B-mode Polarization of The Cosmic Microwave Background

Transcription

1 B-mode Polarization of The Cosmic Microwave Background Yuri Hayashida May 27, / 19

2 Index Reference Introduction Polarization Observation Summary 2 / 19

3 Reference [1] Baumann,D. (2012). TASI Lectures on Inflation, arxiv: [2] Carlisle, M.C.(2014). Sky and Telescope. Direct Evidence of Big Bang Inflation. direct-evidence-of-big-bang-inflation/ (accesed ) [3] The BICEP2/Keck and Planck Collaborations, Phys. Rev. Lett. 114, , 2015 [4] The BICEP2 Collaboration, Phys. Rev. Lett. 112, , 2014 [5] Planck Collaboration. (2014). arxiv: v2 [astro-ph.co] [6] Planck Collaboration. (2015). arxiv: v1 [astro-ph.co] 3 / 19

4 Cosmic Microwave Background What is the CMB? 4 / 19

5 Inflation What is the inflation? 5 / 19

6 Powerspectrum of the Tensor Perturbation The powerspectrum of the tensor perturbation, 2 t, gives the energy scale of the inflation directly. 2 t = 2 π 2 H 2 M 2 pl (1) If we assume slow-roll inflation model, 2 t H 2 V, (2) where V is the infraton potential. 6 / 19

7 Gravitational Wave In the early universe, there were primordial gravitational waves. ds 2 = dt 2 + a 2 (t) ij [ δij + h ij (t, x i ) ] dx i dx j (3) 1. Gravitational waves are transverse. 2. Gravitational waves have two polarization srates. 3. Gravitational waves are spin-2. Therefore, h ij is a rank-2 tensor field. 7 / 19

8 Thomson Scattering The polarization is generated by Thomson scattering. Credit: Leah Tiscione / Sky & Telescope[2] 8 / 19

9 Polarization Stokes Palameter: Q, U (Q ± iu)(ˆn) = l,m a ±2,lm ±2 Y lm (ˆn) (4) where ˆn denotes direction of the sky, and ±2 Y lm is tensor spherical harmonics. 9 / 19

10 Polarization the linear combination α E,lm 1 2 (a 2,lm + a 2,lm ), α B,lm 1 2i (a 2,lm a 2,lm ) two scalor fields (5) E(ˆn) = l,m a E,lm Y lm (ˆn), B(ˆn) = l,m a B,lm Y lm (ˆn) (6) 10 / 19

11 Polarization modes E-mode scalor and tensor perturbation B-mode tensor (and vector) perturbation Two modes of polarization[1] 11 / 19

12 Why is B-mode so important? B-mode polarization of CMB is just a good evidence of the inflation. Moreover, it has some cosmological imformation. 12 / 19

13 BICEP2 In Mar 2014, BICEP2 group announced that they detected B-mode polarization generated by primordial gravitational waves.[4] BICEP2 team [4] 13 / 19

14 BICEP2 BICEP2 was a specialized, low angular resolution experiment which operated from the South Pole from 2010 to [3] Planck Collaboration(2014)[5] 14 / 19

15 BICEP2 BICEP2(2014)[4] 15 / 19

16 Detection...? Taking cross spectra against 100 GHz maps from BICEP1 we find significant correlation and set a constraint on the spectral index of the B-mode excess consistent with CMB and disfavoring dust by 1.7. [4] 16 / 19

17 Detection...? Taking cross spectra against 100 GHz maps from BICEP1 we find significant correlation and set a constraint on the spectral index of the B-mode excess consistent with CMB and disfavoring dust by 1.7. [4]... In Feb 2015, BICEP2/Keck, Planck Collaborations reported that We find strong evidence for dust and no statistically significant evidence for tensor modes. [3] 16 / 19

18 Constraints: Planck results 2015 The constraint on the tensor-to-scalor ratio (Planck 2015 [6]) r 2 t 2 s (7) Planck 2015[6] The energy scale of the inflaion V 1/4 = ( GeV) ( r 0.10 ) 1/4 (8) 17 / 19

19 Constraints: Planck results 2015 Planck(2015)[6] 18 / 19

20 Summary The B-mode polarization on large scales is generated by the primordial gravitational waves. The B-mode polarization is a good evidence of the inflation and has some information about the early universe. This B-mode polarization have not yet detedted. The tensor-to-scalor ratio, r, is constrained r < 0.10 (95% CL, Planck TT+lowP)[6]. Its constraint gives the energy potential of inflation: V 1/4 = ( GeV) ( r 1/ ) 19 / 19