1. Three theoretical issues in physical cosmology I. Nonlinear clustering II. Dark matter III. Dark energy J. Hwang (KNU), H. Noh (KASI) 2009.04.29 1

2. I. Nonlinear clustering 2

3. Is Newton’s gravity sufficient to handle the weakly nonlinear evolution stages of the large scale cosmic structures? 3

4. General Relativistic Newtonian LinearFully Nonlinear Weakly Relativistic Weakly Nonlinear Studies of Large-scale Structure Newtonian Gravity Linear Perturbation ? 4

5. General Relativistic Newtonian LinearFully Nonlinear Weakly Relativistic Weakly Nonlinear Post-Newtonian Approximation Perturbation Theory Perturbation Theory vs. Post-Newtonian “Terra Incognita” Numerical Relativity 5

6. General Relativistic Newtonian LinearFully Nonlinear Weakly Relativistic Weakly Nonlinear Cosmology and Large-Scale Structure Likely to be not relevant in cosmology! Cosmological 1 st order Post-Newtonian (1PN) Cosmological Nonlinear Perturbation (2 nd and 3 rd order) ? 6

7. Perturbation method: Perturbation expansion. All perturbation variables are small. Weakly nonlinear. Strong gravity; fully relativistic! Valid in all scales! Post-Newtonian method: Abandon geometric spirit of GR: recover the good old absolute space and absolute time. Provide GR correction terms in the Newtonian equations of motion. Expansion in Fully nonlinear! No strong gravity situation; weakly relativistic. Valid far inside horizon 7

8. Perturbation Theory 8

9. Relativistic/Newtonian correspondence: Background order: Linear perturbation: Spatial curvature/ Total energy Cosmological constant Friedmann (1922)/Milne and McCrea (1934) Lifshitz (1946)/Bonnor (1957) Density perturbation/Density Density 9

10. Newtonian equations: Peebles (1980) Fully nonlinear! Relativistic equations: Noh-Hwang (2004) To second order! Gravitational waves comoving gauge K=0 10

11. 11

12. Linear order: Second order: Third order: Physical Review D, 72, 044012 (2005). Pure General Relativistic corrections K=0 comoving gauge K=0 comoving gauge 12

13. Physical Review D, 72, 044012 (2005) To linear order: In the comoving gauge, flat background (including Λ ): CMB: Sachs-Wolfe effect Curvature perturbation COBE, WMAP Curvature perturbation in the comoving gauge Curvature perturbation in the zero-shear gauge 13

14. 1. Relativistic/Newtonian correspondence to the second order 2. Pure general relativistic third-order corrections are small ~5x10 -5 3. Correction terms are independent of presence of the horizon. 14

15. 15

16. General relativistic contributions to second-order power spectrum: Physical Review D, 77,123533 (2008) Pure General Relativistic contribution! Relativistic/Newtonian 16

17. Density power spectrum to second-order: Physical Review D, 77,123533 (2008) Pure General Relativistic corrections P 13,Einstein Newtonian: Vishniac (1983) Relativistic: Noh-Hwang (2008) Newtonian P 22 + P 13,Newton K=0 = Λ: Leading order Newtonian terms cancel in the small- scale! 17

18.  Background world model: Relativistic: Friedmann (1922) Newtonian: Milne-McCrea (1934) Coincide for zero-pressure  Linear structures: Relativistic: Lifshitz (1946) Newtonian: Bonnor (1957) Coincide for zero-pressure  Second-order structures: Newtonian: Peebles (1980) Relativistic: Noh-Hwang (2004) Coincide for zero-pressure, no-rotation  Third-order structures: Relativistic: Hwang-Noh (2005) Pure general relativistic corrections δ T/T ~ 10 -5 factor smaller, independent of horizon 18

19. arXiv:0902.4285 19

20. We probe the pure Einstein's gravity contributions to the second-order density power spectrum and present two new results. In the small-scale the Einstein's gravity contribution is still negligibly small. In the large scale we encounter an infrared divergence in the second-order power spectrum due to pure Einstein gravity contribution appearing in the third- order perturbation. 20

