Cosmic Acceleration from the basics to the frontiers

1. Cosmic Acceleration from the basics to the frontiers Je-An Gu(顧哲安) National Center for Theoretical Sciences (NCTS) 2007/04/27 @ Academia Sinica

2. Accelerating Expansion Based on FRW Cosmology (homogeneous & isotropic) Concordance:  = 0.73 , M = 0.27

3. Supernova Observations

5. Supernova (SN) : mapping out the evolution herstory Distance Modulus F: flux (energy/areatime) L: luminosity (energy/time) SN Ia Data: dL(z) [ i.e, dL,i(zi) ] [ ~ x(t) ~ position (time) ] history Type Ia Supernova (SN Ia) : (standard candle) – thermonulear explosion of carbon-oxide white dwarfs –  Correlation between the peak luminosity and the decline rate  absolute magnitude M  luminosity distance dL (distance precision: mag = 0.15 mag dL/dL ~ 7%)  Spectral information  redshift z (z)

6. Distance Modulus 1998 SCP (Perlmutter et. al.) (can hardly distinguish different models)

7. 2004 Fig.4 in astro-ph/0402512 [Riess et al., ApJ 607 (2004) 665] Gold Sample (data set) [MLCS2k2 SN Ia Hubble diagram] - Diamonds: ground based discoveries - Filled symbols: HST-discovered SNe Ia - Dashed line: best fit for a flat cosmology: M=0.29 =0.71

8. Riess et al. astro-ph/0611572 2006

9. Riess et al. astro-ph/0611572 2006

10. Supernova / Acceleration Probe (SNAP) observe ~2000 SNe in 2 years statistical uncertainty mag = 0.15 mag  7% uncertainty in dL sys = 0.02 mag at z =1.5 z= 0.002 mag (negligible)

12. Definition of Acceleration

13. Accelerating Expansion: Definition VD (Volume) Accelerating Expansion :H > 0 , q < 0 Distance L , at time t E.g. 1. Proper distance (Line Acceleration) E.g. 2. L = VD1/3(Domain Acceleration) a large domain D (e.g. size ~ H01)

14. Friedmann-Lemaitre-Robertson-Walker Cosmology Accelerating Expansion :H > 0 , q < 0 Homogeneous & Isotropic Universe :

15. Friedmann-Lemaitre-Robertson-Walker (FLRW)Cosmology Homogeneous & Isotropic Universe : (Dark Energy)

16. Accelerating Expansion: Definition ? ? Issues Space Expansion or Particle Motion ? Gauge Dependence of Acceleration ? Gauge-Independent Definition ? independent of gauge choice (coordinate choice) (frame choice)

17. Models

18. Candidates: Dark Geometryvs. Dark Energy Geometry Matter/Energy ↑ ↑ Dark Geometry Dark Matter / Energy Einstein Equations Gμν＝ 8πGNTμν • (from vacuum energy) • Quintessence • Modification of Gravity • Extra Dimensions • Averaging Einstein Equations (based on FLRW) for an inhomogeneous universe (Non-FLRW)

19. FLRW + CDM Fine-tuning problems: cosmological constant () problem, coincidence problem

20. FLRW + CDM : fine-tuning problems very huge if SSB Phase Transition: Latent heat = vacuum energy (change) ~ TPT (eg. MEW) • Cosmological constant problem How to make  vanish ? Pre-Dark-Energy + Post-Dark-Energy How to make  slightly deviate from 0 ? Why ~ mNOW? • Coincidence problem

21.  Problem & Coincidence Problem • Ratio changes rapidly • with scale factor • But at present time, • WM ~ WL • Why??? Figure 1.1 Ωi ρi / ρc Why ΩΛ ~ ΩM now ? Why acceleratingnow ? Why  so small initially ?

22. FLRW + Quintessence Action : ? Field equation: energy density and pressure : How to achieve it (naturally) ? Quintessence: dynamical scalar field  Slow evolution and weak spatial dependence  V() dominates  w ~ 1Acceleration

23. Non-Quinte: rapidly oscillating mode ~ radiation ~ NR matter time-averaged energy density and pressure :

24. Non-Quinte: ensemble of incoherent oscillators ~ radiation ~ NR matter (i: the phase of i-th oscillator) ensemble-averaged energy density and pressure :

25. Non-Quinte: oscillators ? Thus, Oscillators How about other potentials ?

26. Quinte: a slowly evolving mode or coherent state  (unnaturally small !!)  [V() dominates.] (unnaturally large !!)

27. Tracker Quintessence  

28. Inhomogeneous Cosmo. Model (motivation & final goal: come to the reality) -- Violating cosmological principle --

29. Fundamental Question Is FLRW Cosmologya good approximation ?? If yes, then, WITHOUT DARK ENERGY, there is NO WAY to generate Cosmic Acceleration.

