Logarithmic-corrected $R^2$ Gravity Inflation in the Presence of Kalb-Ramond Fields

TL;DR

This paper investigates how a Kalb-Ramond field influences inflation in a logarithmic corrected $R^2$ gravity model, showing it can enhance gravitational wave predictions while remaining consistent with observations.

Contribution

It demonstrates that the Kalb-Ramond field, modeled as a scalar during inflation, affects inflationary parameters and can improve compatibility with observational data in $F(R)$ gravity.

Findings

Kalb-Ramond field increases primordial gravitational waves.

Model remains compatible with observational data.

The field's effects diminish as the universe expands.

Abstract

In this paper we shall study the inflationary aspects of a logarithmic corrected $R^2$ Starobinsky inflation model, in the presence of a Kalb-Ramond field in the gravitational action of $F(R)$ gravity. Our main interest is to pin down the effect of this rank two antisymmetric tensor field on the inflationary phenomenology of the $F(R)$ gravity theory at hand. The effects of the Kalb-Ramond field are expected to be strong during the inflationary era, however as the Universe expands, the energy density of the Kalb-Ramond field scales as $\sim a^{-6}$ so dark matter and radiation dominate over the Kalb-Ramond field effects. In general, antisymmetric fields constitute the field content of superstring theories, and thus their effect at the low-energy limit of the theory is expected to be significant. As we will show, for a flat Friedmann-Robertson-Walker metric, the Kalb-Ramond field actually reduces to a scalar field, so it is feasible to calculate the observational indices of inflation. We shall calculate the spectral index and the tensor-to-scalar ratio for the model at hand, by assuming two conditions for the resulting Kalb-Ramond scalar field, the slow-roll and the constant-roll condition. As we shall demonstrate, in both the slow-roll and constant-roll cases, compatibility with the latest observational data can be achieved. Also the effect of the Kalb-Ramond field on the inflationary phenomenology is to increase the amount of the predicted primordial gravitational radiation, in comparison to the corresponding $f(R)$ gravities, however the results are still compatible with the observational data.