The New Relationship between Inflation & Gravitational Waves

Transcription

1 The New Relationship between Inflation & Gravitational Waves Tomohiro Fujita (Stanford) Based on arxiv: w/ Dimastrogiovanni(CWRU) & Fasiello(Stanford) In prep w/ Komatsu&Agrawal(MPA); Shiraishi(KIPMU)&Thone(Cambridge); Namba(McGill)&Tada(KIPMU/IAP) 4 th /Mar/2017@Stanford

2 introduction GW detected! It exists! aligo detected GW from BH binary Primordial GW soon? PGW observed by the CMB B-mode Projects are on-going e.g. LiteBIRD (Japan), CMB-S4(US), etc..

3 introduction Why PGW? Universal prediction of inflation Vacuum GW: r vac 10 3 H inf GeV 2 New physics & Model selection

4 introduction Vacuum fluctuation Inflation generates fluctuations from vacuum h k + k 2 2 τ 2 h k = 0, h k = 2 2k e ikτ M Pl. δφ & M Pl h ij are produced with amplitude O H inf because H inf is the only dimensionful quantity. P vac h = 2H 2 inf π 2 2 r P h 2 H M Pl P inf ζ

5 introduction Why PGW? Universal prediction of inflation Vacuum GW: r vac 10 3 H inf GeV 2 New physics & Model selection

6 1 Introduction 6 What if r is detected? We now know ρ inf!

7 Are You Sure??

8 If you detect r 0.05, is it 100% OK to report H inf GeV?

9 introduction No! That s not necessarily true.

10 introduction The Golden Rule H inf GeV r obs /2 can be broken.

11 introduction Axion-SU(2) model Larger GW than h vac can be produced r obs = r vac + r add

12 introduction Axion-SU(2) model Larger GW than h vac can be produced r obs = r vac + r add

13 introduction Axion-SU(2) model Larger GW than h vac can be produced r obs = r vac + r add r obs = r vac 10 3 H inf GeV 2

14 introduction Result H inf GeV H inf GeV

15 introduction Result H inf GeV H inf GeV Alternative GW may lead to overestimate of inflation H

16 introduction Plan of talk 1 Model: Produce additional GW, r ρ inf 2 Observation: TB & EB, Non-G, tilt n t 3 Discussion: Lowest ρ inf for r = 10 3??

17 introduction Plan of talk 1 Model: Produce additional GW, r ρ inf 2 Observation: TB & EB, Non-G, tilt n t 3 Discussion: Lowest ρ inf for r = 10 3??

18 introduction Our scenario GW version of Curvaton mechanism [Enqvist&Sloth(2002), Lyth&Wands(2002), Moroi&Takahashi(2002)] L inflaton + L spectator H inf ρ inf vac P GW ρ spec Source spec P GW L inf is arbitrary and responsible for ζ generation. L spec is added just to produce GW during inf.

19 Model How s it work? Adding axion-su(2) gauge spectator sector L = L inflaton χ 2 μ 4 cos χ f F μν a F aμν λ 4f χf μν a F aμν [cf. Chromo-natural inflation: Adshead&Wyman(2012)]

20 Model How s it work? Adding axion-su(2) gauge spectator sector L = L inflaton Inflaton sector P ζ Decoupled χ 2 U χ 1 4 FF λ 4f χf F spec P GW Axion- SU(2) gauge spectator sector

21 Model Why SU(2)? SVT Decomposition Theorem: At the 1 st order cosmological perturbation, scalar, vector and tensor are decoupled. δs, δv i Source δt ij

22 Model Why SU(2)? SVT Decomposition Theorem: At the 1 st order cosmological perturbation, scalar, vector and tensor are decoupled. δs, δv i Source δt ij

23 Model Why SU(2)? Using the 2 nd order pert., GW can be sourced. spec But it s hard to generate P GW vac PGW. i δs j δs, δv i δv j Source δt ij [Biagetti et al.(2013), Mukohyama et al.(2014), TF et al.(2015), Ferreira et al.(2015), Choi et al.(2015), Namba et al.(2016).]

24 Model Way Out Background vector field V i BG helps. Isotropy is violated V i BG δv j Source δt ij V i BG CMB says the universe is isotropic. U(1) gauge SU(2) gauge Anisotropic BG Isotropic BG is Attractor. [Maleknejad&Erfani(2014)]

25 Model Way Out Background vector field V i BG helps. V i BG δv j Source δt ij CMB says the universe is isotropic. Isotropy is conserved A 3 3 A 2 2 A 1 1 U(1) gauge Anisotropic BG A i a = aa BG t δ i a SU(2) gauge Isotropic BG is Attractor. [Maleknejad&Erfani(2014)]

26 Model BG dynamics V(χ) χ BG V eff A BG 1 2 H2 2 A BG + μ4 sin χ f 3gλ A BG A BG χ BG A BG SU(2) gauge field has non-zero vev while χ is slowly rolling down its potential.

