Dynamics of Cosmological Perturbations in Multi-Speed Inflation

TL;DR

This paper investigates multi-field inflation with different sound speeds, showing how weak coupling allows for decoupled mode analysis and revealing how sound speed ratios influence the power spectrum, including amplification effects.

Contribution

It introduces a method to analyze multi-speed inflation with weakly coupled fields using decoupled normal modes and calculates the resulting power spectrum with explicit dependence on sound speed ratios.

Findings

Fields are coupled gravitationally but can be approximated as decoupled modes under weak coupling.

The curvature perturbation can be computed using the $ abla$ formalism up to leading slow variation order.

Power spectrum shows amplification when sound speed ratios deviate from unity.

Abstract

We study a multi-field inflationary theory with separable Lagrangian, which has different speed of sound for each field. We find that the fields always coupled at perturbative level through gravitational interaction. We show that if the coupling terms among the perturbation fields are weak enough, these fields can be treated as a combination of decoupled fields, which are similar to normal modes in coupled oscillation. By virtue of such fields, the curvature perturbation at the horizon-crossing can be calculated up to the leading order of slow variation parameters via $\delta \mathcal{N}$ formalism. Explicitly, we consider a model of multi-speed DBI inflation, and calculate the power spectrum in detail. The result depends on the ratio of different speeds of sound, and shows an apparent amplification when the ratio deviates from unity.