Gonzalo A. Palma DFI - U. de Chile

Transcription

1 Features of heavy physics in the CMB power spectrum DFI - U. de Chile WITH Ana Achucarro (Leiden) Jinn-Ouk Gong (Leiden & CERN) Sjoerd Hardeman (Leiden) Subodh Patil (LPTEN & CPTH) Based on: & Cambridge

2 In this talk The status of heavy physics during inflation Under which circumstance may we ignore heavy degrees of freedom during inflation? The role of heavy physics during inflation What are their effects on the power spectrum and bispectrum? 01

3 The status of heavy physics Common lore: If heavy degrees of freedom are sufficiently massive, then we can ignore them... How massive? M H They become quickly suppressed on super horizon scales M 2 = M 2 =5H Ignored = Truncated 02

4 The status of heavy physics But: Instead of truncating them, we should integrate them out In inflation the v.e.v. s of massive fields vary as the inflaton evolves! Difficult (if not impossible) to obtain vacuum expectation values of massive fields independent of the inflaton Φ M = Φ 0 (φ) Example: SUGRA 03

5 Multi-field inflation S = gd 4 x M 2 Pl 2 R 1 2 γ abg µν µ φ a ν φ b V (φ) V (φ 1, φ 2 ) φ 2 I will not focus on any specific model Instead, I will ask myself what happens to adiabatic modes under general turns of the inflationary trajectory φ 1 04

6 First step: The background D dt φ a 0 +3H φ a 0 + V a =0 DX a = dx a + Γ a bcx b dφ c φ 2 Flat valley φ 1 05

7 First step: The background D dt φ a 0 +3H φ a 0 + V a =0 φ 2 DX a = dx a + Γ a bcx b dφ c Real trayectory Flat valley φ 1 05

8 First step: The background D dt φ a 0 +3H φ a 0 + V a =0 DX a = dx a + Γ a bcx b dφ c φ 2 N a T a Real trayectory Flat valley φ 1 05

9 First step: The background D dt φ a 0 +3H φ a 0 + V a =0 DX a = dx a + Γ a bcx b dφ c φ 2 N a T a Real trayectory Flat valley φ 1 Tangent and normal vectors T a φ a 0 φ 0 N a γ bc DT b dt DT c dt 1/2 DT a dt 05

10 First step: The background D dt φ a 0 +3H φ a 0 + V a =0 DX a = dx a + Γ a bcx b dφ c φ 2 N a T a N a T a Real trayectory Flat valley φ 1 Tangent and normal vectors T a φ a 0 φ 0 N a γ bc DT b dt DT c dt 1/2 DT a dt 05

11 First step: The background D dt φ a 0 +3H φ a 0 + V a =0 DX a = dx a + Γ a bcx b dφ c φ 2 N a T a N a T a N a T a Real trayectory Flat valley φ 1 Tangent and normal vectors T a φ a 0 φ 0 N a γ bc DT b dt DT c dt 1/2 DT a dt 05

12 First step: The background Slow roll parameters: η a = η T a + η N a Ḣ H 2 η a 1 D φ a 0 H φ 0 dt η = φ 0 H φ 0 η = 2 M Pl κ V Groot Nibbelink & van Tent (2000) (Recall talk by Liam McAllister) Coupling condition Effects of size 4η 2 See our paper: Achucarro, et. al. (2010) H 2 M 2 φ 1 φ 2 06

13 First step: The background Slow roll parameters: η a = η T a + η N a Ḣ H 2 η a 1 D φ a 0 H φ 0 dt η = φ 0 H φ 0 η = 2 M Pl κ 1 V Groot Nibbelink & van Tent (2000) (Recall talk by Liam McAllister) Coupling condition Effects of size 4η 2 See our paper: Achucarro, et. al. (2010) H 2 M 2 φ 1 φ 2 06

14 Second step: Perturbations To make this discussion simple, I consider just two fields: δφ a (T,N) d 2 T dτ 2 + η τ d 2 N dτ 2 η τ dn dτ + dt dτ + k 2 2 τ 2 + δ τ 2 k 2 2 τ 2 + M 2 H 2 τ 2 T +2 η τ 2 N =0 N + η τ 2 T =0 07

