Springer : Model-independent approach to effective sound speed in multi-field inflation

Romano, Antonio Enea; Turzyński, Krzysztof; Vallejo-Peña, Sergio Andrés

doi:10.1140/epjc/s10052-022-10669-3

Article
Report number	arXiv:2006.00969
Title	Model-independent approach to effective sound speed in multi-field inflation
Related title	The momentum-dependent effective sound speed and multi-field inflation
Author(s)	Romano, Antonio Enea (CERN ; ICRA, Pescara ; Antioquia U.) ; Vallejo-Peña, Sergio Andrés (ICRA, Pescara ; Antioquia U.) ; Turzyński, Krzysztof (Warsaw U.)
Publication	2022-08-30
Imprint	2020-05-29
Number of pages	16
In:	Eur. Phys. J. C 82 (2022) 767
DOI	10.1140/epjc/s10052-022-10669-3
Subject category	hep-th ; Particle Physics - Theory ; astro-ph.CO ; Astrophysics and Astronomy ; gr-qc ; General Relativity and Cosmology
Abstract	For any physical system satisfying the Einstein's equations, the comoving curvature perturbations satisfy an equation involving the momentum-dependent effective sound speed, valid for any system with a well defined energy-stress tensor, including multi-fields models of inflation. We derive a general model-independent formula for the effective sound speed of comoving adiabatic perturbations, valid for a generic field-space metric, without assuming any approximation to integrate out entropy perturbations, but expressing the momentum-dependent effective sound speed in terms of the components of the total energy-stress tensor. As an application, we study a number of two-field models with a kinetic coupling between the fields, identifying the single curvature mode of the effective theory and showing that momentum-dependent effective sound speed fully accounts for the predictions for the power spectrum of curvature perturbations. Our results show that the momentum-dependent effective sound speed is a convenient scheme for describing all inflationary models that admit a single-field effective theory, including the effects of entropy perturbations present in multi-fields systems.
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0) publication: © 2022-2025 The Author(s) (License: CC-BY-4.0), sponsored by SCOAP³

$Evolutions of the amplitude of curvature perturbation $\R$ given in eq.~(\ref{eq:Rsol}) for different sound speeds $\tilde{v}_k^2\propto a^p$ with different values of $p$ is shown as thick lines. Color coding corresponds to late-time behavior: freezing (red), decaying (blue) and growing (black); the special case of $p=4$ is shown in green. Thin green lines indicate the real and imaginary part of of $\R$ for $p=4$. Normalization of $\R$ is arbitrary.$ $Numerical calculations in single-field effective theories with constant reduced sound speed; model described in Section~\ref{sec:ss-1}. Left panel: evolution of the sound speed given by eq.~(\ref{ck}) for initial conditions leading to a freezing adiabatic mode (red solid line) and for initial conditions leading to a decaying adiabatic mode (blue dashed lines); thin dashed line corresponds to the value (\ref{eq:vsgel2a}). Right panel: evolution of the instantaneous power spectra in the full theory and in the effective theory; color coding described in Table~\ref{tab1}; thin dashed line corresponds to the asymptotic value (\ref{eq:ppsf1}). $N=0$ corresponds to the Hubble radius crossing$ $Enhancement of the power spectrum of curvature perturbations predicted by eq.~(\ref{eq:enhf}).$ Show more plots

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Element opprettet 2020-07-01, sist endret 2024-03-08

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