CMB bispectrum. Takashi Hiramatsu. Collaboration with Ryo Saito (YITP), Atsushi Naruko (TITech), Misao Sasaki (YITP)

Transcription

1 Workshop, 03 Aug Hirosaki Univ. CMB bispectrum Takashi Hiramatsu Yukawa Institute for Theoretical Physics (YITP) Kyoto University Collaboration with Ryo Saito (YITP), Atsushi Naruko (TITech), Misao Sasaki (YITP)

2 Introduction 2/21

3 Born in quantum-mechanical process? Inflation Reheating (Big-bang) Radiation-dominated universe Nucleosysthesis Matter-dominated universe Recombination / Decoupling Dark age Star formation / Reionisation Λ-dominated universe (accelerating expansion) Now Friedmann-Lemaitre-Robertson-Walker spacetime Friedmann equation (K=0) 3/21

4 Inflation field with some potential Accelerating expansion is realised by a almost flat potential 4/21

5 Decay of inflations into standard model particles = vast entropy production in the Universe = beginning of the hot Universe (Radiation) NOTE : At this temperature, all particles are relativistic. Heavy particles become non-relativistic earlier. 5/21

6 Light elements are synthesised 6/21

7 Matter-Radiation equality time However the Universe is still opaque due to the tight coupling between electons and photons vir the Thomson scattering. 7/21

8 Last-scattering surface Recombination of electrons Decouling of photons Thomson scattering free-streaming 8/21

9 Neutral atoms are ionised by UV photons from 1st-stars 9/21

10 Accelerating expansion comes again, which has been revealed by Type-I SNe observations What drives it? Dark energy or Λ = something having negative pressure Breakdown of General Relativity at large scales = extended gravitational theories including GR 10/21

11 Status of the present Universe Hubble parameter : Photon temperature : Age : Cold dark-matter : Baryons : Dark energy : 11/21

12 Inflaton and spacetime (metric) are quantum-mechanically fluctuated WMAP, Planck, LiteBIRD, PIXIE,... SDSS, Subaru,... DECIGO, elisa, aligo,... Large-scale Cosmic microwave Inflationary structure gravitational-wave background background /21

13 Microwave radiation from last-scattering surface - Almost isotropic - Almost complete blackbody radiation with (cf. COBE) - Tiny anisotropic fluctuations with 13/21

14 Many kinds of information on the history of the Universe come out. Angular power spectrum of temperature fluctuations 2-point function (Power spectrum) of primordial curvature pertubation Planck Collaboration, arxiv:// /21

15 3-point function (Bispectrum) Bispectrum gives the statistical properties beyond the power specttrum, Gaussian : Non-Gaussian : 15/21

16 But, unfortunately, it is not the case. New inflation Chaotic inflation Power-law inflation DBI inflation K-inflation Hybrid inflation MSSM inflation Brane inflation inflation after inflation? primordial generated by non-linearity... It is crutial to correctly remove the non-linear contributions for estimating primordial one. If done, we can kill a large number of inflation models. 16/21

17 Basic equations 17/21

18 Dodelson, Modern cosmology, (Academic press) Matsubara, Uchuron no Butsuri (Tokyo Univ.) Photon/Neutrino Boltzmann eqs. Collision term of Thomson scattering (only for photons) CDM/Baryon Continuity/Euler eqs. Photon's Thomson scattering term is derived from Boltzmann eq. of baryons. Gravity Perturbed Einstein eqs. 18/21

19 Photon temperature Photon polarisation Massless neutrino temperature

20 20/21

21 21/21

22 22/21

23 Line-of-sight formula Seljak, Zaldarriaga, APJ 469 (1996) 437 directly solving suppressed by tight-coupling between baryons-photons 23/21

24 -- Assumptions -- Adiabatic initial condition Ma, Bertschinger, APJ 455 (1995) 7 Unchanged potential, Radiation dominant, Similarly fluctuated, Superhorizon, Tight-coupling, Negligible photon's quadrupole, Negligible neutrino's octapole Recombination history Peebles-Weinberg scheme or Seager's scheme (Recfast) Peebles, APJ 153 (1968) 1 Weinberg, Cosmology (Oxford Univ. Press) Seager et al., APJ 523 (1999) L1 Reionisation by Planck. Lewis, CAMB note 24/21

