill

2. 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?

3. Paul Frampton Rencontres du Vietnam August 2004 Einstein - Friedmann Equation The Einstein field equations relate geometry (LHS) to distribution of mass-energy (RHS) • Addition to luminous + dark matter • - Cosmological constant, L? • More generally, DARK ENERGY • We hesitate to change this? • - But checked accurately only at SS scales. • higher-dimensional gravity?

4. 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.

5. 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.

6. Paul Frampton Rencontres du Vietnam August 2004 e+ p+ p+ π+ e+ p- p- π - e- e-  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 theproblem = ? 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 ?

7. Paul Frampton Rencontres du Vietnam August 2004 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 ,

8. Paul Frampton Rencontres du Vietnam August 2004 Dynamical scalar field now called Quintessence generically E.g. Scalingpotentials E.g. Tracker potentials The Quintessence possibility Wetterich 1988, Ferreira & Joyce 1998 V~e-Q V~((Q-a)b+c) e-Q Albrecht & Skordis 2000 V~Q- Ratra & Peebles 1988 . Wang, Steinhardt, Zlatev 1999 V~exp(M/Q-1)

9. Paul Frampton Rencontres du Vietnam August 2004 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 Approaches to the coincidence problem Dodelson , Kaplinghat, Stewart 2000 V~M4e-Q(1+Asin Q)

10. Paul Frampton Rencontres du Vietnam August 2004 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? Modifications to gravity

11. 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, a • An example is an effective tachyonic action(Gibbons astro-ph/0204008 ) cs2= a|w|

12. Paul Frampton Rencontres du Vietnam August 2004 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) Phantom dark energy : w<-1

13. 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

14. 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.

15. 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: • An infinite lifetime universe where dark energy is dominant at all future times. • A disappearing dark energy where the universe becomes (again) matter dominated.

16. Paul Frampton Rencontres du Vietnam August 2004 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 Issues for the case w < -1

17. Paul Frampton Rencontres du Vietnam August 2004 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 (continued)

18. Paul Frampton Rencontres du Vietnam August 2004 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. Stability issues for w < -1

19. 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

20. Paul Frampton Rencontres du Vietnam August 2004 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. Further evidence for Dark Energy

21. Paul Frampton Rencontres du Vietnam August 2004 L VERY preliminary evidence for w < -1? WMAP TT + SN1a WMAP TT ElgarØy and Multimäki 2004

22. 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. -

23. 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.