27 Model BG dynamics Numerical Result V(χ) χ BG V eff A BG 1 2 H2 2 A BG + μ4 sin χ f 3gλ A BG 5A BG /f A BG χ BG A BG SU(2) gauge field has non-zero vev while χ is slowly rolling down its potential. A BG

28 Model Flow of dynamics BG: Axion χ BG Vector A i BG Pert: t ij = A i BG δa j GW (s) h ij

29 Coupling of Tensor perturbations The T.T. component of A i δa j is named t ij A BG (i δa a j) t ij, i t ij = t ij = 0 The EoM for GW mode function gets source terms h k + k 2 2 τ 2 h k = O Ω A 1/2 tk Now GW has the inhomogeneous solution!

30 Model Beat vacuum We can source h ij at linear order. However A i BG δa j t ij h ij, Source h vac ij Both are 1 st order. No reason for h source h vac. We need to amplify the former, but how? Instability of tensor pert. of SU(2)

31 Instability of Chiral Tensor Background χ and A BG break the parity symmetry (SSB), 0 χ t, x P χ t, x 0 A a i = aa BG a δ P i aa BG a δ i Therefore, when we use left/right-handed polarization t R/L 1 2 t+ ± it, h R/L 1 2 h+ ± ih t R and t L behave in different ways.

32 Instability of Chiral Tensor The EoMs for tensor perturbations are h R,L h 1/2 x 2 R,L = O Ω A tr,l t R,L m Qξ 2 m 1/2 x 2 x Q + ξ t R,L = O Ω A hr,l x kη m Q ga BG /H ξ λ χ/2fh A i a aδ i a A BG

33 Instability of Chiral Tensor The EoMs for tensor perturbations are h R,L h 1/2 x 2 R,L = O Ω A tr,l t R,L m Qξ 2 m 1/2 x 2 x Q + ξ t R,L = O Ω A hr,l FF gε ijk A i A j A k, χf F χε ijk A i j A k R,L R,L where we have used ε ijk k i e jl k = ke kl k. ε ijk terms make t R instable (but not t L ) h R h L : Chiral GW is generated! x kη m Q ga BG /H ξ λ χ/2fh A i a aδ i a A BG

34 Instability of Chiral Tensor Peak amp.~ e 1.8m Q Use L/R tensor polarization, h R,L h + ± ih / 2, m Q gabg H Tensor EoMs are = 7 h R h R,L h 1/2 x 2 R,L = O Ω A tr,l t R,L m Qξ 2 m 1/2 x 2 x Q + ξ t R,L = O Ω A hr,l t R FF gε ijk A i A j A k, χf F χε ijk A i j A k ε ijk terms make t R instable (but not t L ) h L h R h L : Chiral GW is generated! t L m Q ga BG /H ξ λ χ/2fh A i a aδ i a A BG

35 Instability of Chiral Tensor Peak amp.~ e 1.8m Q Use L/R tensor polarization, h R,L h + ± ih / 2, m Q gabg H Tensor EoMs are = 7 h R h R,L h 1/2 x 2 R,L = O Ω A tr,l t R,L m Qξ 2 m 1/2 t x 2 x Q + ξ t R,L = O Ω A hr,l Fully R Chiral GW FF gε ijk A i A j A k, χf F χε ijk A i j A k ε ijk terms make t R instable (but not t L ) h L h R h L : Chiral GW is generated! t L m Q ga BG /H ξ λ χ/2fh A i a aδ i a A BG

36 introduction Result H inf GeV H inf GeV (s) Sourced GW h ij can be much larger vac than vacuum h ij

37 introduction Axion-SU(2) model Larger GW than h vac can be produced r obs = r vac + r add r obs doesn t fix H inf Distinguishable w/ Polarization h R h L Non-Gaussianity hhh Tensor tilt n t

38 introduction Plan of talk 1 Model: Produce additional GW, r ρ inf 2 Observation: TB & EB, Non-G, tilt n t 3 Discussion: Lowest ρ inf for r = 10 3??

39 introduction TB, EB correlation Chiral GW induces TB & EB cross correlations TT, TE, EE, BB h R h R + h L h L TB, EB h R h R h L h L By detecting TB & EB correlations, we can distinguish h (s) from h vac

40 introduction LiteBIRD CMB satellite mission Will be launched in 2020s Aims to detect r 10 3

41 Model prediction S/N for TB+EB w/ lensing effect (no delensing) LiteBIRD instrumental noise 2% foreground contamination

42 S/N ratio for TB+EB

43 Model prediction Excellent Template P h σ 0.3ΔN, r P ζ k p = arbitrary (depend on χ i ) ΔN P h (s) is the Gaussian shape. k p k

44 Model prediction S/N for TB+EB w/ lensing effect (no delensing) LiteBIRD instrumental noise 2% foreground contamination TB + EB can be detected by LiteBIRD for r > 0.03.