25 Relative error from CAMB (%) parameters existing codes CMBFAST : Seljak, Zaldarriaga, APJ469 (1996) 437 CAMB : Lewis, Challinor, APJ538 (2000) 473 CLASS II : Blas, Lesgourgues, Tram, JCAP 1107 (2011) 034 CosmoLib : Huang, JCAP 1206 (2012) /21

26 Tensor TT Tensor TE Tensor EE, BB All kinds of spectra are consistent to those computed by CAMB with ~1% 26/21

27 nd 2 -order 27/21

28 Linear Boltzmann eqs. Line-of-sight formula CAMB, CMBfast, Class, CosmoLib,... 2nd-order Boltzmann eqs. CMBquick, SONG, CosmoLib2 2nd-order cmb2nd cmb2nd (future work) line-of-sight formula CMBquick : Pitrou, Uzan, Bernardeau, JCAP 07 (2010) 003] SONG : Petinarri et al., JCAP 1304 (2013) 003 CosmoLib2 : Huang, Vernizzi, PRL 110 (2013) /21

29 Line-of-sight is bended by the gravity potential 'curve'-of-sight Boltzmann equation for the photon intesity Get the integral form Expand the integrand up to 2nd-order = Integral solution including 2nd-order geodesic effect Quite schematically,... R.Saito, Naruko, Hiramatsu, Sasaki, JCAP10(2014)051 [arxiv: ] (cf. Fidler, Koyama, Pettinari, JCAP 04 (2015) 037) 29/21

30 More presicely,... and expanding it up to 2nd-order of the solution of geidesic eq., 30/21

31 R.Saito, Naruko, Hiramatsu, Sasaki, JCAP10(2014)051 [arxiv: ] Temp. fluc. on LSS TD L ISW D 1st-order LOS = [Source on LSS] + [ISW] We find totally 7 combinations that contribute to [Source] x [gravitational] Source x ISW Source x Lensing Source x Time-delay Source x Deflection [ISW] x [gravitational] ISW x ISW ISW x Lensing ISW x Time-delay 31/21

32 [source] x [gravitational] e.g. source x lensing 32/21

33 Quantify the magnitude of NG signals templates Bispectrum templates Gangui et al., APJ 430 (1994) 447 Verde et al., MNRAS 313 (2000) L141 Komatsu, Spergel, PRD63 (2001) /21

34 is minimised. local-type equilateral-type orthogonal-type Komatsu, Spergel, PRD63 (2001) /21

35 (Single-template fitting) Local Equilateral Orthogonal Folded Source x ISW 1.25(-3) 1.24(0) 4.11(-2) 3.93(-1) Source x Lensing 8.86(0) -4.57(-1) -2.83(+1) 4.35(+1) Source x Time-delay 2.82(-1) 4.35(-1) -3.45(-1) 6.93(-1) Source x Deflection 1.82(-2) 1.76(-1) -3.00(-1) 5.27(-1) ISW x ISW 1.31(-4) 5.19(-2) 1.13(-1) 1.64(-3) ISW x Lensing 7.63(-2) 1.60(-1) -6.19(-1) 1.01(0) -1.84(-1) -1.48(-1) 1.33(-1) -2.59(-1) ISW x Time-delay m309e - Lensing effect ([Src x Lens] + [ISW x Lens]) dominates as expected. - The whole lensing effect leads to 35/21

36 CMB lensing Remapping approarch Last-scattering surface Neglecting the thickness of LSS Goldberg, Spergel, PRD 59 (1999) Hu, PRD 62 (2000) Zaldarriaga, PRD 62 (2000) Lensing potential Review : Lewis, Challinor, PR 429 (2006) 1 Taylor expansion Hanson et al., PRD 80 (2009) Leading contribution to lensing bispectrum 5 perms. 36/21

37 Remapping approach 5 perms. Recovery of remapping approach Local Remapping 8.94(0) Equilateral Orthogonal -2.40(-1) -2.91(+1) Folded 4.48(+1) m309e Local Curve-of-sight 8.93(0) Equilateral Orthogonal -2.97(-1) -2.89(+1) Folded 4.45(+1) m309e We, for the first time, justify the remapping approach as a scheme to estimate the lensing effect. In the other words, the effect of LSS width is so tiny. 37/21

