Antisymmetric tensor fields in modified gravity: a summary

TL;DR

This paper reviews the role of antisymmetric Kalb-Ramond fields in modified gravity, highlighting their significant impact on early universe inflation and gravitational waves, while diminishing in influence over cosmic evolution.

Contribution

It provides a comprehensive analysis of KR fields in various modified gravity models, including their couplings, effects on inflation, and potential observational signatures through quantum entanglement.

Findings

KR field energy density decreases faster than radiation and matter during expansion.

KR field influences early universe inflation and increases primordial gravitational radiation.

Higher-dimensional models suppress KR couplings, explaining their negligible present-day effects.

Abstract

We provide various aspects of second rank antisymmetric Kalb-Ramond (KR) field in modified theories of gravity. The KR field energy density is found to decrease with the expansion of our universe at a faster rate in comparison to radiation and matter components. Thus as the Universe evolves and cools down, the contribution of the KR field on the evolutionary process reduces significantly, and at present it almost does not affect the universe evolution. However the KR field has a significant contribution during early universe, in particular, it affects the beginning of inflation as well as increases the amount of primordial gravitational radiation and hence enlarges the value of tensor to scalar ratio in respect to the case when the KR field is absent. In regard to the KR field couplings, it turns out that in four dimensional higher curvature inflationary model the couplings of the KR field to other matter fields is given by $1/M_{Pl}$ i.e same as the usual gravity-matter coupling. However in higher dimensional higher curvature model the KR couplings get an additional suppression over $1/M_{Pl}$ and thus gives a better explanation of why the present universe carries practically no footprint of the Kalb-Ramond field in comparison to the 4D higher curvature model. The higher curvature term in 5D action acts as a suitable stabilizing agent in the dynamical stabilization mechanism of the extra dimensional modulus field from the perspective of effective on-brane theory. Based on the evolution of KR field, one intriguing question can be - sitting in present day universe, how do we confirm the existence of the Kalb-Ramond field which has considerably low energy density in our present universe but has a significant impact during early universe ? We try to answer this question by the phenomena "cosmological quantum entanglement" which indeed carries the information of early universe.