45 introduction Non-Gaussianity Large h R h R h R Large t R t R t R The EoM for SU(2) gauge field is non-linear

46 introduction Result

47 introduction Non-Gaussianity Model prediction (preliminary): k 2 1 k 2 2 k 2 equil 3 B h Planck 2015 XVII constraint on h R h R h R k 2 1 k 2 2 k 2 equil 3 B h = 3.5 ± Note: Planck analysis assumes different shape of NG

48 introduction Non-Gaussianity Model prediction (preliminary): k 1 2 k 2 2 k 3 2 B h equil Planck 2015 XVII constraint: k 1 2 k 2 2 k 3 2 B h equil = 3.5 ± GW NG may be detected soon? Note: Planck analysis assumes different shape of NG

49 introduction Axion-SU(2) model Larger GW than h vac can be produced r obs = r vac + r alt Distinguishable w/ Polarization h R h L Non-Gaussianity hhh Tensor tilt n t

50 Model prediction Excellent Template P h σ 0.3ΔN, k p = arbitrary (depend on χ i ) ΔN P h (s) is the Gaussian shape. k p k

51 Model prediction Excellent Template V(χ) χ BG P h σ 0.3ΔN, χ BG k p = arbitrary (depend on χ i ) ΔN P h (s) is the Gaussian shape. k p k

52 introduction Blue/Red tilt P h P h (s) Blue tilt k pivot k p k

53 introduction Blue/Red tilt P h P h (s) Red tilt k p k pivot k

54 introduction Blue/Red tilt P h P h (s) Scaleinvariant k pivot k Consistency relation: n T = r/8

55 introduction Blue/Red tilt P h P h (s) Scaleinvariant k pivot k Consistency relation: n T = r/8

56 introduction Plan of talk 1 Model: Produce additional GW, r ρ inf 2 Observation: TB & EB, Non-G, tilt n t 3 Discussion: Lowest ρ inf for r = 10 3??

57 Preliminary Lowest ρ inf for r = 10 3 What s the lowest possible ρ inf generating detectable r?? 10 1 GeV BBN Where? GeV Vac GW 1/4 ρ inf

58 Preliminary Lowest ρ inf for r = 10 3 What s the lowest possible ρ inf generating detectable r?? Here!!? 10 1 GeV BBN GeV Vac GW 1/4 ρ inf

59 Preliminary Lowest ρ inf for r = 10 3 What s the lowest possible ρ inf generating detectable r?? H inf can go down to the BBN bound, ρ inf 10 1 GeV Analytic estimate: P h (s) ~ ΩA e 3.6m Q P h vac, Lowering H and increasing m Q, we can keep r = 10 3.

60 Model Revisit r(h inf ) One can show r is prop to energy fraction of GW at H.C., r P h k Ω GW k dρ GW/dlnk M 2 Pl H 2 inf With the energy source, we can keep Ω GW k if H inf vac dρ srouce GW 4 dρ H GW dlnk inf HC dlnk HC vac dρ tr H 4 dlnk inf e 3.6m Q 2 H inf HC Tuning e 3.6m Q H 2, nothing bans a small ρ inf

61 Instability of Chiral Tensor Peak amp.~ e 1.8m Q Use L/R tensor polarization, h R,L h + ± ih / 2, m Q gabg H Tensor EoMs are = 7 h R h R,L h 1/2 x 2 R,L = O Ω A tr,l t R,L m Qξ 2 m 1/2 x 2 x Q + ξ t R,L = O Ω A hr,l t R FF gε ijk A i A j A k, χf F χε ijk A i j A k ε ijk terms make t R instable (but not t L ) h L h R h L : Chiral GW is generated! t L m Q ga BG /H ξ λ χ/2fh A i a aδ i a A BG

62 Preliminary Lowest ρ inf for r = 10 3 What s the lowest possible ρ inf generating detectable r?? H inf can go down to the BBN bound, ρ inf 10 1 GeV Analytic estimate: P h (s) ~ ΩA e 3.6m Q P h vac, Lowering H and increasing m Q, we can keep r = 10 3.

63 Are You Sure??

64 Preliminary Possible obstacles 1 Scalar perturbations: δχ, δq, M ζ 2 Spectral index: 3 Energy hierarchy: 4 Backreaction: ρ A H φ EoM n s ρ φ > ρ χ, ρ A > ρ tr t R t R EoM of χ, A BG 5 Perturbativity: t R t R Tree > 1loop

65 Preliminary Possible obstacles 1 Scalar perturbations: δχ, δq, M ζ 2 Spectral index: 3 Energy hierarchy: 4 Backreaction: ρ A H φ EoM n s ρ φ > ρ χ, ρ A > ρ tr t R t R EoM of χ, A BG 5 Perturbativity: t R t R Tree > 1loop

66 Preliminary Weak gravity conjecture Following e 3.6m Q H 2, m Q ga BG /H grows a lot. H BBN GeV BR requires extremely small SU(2) self-coupling constant g Banned by WGC?? [Thanks to Prof. Reece (Harvard)]

67 Comments Welcome

68 Summary Axion-SU(2) model Larger GW than h vac can be produced r obs = r vac + r alt r obs doesn t fix H inf Distinguishable w/ Let s observe it! Polarization h R h L TB&EB correlation Non-Gaussianity hhh Tensor tilt n t n T = r/8 large B h equil Lowest ρ inf for r = 10 3 r Ω GW k Ω source (k) BBN bound??