Abstract
A surprising feature of our present four dimensional universe is that its evolution appears to be governed solely by spacetime curvature without any noticeable effect of spacetime torsion. In the present paper, we give a possible explanation of this enigma through “cosmological evolution” of spacetime torsion in the backdrop of a higher dimensional braneworld scenario. Our results reveal that the torsion field may had a significant value at early phase of our universe, but gradually decreased with the expansion of the universe. This leads to a negligible footprint of torsion in our present visible universe. We also show that at an early epoch, when the amplitude of the torsion field was not suppressed, our universe underwent through an inflationary stage having a graceful exit within a finite time. To link the model with observational constraints, we also determine the spectral index for curvature perturbation (n_s) and tensor to scalar ratio (r) in the present context, which match with the results of Planck 2018 (combining with BICEP-2 Keck-Array) data (Akrami et al. in arXiv:1807.06211 [astro-ph.CO], 2019; Ade et al. in Phys Rev Lett 116:031302 https://doi.org/10.1103/PhysRevLett.116.031302, arXiv:1510.09217 [astro-ph.CO], 2016).
Highlights
A surprising feature of the present universe is that its large scale behaviour appears to be controlled by one type of geometrical deformation only, namely curvature; while we notice practically no effect of another type of deformation, namely torsion
It has been already shown that a rank-2 antisymmetric tensor field, generally known as Kalb–Ramond (KR) field (BM N ), can act as a source of spacetime torsion where the torsion is identified with rank-3 antisymmetric field strength tensor HM N L having a relation
We consider a five dimensional braneworld model with spacetime torsion caused by a rank-2 antisymmetric Kalb– Ramond (KR) field in the bulk
Summary
A surprising feature of the present universe is that its large scale behaviour appears to be controlled by one type of geometrical deformation only, namely curvature; while we notice practically no effect of another type of deformation, namely torsion. There is a recent work on spacetime torsion with antisymmetric tensor fields in higher curvature gravity model in the context of both four dimensional and five dimensional spacetime [26], where the authors showed that due to the effect of higher curvature term(s), the amplitude of torsion field gets suppressed in the course of the universe evolution. One of our authors showed earlier that the amplitude of KR field may be significant and can play a relevant role in the early phase of the universe This motivates to explore whether the “dynamical evolution” of KR field (from early universe) leads to a negligible footprint of torsion on the present universe in the backdrop of braneworld scenario. Their implications and possible consequences are discussed in the remaining part of the paper
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