Antisymmetric Tensor Fields in Modified Gravity: A Summary

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/MPl (where MPl is known as the “reduced Planck mass” defined by MPl=18πG with G is the “Newton’s constant”) i.e., same as the usual gravity–matter coupling; however in the context of higher dimensional higher curvature model the KR couplings get an additional suppression over 1/MPl. Thus in comparison to the four dimensional model, the higher curvature braneworld scenario gives a better explanation of why the present universe carries practically no footprint of the Kalb–Ramond field. The higher curvature term in the higher dimensional gravitational 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 (with respect to the other components) 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. Finally, we briefly discuss some future perspectives of Kalb–Ramond cosmology at the end of the paper.

Inflation with an antisymmetric tensor field

“…This has motivated the exploration of alternative inflation models where the driving field is not a scalar. Several vector and tensor field models have been explored in the past [22][23][24][25][26][27][28][32][33][34][35]. Vector field models have been shown to suffer from generic ghost and gradient instabilities [28][29][30].…”

Torsion in string-inspired cosmologies and the universe dark sector

“…At this point we should also mention the so-called teleparallel theories of gravity [86][87][88][89][90], which, in contrast to the aforementioned contorted theories of gravity, in which both the metric and the torsion fields 4 For another model with dynamical, "running", dark energy, where the space-time is associated with a dynamical field (dynamical space time), and its phenomenological consequences, see [60,61]. 5 At this point we mention that there are several interesting works in the literature dealing with the rôle of string-inspired KR fields in cosmology, for instance, in the context of modified gravity models we refer the reader to the works in [69][70][71][72] for further details and comparison with our results reported in this review. For brane-world models, see, eg.…”

Inflation with antisymmetric tensor field: new candidates

“…This has motivated the exploration of alternative inflation models where the driving field is not a scalar. Several vector and tensor field models have been explored in the past [23][24][25][26][27][28][29][30][31][32][33]. Vector field models have been shown to suffer from generic ghost and gradient instabilities [32,34,35].…”