Running of the Running and Entropy Perturbations During Inflation

TL;DR

This paper investigates how two-field inflation models with isocurvature to curvature mode transfer can produce larger and positive running of the running, challenging standard single-field slow-roll expectations.

Contribution

It explores the potential of two-field inflation models to generate a hierarchy of spectral runnings, especially positive and larger 2s, by analyzing isocurvature to curvature transfer effects.

Findings

Two-field models can produce positive 2s larger than 1s.

Transfer of power from isocurvature to curvature modes broadens phenomenological possibilities.

Standard single-field slow-roll models are less capable of achieving such runnings.

Abstract

In single field slow-roll inflation, one expects that the spectral index $n_s -1$ is first order in slow-roll parameters. Similarly, its running $\alpha_s = dn_s/d \log k$ and the running of the running $\beta_s = d\alpha_s/d \log k$ are second and third order and therefore expected to be progressively smaller, and usually negative. Hence, such models of inflation are in considerable tension with a recent analysis hinting that $\beta_s$ may actually be positive, and larger than $\alpha_s$. Motivated by this, in this work we ask the question of what kinds of inflationary models may be useful in achieving such a hierarchy of runnings, particularly focusing on two--field models of inflation in which the late-time transfer of power from isocurvature to curvature modes allows for a much more diverse range of phenomenology. We calculate the runnings due to this effect and briefly apply our results to assessing the feasibility of finding $|\beta_s| \gtrsim |\alpha_s|$ in some specific models.