The accelerated expansion of the universe and the cosmological constant problem

1. Spring Summer School on Strings Cosmology and Particles 31 March – 4 April 2009, Belgrade-Niš, Serbia The accelerated expansion of the universe and the cosmological constant problem Hrvoje Štefančić, Theoretical Physics Division, Ruđer Bošković Institute, Zagreb, Croatia

2. Big issues - observational and theoretical • Present accelerated expansion of the universe – observational discovery • The cosmological constant (vacuum energy) problem – theoretical challenge

3. Our concept of the (present) universe • Evolution dominated by gravity • the interactions governing the evolution of the universe have to have long range to be effective at cosmological distances • matter is neutral at cosmological (and much smaller) scales • General relativity • Known forms of matter (radiation, nonrelativistic matter) • Four dimensional universe

4. The observed universe • Isotropic (CMB, averaged galaxy distribution at scales > 50-100 Mpc) • Homogeneous – less evidence (indirect) – Copernican principle • Homogeneous and isotropic – Cosmological principle • Robertson-Walker metric !

5. Expansion of the universe • Hubble (1929) – dynamical universe • Cosmological redshift • Standard forms of matter lead to decelerated expansion • Inflation – early epoch of the accelerated expansion • 1998 – universe accelerated (decelerated universe expected)

6. FRW model – theoretical description of the expansion • Contents: cosmic fluids (general EOS) • General relativity in 4D • Friedmann equation • Continuity equation (Bianchi identity - covariant conservation of energy-momentum tensor) • Acceleration

7. FRW model • Critical density • Omega parameters • Cosmic sum rules

8. Cosmological observations – mapping the expansion • Standard candles (luminosity distance) • Supernovae Ia, GRB • Standard rulers • CMB (cosmic microwave background) • BAO (baryonic acoustic oscillations) • Others (gravitational lensing...)

9. Supernovae of the type Ia • Standard candles – known luminosity • Binary stars – physics of SNIa understood • Light curve fitting • Luminosity distance – can be determined both observationally and theoretically • SNIa dimming – signal of the accelerated expansion

10. Cosmological observations - SNIa • http://imagine.gsfc.nasa.gov/docs/science/know_l2/supernovae.html • http://www.astro.uiuc.edu/~pmricker/research/type1a/

11. Cosmological observations - CMB • http://map.gsfc.nasa.gov/

12. Cosmological observations - LSS • structure at cosmological scales (LSS) • http://cas.sdss.org/dr5/en/tools/places/

13. Standard cosmological model (up to 1998) • Destiny determined by geometry • Interplay of spatial curvature and matter content (Ωm + Ωk=1) • Even EdS model advocated (Ωm=1)

14. Spatial curvature • COBE – spatial curvature is small. • EdS must do the job (models with considerable Ωk are ruled out by the observation of CMB temperature anisotropies

15. SNIa observations (1998) • Observations by two teams • High z SN Search Team, Riess et al., http://cfa-www.harvard.edu/supernova//home.html • Supernova Cosmology Project, Perlmutter et al., http://supernova.lbl.gov/ • ΛCDM model – fits the data very well • Measurement in the redshift range where the expansion of the universe is really accelerated or there is the transition from decelerated to accelerated expansion – “direct measurement”

16. CMB and BAO • Influence to the determination of the acceleration – indirectly • CMB – mainly through the distance to the surface of last scattering • BAO – similarly

17. Combining observational data • Degeneracies of cosmic parameters - different combinations of cosmic parameters may produce the same observed phenomena • Removal of degeneracies – using different observations at different redshifts (redshift intervals) • SNIa + WMAP + BAO – precision cosmology

18. Observational constraints to the DE EOS • E. Komatsu et al., Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation • http://arxiv.org/abs/0803.0547

19. Accelerated expansion • In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model) • Do we interpret the observational data correctly?

20. Classification of theoretical approaches • ll R. Bean, S. Caroll, M. Trodden, Insights into dark energy: interplay between theory and observation. Rachel Bean (Cornell U., Astron. Dept.) , Sean M. Carroll (Chicago U., EFI & KICP, Chicago) , Mark Trodden (Syracuse U.) . Oct 2005. 5pp. White paper submitted to Dark Energy Task Force. http://arxiv.org/abs/astro-ph/0510059

21. Distorted signals and unjustified assumptions? • Photons from SNIa convert to axions in the intergalactic magnetic field • light signal dissipated • Reduction in intensity confused for the effects of acceleration • C. Csaki, N. Kaloper, J. Terning, Phys. Rev. Lett. 88 (2002) 161302 • does not work (very interesting attempt – invokes more or less standard (or at least already known physics) • connection with the phantom “mirage”

22. Distorted signals and unjustified assumptions? • The influence of inhomogeneities (below 50-100 Mpc) • Nonlinearity of GR in its fundamental form • Solving Einstein equations in an inhomogeneous universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe • No additional components (just NR matter) • The acceleration is apparent • The perceived acceleration begins with the onset of structure formation – very convenient for the cosmic coincidence problem • The effect is not sufficient to account for acceleration, but is should be taken into considerations in precise determination of cosmic parameters

23. Distorted signals and unjustified assumptions? • Inhomogeneities at scales above the Hubble horizon • Underdense region • Relinquishing the Copernican principle? • Falsifiability? • No additional components • The effect of “super large scale structure”