21. P 13,Einstein P 22 P 11 P 13,Newton 21

22. Dashed line: negative P 13,Einstein P 22 P 11 P 13,Newton P Total P 22 + P 13,Newton 22

23. P 13,Einstein Large-scale limit (k →0, r →∞ ): P 13,Newton Leading orderNext-to-leading order 23

24. P 13,Einstein P 13,Newton Leading order Next-to-leading order 24

25. In the large scale we encounter an infrared divergence in the next-to-leading-order power spectrum due to pure Einstein gravity contribution appearing in the third-order perturbation. Despite cancellations of the leading-order and next-to-leading order terms in P 13,Newton, no such cancellations occur in P 13,Einstein. arXiv:0902.4285 Whole calculations reserved in http://bh.knu.ac.kr/~jchan/third-order-note.pdfhttp://bh.knu.ac.kr/~jchan/third-order-note.pdf 25

26. P 13,Einstein Small-scale limit (k →∞, r →0 ): P 13,Newton Leading orderNext-to-leading order Leading order 26 P 22

27. P 13,Einstein P 13,Newton Leading order Next-to-leading order 27

28. In the small-scale the Einstein's gravity contribution is still negligibly small. Due to cancellation of the leading-order and next-to-leading order terms in P 13,Einstein, despite a cancellation between P 22 in P 13,Newton. 28

29. II. Dark Matter 29

30. arXiv:0902.4738 30

31. The axion as a coherently oscillating scalar field acts as a cold dark matter in nearly all cosmologically relevant scales. Deviation from purely pressureless medium appears in very small scale where axion reveals a peculiar equation of state. 31

32. Background equations: Thus, axion behaves as a zero-pressure fluid. Solutions: Strictly ignore: 32

33. Perturbation equations (comoving gauge): Solution for vanishing cosmological constant: Sound speed and Jeans scale: ~ Solar system scale 33

34. III. Dark Energy 34

35. arXiv:0904.4007 35

36. When the dynamical dark energy deviates from the cosmological constant, substantial differences could appear in the matter power spectrum and the cosmic microwave background radiation anisotropy power spectra depending on whether we include the dark energy perturbations or not. 36

37. For cosmological constant (CDM-comoving gauge, CCG): For scalar field dark energy (CCG): Dark energy perturbation 37

38. Double exponential potential model: Analysis in three temporal gauges: CDM comoving gauge (CCG): Uniform expansion gauge (UEG): Uniform curvature gauge (UCG): Intrinsic curvature Expansion scalar of the normal-frame ~Trace of extrinsic curvature Perturbed velocity of CDM 38

39. Background evolution: ● Parameters following Bassett et al. JCAP 0807 007 (2008): Ω ,initial =0.045 (PNN limit) ● Five-year WMAP for ΛCDM : Ω m =0.274 (Ω c =0.2284, Ω b =0.0456), Ω Λ =0.726, h=0.705, n s =0.960, σ 8 =0.812, T 0 =2.725K,Y He =0.24, by Hinshaw et al. ApJS 180 225 (2009) without neutrino and reionization. ● Binned SNIa data based on the Union sample of Kowalski et al. ApJ 686 749 (2008). 39 Scaling

40. Background evolution: ● W ithout binning. 40

41. Power spectra: CMBFast ----------------------------------------------------------------------------------------------------------------------------------------------- Our code  CDM ( 2 =1.) ----------------------------------------------------------------------------------------------------------------------------------------------- ΛCDM  CDMs ΛCDM All gauges give the same result 41

42. Power spectra: ( 2 =1.) CCG off UEG off Pert on ΛCDM 42

43. Ignoring the dark energy perturbations leads to significant deviations in power spectra which even depend on the gauge choice. By ignoring the dark energy perturbation the perturbed system of equations becomes inconsistent. 43