15 Second step: Perturbations To make this discussion simple, I consider just two fields: δφ a (T,N) Tolley & Wayman (2010) Chen & Wang (2010) Cremonini, Lalak & Turzynski (2011) Baumann & Green (2011) d 2 T dτ 2 + η τ d 2 N dτ 2 η τ dn dτ + dt dτ + k 2 2 τ 2 + δ τ 2 k 2 2 τ 2 + M 2 H 2 τ 2 T +2 η τ 2 N =0 N + η τ 2 T =0 07

16 Second step: Perturbations To make this discussion simple, I consider just two fields: δφ a (T,N) d 2 T dτ 2 + η τ d 2 N dτ 2 η τ dn dτ + dt dτ + Flat direction (adiabatic mode) k 2 2 τ 2 + δ τ 2 k 2 2 τ 2 + M 2 H 2 τ 2 T +2 η τ 2 N =0 N + η τ 2 T =0 07

17 Second step: Perturbations To make this discussion simple, I consider just two fields: δφ a (T,N) Perpendicula direction (massive mode) d 2 T dτ 2 + η τ d 2 N dτ 2 η τ dn dτ + dt dτ + Flat direction (adiabatic mode) k 2 2 τ 2 + δ τ 2 k 2 2 τ 2 + M 2 H 2 τ 2 T +2 η τ 2 N =0 N + η τ 2 T =0 07

18 Second step: Perturbations To make this discussion simple, I consider just two fields: δφ a (T,N) Perpendicula direction (massive mode) d 2 T dτ 2 + η τ d 2 N dτ 2 η τ dn dτ + dt dτ + Flat direction (adiabatic mode) k 2 2 τ 2 + δ τ 2 k 2 2 τ 2 + M 2 H 2 τ 2 T +2 η τ 2 N =0 N + η τ 2 T =0 07

19 Second step: Perturbations To make this discussion simple, I consider just two fields: δφ a (T,N) Perpendicula direction (massive mode) d 2 T dτ 2 + η τ d 2 N dτ 2 η τ dn dτ + dt dτ + Flat direction (adiabatic mode) k 2 2 τ 2 + δ τ 2 k 2 2 τ 2 + M 2 H 2 τ 2 T +2 η τ 2 N =0 N + η τ 2 T =0 07

20 Second step: Perturbations To make this discussion simple, I consider just two fields: δφ a (T,N) Perpendicula direction (massive mode) d 2 T dτ 2 + η τ d 2 N dτ 2 η τ dn dτ + dt dτ + Flat direction (adiabatic mode) k 2 2 τ 2 + δ τ 2 k 2 2 τ 2 + M 2 H 2 τ 2 Not possible to truncate N =0 T +2 η τ 2 N =0 N + η τ 2 T =0 07

21 Artificial example To make this discussion simple, I consider just two fields: η (N) = η max cosh 2 [2(N N 0 )/ N] η N N 08

22 Features in the primordial spectrum P R (k) η (N) = η max cosh 2 [2(N N 0 )/ N] M 2 /H 2 = 300 N =1/4 η max =5 k Mpc 1 09

23 Features in the primordial spectrum P R (k) η (N) = η max cosh 2 [2(N N 0 )/ N] 4η2 maxh 2 M M 2 /H 2 = 300 N =1/4 η max =5 k Mpc 1 09

24 Features in the primordial spectrum P R (k) H N η (N) = η max cosh 2 [2(N N 0 )/ N] 4η2 maxh 2 M M 2 /H 2 = 300 N =1/4 η max =5 k Mpc 1 09

25 Features in the primordial spectrum P R (k) H N More realistic situations: Atal, Céspedes, Palma (2011) η (N) = η max cosh 2 [2(N N 0 )/ N] 4η2 maxh 2 M M 2 /H 2 = 300 N =1/4 η max =5 k Mpc 1 09

26 Features in the power spectrum? 1.5 P 0 k k Mpc 1 Tocchini-Valentini, Douspis & Silk (2004) For more recent discussions see: Hlozek et. al. (2011) Aich et. al. (2011) 10

27 Effective theory If the heavy field is very massive we can deduce a single field effective theory encapsulating the effects coming from turns S = 1 2 dτd 3 x dϕ 2 ϕ e β(τ, 2) ϕ ϕ Ω(τ, 2 )ϕ dτ e β(τ,k2) =1+ 4η 2 M 2 /H 2 2+ η 2 + k2 /(ah) 2 Ω(τ,k 2 ) = Ω 0 (τ) β 2 β 2 ahβ (1 + η ) Ω 0 (τ) = a 2 H 2 ( η 4η ξ η 2 2 ) 2 11