24. Mechanism of the acceleration • No acceleration in the “old standard cosmological model” • Our (pre)concepts of the universe have to be modified • Modifying contents – dark energy (+ DM) • Modyfing gravity – modified (dark) gravity • Modifying dimensionality – new (large) dimesions – braneworld models • ... • and combinations

25. Dark energy • Acceleration by adding a new component – a dark energy component • Key property – sufficiently negative pressure • Physical realization of a negative pressure? • Geometric effect (Lambda from the left side of Einstein eq.) • Dynamics of scalar field - domination of potential energy over kinetic energy • Corpuscular interpretation – unusual dispersion relation – energy decreasing with the size of momentum

26. Dark energy • DE equation of state • Dynamics of ρd in terms of a • w > -1: quintessence • w = -1: cosmological term • w < -1: phantom energy • Multiple DE components • Crossing of the cosmological constant barrier

27. Dark sector • DE interacting with other cosmic components • Interaction with dark matter • Unification of dark matter and dark energy • Chaplygin gas • EOS • scaling with a

28. DE models • Cosmic fluid • Scalar fields (quintessence, phantom) • ... • Effective description of other acceleration mechanisms (at least at the level of global expansion)

29. ΛCDM • Benchmark model • Only known concepts (CC, NR matter, radiation) • small number of parameters • The size of Λ not understood – cosmological constant problem(s) • Problems with ΛCDM cosmology

30. Quintessence • Dynamics of a scalar field in a potential • Freezing vs. thawing models • “tracker field” models • k-essence (noncanonical kinetic terms)

31. Phantom energy • Energy density growing with time • Big rip • Stability • Problems with microscopic formulation • Instability to formation of gradients • Effective description

32. Singularities • New types of singularities • Finite time (finite scale factor) singularities • Sudden singularities

33. Modified gravity • Modification of gravity at cosmological scales • Dark gravity (effective dark energy) • F(R) gravity – various formulations (metric, Palatini, metric-affine) • Conditions for stability • Stringent precision tests in Solar system and astrophysical systems

34. Braneworlds • Matter confined to a 4D brane • Gravity also exists in the bulk • Dvali-Gabadadaze-Poratti (DGP) • Different DGP models – discussion of the status! • Phenomenological modifications of the Friedmann equation – Cardassian expansion

35. The cosmological constant • Formally allowed – a part of geometry • Introduced by Einstein in 1917 – a needed element for a static universe • Pauli – first diagnosis of a problem with zero point energies • Identification with vacuum energy – Zeldovich 1967 • Frequently used “patch”

36. The expansion with the cosmological constant J. Solà, hep-ph/0101134v2

37. The expansion with the cosmological constant

38. Contributions to vacuum energy • Zero point energies – radiative corrections • Bosonic • Fermionic • Condensates – classical contributions • Higgs condensate • QCD condensates • ...

39. Zero point energies • QFT estimates • real scalar field • spin j

40. Condensates • Phase transitions leave contributions to the vacuum energy • Higgs potential • minimum at • contribution to vacuum energy

41. The size of the CC • Many disparate contributions • Virtually all many orders of magnitude larger than the observed value • ZPE - Planck scale “cutoff” ≈1074 GeV4 • ZPE - TeV scale “cutoff” ≈1057 GeV4 • ZPE - ΛQCD scale “cutoff” ≈10-5 GeV4 • Higgs condensate ≈ -108 GeV4 • melectron4 ≈10-14 GeV4 • The observed value

42. The “old” cosmological constant problem – the problem of size • Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field) • Huge fine-tuning implied • How huge and of which nature • Numerical example: 10120 1 -0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 =0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 • Financial example Instability to variation of a single contribution (parameter)

43. The “old” cosmological constant problem • Fundamental theoretical problem – the problem of the vacuum energy density • All proposed solutions assume that the “old” CC problem is somehow solved • ΛCDM model – CC relaxed to the observed value • DE models and other models – CC is zero or much smaller in absolute value compared to the observed DE energy density • Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism, the “old” CC problem must be resolved

44. DE vs CC • Raphael Bousso, “TASI lectures on the cosmological constant” • “If a poet sees something that walks like a duck and swims like a duck and quacks like a duck, we will forgive him for entertaining more fanciful possibilities. It could be a unicorn in a duck suit – who's to say! But we know that more likely, it's a duck.” • Conditions for a mechanism solving the CC problem

45. Proposed solutions of the “old” CC problem • Classification (closely following S. Nobbenhuis, gr-qc/0609011) • Symmetry • Back-reaction mechanisms • Violation of the equivalence principle • Statistical approaches

46. Symmetry • Supersymmetry • Scale invariance • Conformal symmetry • Imaginary space • Energy → - Energy • Antipodal symmetry

47. Back-reaction mechanisms • Scalar • Gravitons • Running CC from Renormalization group • Screening caused by trace anomaly

48. Violation of the equivalence principle • Non-local Gravity, Massive gravitons • Ghost condensation • Fat gravitons • Composite gravitons as Goldstone bosons

49. Statistical approaches • Hawking statistics • Wormholes • Anthropic Principle

50. The cosmic coincidence problem – the problem of timing • Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch? • A problem in a DE (CC) approach to the problem of accelerated expansion: • DE (CC) energy density scale very differently with the expansion (if presently comparable they were very different in the past and will be very different in the future • NR: ρ ~ a-3 • DE: ρ ~ a-3(1+w) , slower than a-2 , CC: ~ 1 • Also present in many approaches not based on DE