Beta-function formalism for k-essence constant-roll inflation

TL;DR

This paper applies the beta-function formalism to analyze constant-roll inflation within k-essence models, simplifying the equations and exploring compatibility with observational data across different models.

Contribution

It introduces a first-order differential equation approach for constant-roll k-essence inflation, broadening the analysis to various cosmological models.

Findings

The second slow-roll parameter must be positive for small first slow-roll parameter.

Non-canonical and tachyon models do not match observational data.

DBI model can produce results consistent with observations.

Abstract

The beta function formalism is being used to study the constant-roll inflation in the k-essence model. Assuming the second slow-roll parameter as a constant leads to a first-order differential equation for $\beta$-function which is much easier to solve and find a solution than the second (non-linear) order equation that we have in corresponding standard constant-roll inflation. Many cosmological models are known as a subclass of k-essence, so we will try to consider the model as general as possible. It is determined that the second slow-roll parameter should be positive to produce a small value for the first slow-roll parameter. The scenario is considered for three well-known cosmological models, and it is clarified that for the non-canonical and tachyon model, the scalar spectral index never reaches the observational range, however for the DBI model, we could arrive at a result consistent with observational data.