38 Extension 38/21

39 Leading contributions Tensor Curve-of-sight A : Source or ISW B : Gravitational 39/21

40 Source x ISW Source x Lensing Source x Time-delay Source x Deflection ISW x ISW ISW x Lensing ISW x Time-delay Source x ISW Source x Lensing Source x Time-delay Source x Deflection ISW x ISW ISW x Lensing ISW x Time-delay ISW x Deflection Source x ISW Source x Lensing Source x Time-delay Source x Deflection ISW x ISW ISW x Lensing ISW x Time-delay ISW x Deflection Totally,we have =29 kinds of fnl. 40/21

41 PRELIMINARY (Single-template fitting) Local Equilateral Orthogonal Folded Source x ISW -2.14(-1) 1.42(-2) 3.69(-1) -5.64(-1) Source x Lensing -6.65(-1) 1.23(-1) 1.66(0) -2.52(0) Source x Time-delay -3.68(-2) -1.17(-3) 5.27(-2) -8.17(-2) Source x Deflection -1.53(-2) -5.50(-2) 1.39(-1) -2.34(-1) ISW x ISW -1.75(-3) 1.58(-3) 9.20(-3) -1.36(-2) ISW x Lensing -5.17(-3) -6.34(-3) 3.47(-2) -5.58(-2) 4.89(-2) 2.24(-3) -5.00(-2) 7.79(-2) ISW x Time-delay m320c 41/21

42 PRELIMINARY (Single-template fitting) Local Equilateral Orthogonal Folded Source x ISW 3.38(-7) -3.32(-5) -1.34(-5) 8.46(-6) Source x Lensing 1.09(-5) 2.71(-4) 2.31(-5) 6.40(-5) Source x Time-delay 6.05(-5) 4.03(-5) -3.95(-5) 7.57(-5) Source x Deflection 4.34(-9) -3.40(-5) -6.80(-6) -1.98(-6) ISW x Lensing 1.32(-3) -3.09(-2) -2.45(-2) 2.65(-2) ISW x Time-delay -1.12(-4) -3.53(-4) 1.57(-4) -3.72(-4) ISW x Deflection -9.25(-5) 3.62(-3) 2.96(-3) -3.24(-3) m320c 42/21

43 PRELIMINARY (Single-template fitting) Local Source x ISW Equilateral Orthogonal Folded 1.16(-7) 6.96(-7) -4.67(-6) 7.47(-6) Source x Lensing -8.31(-7) -1.97(-5) -3.01(-6) -2.59(-6) Source x Time-delay -1.60(-5) -3.91(-7) 1.43(-5) -2.22(-5) Source x Deflection 3.00(-7) 4.66(-5) 7.52(-6) 5.52(-6) ISW x ISW -6.39(-5) -6.39(-4) 7.63(-4) -1.41(-3) ISW x Lensing -7.64(-5) 1.36(-3) 1.02(-3) -1.07(-3) ISW x Time-delay 1.39(-5) 5.79(-5) -1.77(-4) 2.94(-4) ISW x Deflection 1.80(-5) -3.59(-3) -1.82(-3) 1.50(-3) m320c 43/21

44 PRELIMINARY (Single-template fitting) Local Equilateral Orthogonal Scalar x Scalar 9.05(0) 1.46(0) -2.94(+1) Scalar x Tensor -8.89(-1) 7.83(-2) 2.21(0) Tensor x Scalar 1.18(-3) -2.74(-2) -2.14(-2) 2.30(-2) Tensor x Tensor -1.25(-4) -2.78(-3) -2.04(-4) -7.07(-4) Folded 4.59(+1) -3.39(0) m320c 44/21

45 New CMB Boltzmann code implemeting 'curve'-of-sight formulas * 1st-order scalar and tensor are completed. (TT, TE, EE, BB) * Different schemes from CAMB, but consistent within O(1)% * Implemented curve -of-sight formulas (2nd-order line-of-sight) for scalar and tensor temperature fluctuations. * Implemented Komatsu-Spergel bispectrum estimator. * Implemented 2nd-order equations only for gravity and matter. (skipped today) * Implemented remapping approximation. 45/21

46 To-do - Implement pure 2nd-order Boltzmann equations for radiation : Petinarri et al., JCAP 1304 (2013) 003 (cf. SONG, CosmoLib2) SONG CosmoLib2 : Huang, Vernizzi, PRL 110 (2013) Implement the curve-of-sight formulas for polarisation Applications? - 2nd-order gravitational waves, magnetic field from [1st-order]2 e.g. Saga et al., PRD 91 (2015) Saga et al., PRD 91 (2015) y-distortion to photon's distribution function? 46/21