The intriguing question, why the present scale of the universe is free from any perceptible footprints of rank-2 antisymmetric tensor fields (generally known as Kalb-Ramond fields), is addressed. A quite natural explanation of this issue is given from the angle of higher-curvature gravity, both in four- and in five-dimensional spacetime. The results here obtained reveal that the amplitude of the Kalb-Ramond field may be actually large and play a significant role during the early universe, while the presence of higher-order gravity suppresses this field during the cosmological evolution, so that it eventually becomes negligible in the current universe. Besides the suppression of the Kalb-Ramond field, the extra degree of freedom in $F(R)$ gravity, usually known as scalaron, also turns out to be responsible for inflation. Such $F(R)$ gravity with Kalb-Ramond fields may govern the early universe to undergo an inflationary stage at early times (with the subsequent graceful exit) for a wider range of $F(R)$ gravity than without antisymmetric fields. Furthermore, the models—in four- and five-dimensional spacetimes—are linked to observational constraints, with the conclusion that the corresponding values of the spectral index and tensor-to-scalar ratio closely match the values provided by the Planck survey 2018 data.

• Received 7 November 2018

DOI:https://doi.org/10.1103/PhysRevD.99.063506