28 Effective theory If the heavy field is very massive we can deduce a single field effective theory encapsulating the effects coming from turns S = 1 2 dτd 3 x dϕ 2 ϕ e β(τ, 2) ϕ ϕ Ω(τ, 2 )ϕ dτ e β(τ,k2) =1+ 4η 2 M 2 /H 2 2+ η 2 + k2 /(ah) 2 Ω(τ,k 2 ) = Ω 0 (τ) β 2 β 2 ahβ (1 + η ) Ω 0 (τ) = a 2 H 2 ( η 4η ξ η 2 2 ) 2 11

29 Effective theory If the heavy field is very massive we can deduce a single field effective theory encapsulating the effects coming from turns S = 1 2 dτd 3 x dϕ 2 ϕ e β(τ, 2) ϕ ϕ Ω(τ, 2 )ϕ dτ e β(τ,k2) =1+ 4η 2 M 2 /H 2 2+ η 2 + k2 /(ah) 2 Ω(τ,k 2 ) = Ω 0 (τ) β 2 β 2 ahβ (1 + η ) Ω 0 (τ) = a 2 H 2 ( η 4η ξ η 2 2 ) 2 11

30 Effective theory If the heavy field is very massive we can deduce a single field effective theory encapsulating the effects coming from turns P R (k) Effective theory v/s full theory k Mpc 1 12

31 Non-Gaussianities If the heavy field is very massive we can deduce a single field effective theory encapsulating the effects coming from turns S = 1 2 dτd 3 x dϕ 2 ϕ e β(τ, 2) ϕ ϕ Ω(τ, 2 )ϕ dτ e β(τ,k2) =1+ 4η 2 M 2 /H 2 2+ η 2 + k2 /(ah) 2 c 2 s 1+ 4η2 M 2 /H 2 1 Generalisation of Tolley & Wyman (2010) See also: Cremonini, Lalak, Turzynski (2010) 13

32 Non-Gaussianities If the heavy field is very massive we can deduce a single field effective theory encapsulating the effects coming from turns S = 1 2 dτd 3 x dϕ 2 ϕ e β(τ, 2) ϕ ϕ Ω(τ, 2 )ϕ dτ e β(τ,k2) =1+ Non Gaussianities? 4η 2 M 2 /H 2 2+ η 2 + k2 /(ah) 2 c 2 s 1+ 4η2 M 2 /H 2 1 Generalisation of Tolley & Wyman (2010) See also: Cremonini, Lalak, Turzynski (2010) 13

33 Non-Gaussianities We find that the most relevant interaction term is of the form L 2 H2 4M Pl (3 +2η 2 )T 3 Squeezed shape for non-gaussianities f NL = 15 c 3 s η 2 (Preliminary!) k2/k1 Achúcarro et. al. (2011) 0.5 k3/k See also: Chen & Wang (2010); Baumann & Green (2011) 14

34 Non-Gaussianities We find that the most relevant interaction term is of the form L 2 H2 4M Pl (3 +2η 2 )T 3 Squeezed shape for non-gaussianities f NL = 15 c 3 s η 2 (Preliminary!) k2/k1 Achúcarro et. al. (2011) 0.5 k3/k See also: Chen & Wang (2010); Baumann & Green (2011) 14

35 Concluding remarks Features might offer a direct insight on heavy physics Heavy fields allow fast turns to happen under control Fast turns produce features in the primordial spectrum These features come together with particular non-gaussian signatures 15

36 Concluding remarks Features might offer a direct insight on heavy physics Why? Heavy fields allow fast turns to happen under control Fast turns produce features in the primordial spectrum These features come together with particular non-gaussian signatures 15

37 Concluding remarks Features might offer a direct insight on heavy physics Why? Heavy fields allow fast turns to happen under control And Fast turns produce features in the primordial spectrum These features come together with particular non-gaussian signatures 15

38 Concluding remarks Features might offer a direct insight on heavy physics Why? Heavy fields allow fast turns to happen under control And Fast turns produce features in the primordial spectrum Additionally These features come together with particular non-gaussian signatures 15