Strongly coupled perturba1ons in two- field infla1onary models

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1 Strongly coupled perturba1ons in two- field infla1onary models Krzysztof Turzyński Department of Physics, University of Warsaw with Sera Cremonini (Texas A&M and Cambridge) and Zygmunt Lalak (Warsaw)

2 Introduc1on On super- Hubble scales, along a turn in the infla1onary trajectory, there is a coupling between the adiaba)c and entropy modes and the la0er can source the former. Hubble radius crossing Gordon et al, 2000 instantaneous entropy (isocurvature) perturba1on instantaneous adiaba1c (curvature) perturba1on

3 Introduc1on Hubble radius crossing e.g. Groot Nibbelink & Van Tent 2000, 2001, DiMarco & Finelli, 2005, Peterson & Tegmark 2010, Achucarro et al On super- Hubble scales, when the infla1onary trajectory turns away from geodesic lines in the field space, there is a coupling between the adiaba)c and entropy modes and the la0er can source the former. instantaneous entropy (isocurvature) perturba1on instantaneous adiaba1c (curvature) perturba1on

4 Quasi- single field infla1on geodesic lines infla1onary trajectory weak coupling Chen & Wang, 2009 θ/h

5 Quasi- single field infla1on geodesic lines infla1onary trajectory b(φ) φ weak coupling Chen & Wang, 2009 θ/h possibility of a strong coupling 1 M 2 P b 2 e.g. roule_e infla1on, Bond et al applica1on with a weak coupling Cremonini, Lalak & KT, 2010

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7 Quasi- single field infla1on Toy model b(φ) = φ/m, M M P 2 φ φ0 V (φ, χ) =V 0 1+α + β χ M P M P small, slow- roll =2β 2 large, m H or η ss = m 2 /3H 2 1 b(φ) φ EOMs for perturba1ons solve semi- analy1cally (alas, no 1me) solve numerically Lalak, Langlois, Pokorski & KT, 2007 possibility of a strong coupling 1 M 2 P b 2 e.g. roule_e infla1on, Bond et al. 2006

8 Quasi- single field infla1on Toy model b(φ) = φ/m, M M P 2 φ φ0 V (φ, χ) =V 0 1+α + β χ Homogeneous EOMs M P φ +3H φ + V φ b e 2b χ 2 =0, χ +3H χ +2b φ χ + e 2b V χ =0 M P b(φ) φ possibility of a strong coupling 1 M 2 P b 2 e.g. roule_e infla1on, Bond et al. 2006

9 Quasi- single field infla1on Toy model b(φ) = φ/m, M M P 2 φ φ0 V (φ, χ) =V 0 1+α + β χ M P M P parameters ξ, m /H Homogeneous EOMs φ +3H φ + V φ b e 2b χ 2 =0, χ +3H χ +2b φ χ + e 2b V χ =0 EOMs for perturba1ons d 2 dτ 2 + k ξ τ 2 + τ 2ξ solve semi- analy1cally (alas, no 1me) solve numerically Lalak, Langlois, Pokorski & KT, 2007 τ 0 d 0 4ξ dτ + τ 2 2ξ 1 m 2 τ 2 τ 2 H 2 possibility of a strong coupling 1 M 2 P b 2 b(φ) φ ucur u iso =0 e.g. roule_e infla1on, Bond et al M 2 P b 2 ξ 2

10 Quasi- single field infla1on Later development For k τ < ξ and m ξh curvature perturba1ons described by an effec1ve theory with a single degree of freedom and a modified dispersion rela1on. ω 2 = m2 4ξ 2 H 2 k2 ph + 1 4ξ 2 H 2 k4 ph Baumann & Green, 2011; first term: Tolley & Wyman, 2009, Achucarro et al, 2010 see also: Ashoorioon et al parameters ξ, m /H b(φ) φ possibility of a strong coupling 1 M 2 P b 2 e.g. roule_e infla1on, Bond et al M 2 P b 2 ξ 2

11 ξ = 300, m 2 = 5000H 2 Perturba1ons evolve without feeling space1me curvature or mass k τ = ξ Perturba1ons below 1 st mass threshold: decay faster by a 1/2 k τ = m /H Perturba1ons below 2 nd mass threshold: only curvature perturba1ons survive k τ =1/c s Curvature perturba1ons freeze in P R P sf A C B single- field infla1on, c s = curvature perturba1ons single- field infla1on, c s <1 isocurvature perturba1ons N

12 ξ = 300, m 2 0 Perturba1ons evolve without feeling space1me curvature or mass k τ = ξ Perturba1ons below 1 st mass threshold: decay faster by a 1/2 P R P sf A C π σ model of Baumann & Green, 2011 single- field infla1on, c s = k τ = ξ 10 2 curvature perturba1ons 10 2 Curvature perturba1ons freeze in N isocurvature perturba1ons

13 Conclusions 1. Simple super- Hubble evolu1on (curvature perturba1ons frozen in, isocurvature perturba1ons decay) preceded by a non- trivial behavior within the Hubble radius 2. Effec1ve theory (with a heavy [?] field integrated out) correctly describes the late 1me dynamics and in some cases the amplitudes of the perturba1ons (accidental?) 3. [not shown] For some parameter choices the modes experience a transient tachyonic instability at the Hubble radius crossing amplifica1on of the curvature perturba1ons