30. Fundamental Question Is FLRW Cosmologya good approximation ?? Acceleration from Inhomogeneity??

31. Is FLRW Cosmology a good approximation ?? ………… YES ! YES ! YES !

32. FLRW Cosmology Friedmann-Lemaitre-Robertson-Walker (FLRW) Cosmology homogeneous & isotropic  Robertson-Walker (RW) metric Einstein equations: G= 8 GT Representing the “real” situation of the energy contents of our universe

33. Is FLRW Cosmologya good approximation ?? YES NO In general, averaging/coarse graining is NOT VALID for Einstein equations. (due to the non-linearity) (homogeneous & isotropic) Apparently, our universe is NOT homogeneous & isotropic. At large scales, after averaging, the universe IS homogeneous & isotropic.

34. Einstein equations For which satisfy Einstein equations, in general DONOT.

35. Is FLRW Cosmologya good approximation ?? Ishibashi & Wald[gr-qc/0509108] perturbed metric, non-perturb T Toy Model [ h(t)<< 1 ] Contributions from metric perturbations are negligible. Averaged Einstein equations: eff peff YES NO Issues : (1) Do these requirements fit the real situation of our universe ? (2) (How much) Can we trust the perturbative analysis ?

36. Is FLRW Cosmologya good approximation ?? might be significant cannot generate acceleration YES NO Newtonianly perturbed metric weffpeff / eff 8G eff 8G peff

37. Acceleration from Inhomogeneity?? Acceleration from reality?? -- Don’t know. (i.e. from the inhomogeneities of our universe)   General possibility?? -- To be discussed

38. Do we really need Dark Energy?? YES NO

39. NeedDark Energy?? YES based on FLRW cosmology could be model-dependent FLRW Cosmology: Acceleration Dark Energy homogeneous & isotropic  RW metric : Einstein equations: (G= 8 GT) Cosmic acceleration requires negative pressure (repulsive/anti gravity).

40. Do we really need Dark Energy?? YES NO concentrate, balance.… Join the dark. Intuitively, Normal matter  attractive gravity  slow down the expansion Common Intuition / Consensus Chuang,Gu &Hwang [astro-ph/0512651] (  need dark energy ) We found line/domain accel. Examples (generated by inhomog)(not by DE) based on the LTBsolution. (Lemaitre-Tolman-Bondi) (exact solution) (dust fluid) (spherical symmetry)

41. Examples of Acceleration : q< 0 Over-density Under-density Acceleration Deceleration Deceleration

42. Examples of Line (Radial) Acceleration : qL < 0 Inhomogeneity Acceleration

43. Acceleration from Inhomogeneity?? YES NO You are illusion !! Mr. Anderson, … Fake!?Illusion!? E.g. FLRW decel. FLRW decel.  Domain Acceleration !! No physically observable effects of acceleration[regarding,e.g., dL(z)] Warning!! Be careful (!!) when connecting two regions. There could exist singularity which leads to strange pheno. E.g. a lesson from Nambu & Tanimoto (incorrect accel. example)[gr-qc/0507057] (perhaps NOT exist at all !!)

44. Acceleration from Inhomogeneity?? YES NO Fake!?Illusion!? Issuesgauge-dep of acceleration definition of acceleration frame acceleration !?

45. Frame Acceleration VD (Volume) Distance L , at time t E.g. 1. Proper distance (Line Acceleration) E.g. 2. L = VD1/3(Domain Acceleration) (e.g. size ~ H01) a large domain D A system consisting of freely moving particles (interacting only through gravity)

46. Frame Acceleration VD (Volume) Distance L , at time t E.g. 1. Proper distance (Line Acceleration) E.g. 2. L = VD1/3(Domain Acceleration) (e.g. size ~ H01) a large domain D A system consisting of freely moving particles (interacting only through gravity)

47. Definition of Acceleration (revisit) ? ? ? Issues Gauge-Independent Definition ? independent of gauge choice (coordinate/frame choice) Space Expansion or Particle Motion ? Frame Acceleration ?

48. Definition of Acceleration (revisit) VD (Volume) Distance L , at time t proper distance between two freely moving particles E.g. 1. Proper distance (Line Acceleration) E.g. 2. L = VD1/3(Domain Acceleration) L a large domain D (e.g. size ~ H01) constant particle number inside • Gauge-independent definitionofaccelerating expansion? (maybe no) • Avoid confusion fromparticle motion&frame acceleration? Consider a system consisting of freely moving particles Interacting with each other only through gravity

49. Definition of Acceleration (revisit) (line) proper distance between two freely moving particles proper distance between two points fixed in space (domain) constant particle number inside size of a domain with its boundary fixed in space Benefitsof Comoving/Synchronous Gauge Universal time(?)  Avoiding frame acceleration.  Avoiding confusionaboutparticle motionandspace expansion.

50. Summary and Perspectives