Resurrecting the Power-law, Intermediate, and Logamediate Inflations in the DBI Scenario with Constant Sound Speed

TL;DR

This paper explores various inflationary models within the DBI scalar field framework with constant sound speed, showing they can fit Planck 2015 data better than in the canonical case, and constrains sound speed and model parameters.

Contribution

It demonstrates that power-law, intermediate, and logamediate inflation models become compatible with observational data in the DBI scenario with subluminal sound speed, extending their viability beyond canonical predictions.

Findings

Models fit Planck 2015 data with c_s<1

Sound speed c_s constrained to be ≥0.087

Running of spectral index compatible with data

Abstract

We investigate the power-law, intermediate, and logamediate inflationary models in the framework of DBI non-canonical scalar field with constant sound speed. In the DBI setting, we first represent the power spectrum of both scalar density and tensor gravitational perturbations. Then, we derive different inflationary observables including the scalar spectral index $n_s$, the running of the scalar spectral index $dn_s/d\ln k$, and the tensor-to-scalar ratio $r$. We show that the 95\% CL constraint of the Planck 2015 T+E data on the non-Gaussianity parameter $f_{{\rm NL}}^{{\rm DBI}}$ leads to the sound speed bound $c_{s}\geq0.087$ in the DBI inflation. Moreover, our results imply that, although the predictions of the power-law, intermediate, and logamediate inflations in the standard canonical framework ($c_s=1$) are not consistent with the Planck 2015 data, in the DBI scenario with constant sound speed $c_s<1$, the result of the $r-n_s$ diagram for these models can lie inside the 68\% CL region favored by the Planck 2015 TT,TE,EE+lowP data. We also specify the parameter space of the power-law, intermediate, and logamediate inflations for which our models are compatible with the 68\% or 95\% CL regions of the Planck 2015 TT,TE,EE+lowP data. Using the allowed ranges of the parameter space of the intermediate and logamediate inflationary models, we estimate the running of the scalar spectral index and find that it is compatible with the 95\% CL constraint from the Planck 2015 TT,TE,EE+lowP data.