Strong scale dependent bispectrum in the Starobinsky model of inflation

TL;DR

This paper analytically calculates the dominant tree-level bispectrum in the Starobinsky inflation model, revealing scale-dependent behaviors with oscillations and amplitude growth on small scales, and decay on large scales.

Contribution

It provides the first analytical computation of the bispectrum in the Starobinsky model, highlighting its scale-dependent features and oscillatory behavior.

Findings

Bispectrum amplitude decays as (k/k_0)^2 on large scales.

Bispectrum oscillates with frequency 3/k_0 on small scales.

Amplitude of non-linearity parameter grows linearly on small scales.

Abstract

We compute analytically the dominant contribution to the tree-level bispectrum in the Starobinsky model of inflation. In this model, the potential is vacuum energy dominated but contains a subdominant linear term which changes the slope abruptly at a point. We show that on large scales compared with the transition scale $k_0$ and in the equilateral limit the analogue of the non-linearity parameter scales as $(k/k_0)^2$, that is its amplitude decays for larger and larger scales until it becomes subdominant with respect to the usual slow-roll suppressed corrections. On small scales we show that the non-linearity parameter oscillates with angular frequency given by $3/k_0$ and its amplitude grows linearly towards smaller scales and can be large depending on the model parameters. We also compare our results with previous results in the literature.