A possible testbed for warped extra dimension from the angle of Buchdahl's limit

We consider a five dimensional AdS warped spacetime in presence of a massive scalar field in the bulk. The scalar field potential fulfills the requirement of modulus stabilization even when the effect of backreaction of the stabilizing field is taken into account. In such a scenario, we investigate the possible role of modulus field on a compact stellar structure from the perspective of four dimensional effective theory. Our result reveals that in the presence of the modulus field, the upper bound of mass-radius ratio (generally known as Buchdahl's limit) of a star can go beyond the general relativity prediction. Interestingly this provides a natural testbed for the existence of such higher dimensional modulus field.Comment: 17 pages, 2 figure

Dynamical suppression of spacetime torsion

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 \cite{Planck}.Comment: EPJC accepte

Inflationary scenario from higher curvature warped spacetime

We consider a five dimensional AdS spacetime, in presence of higher curvature term like $F(R) = R + \alpha R^2$ in the bulk, in the context of Randall-Sundrum two-brane model. Our universe is identified with the TeV scale brane and emerges as a four dimensional effective theory. From the perspective of this effective theory, we examine the possibility of "inflationary scenario" by considering the on-brane metric ansatz as an FRW one. Our results reveal that the higher curvature term in the five dimensional bulk spacetime generates a potential term for the radion field. Due to the presence of radion potential, the very early universe undergoes a stage of accelerated expansion and moreover the accelerating period of the universe terminates in a finite time. We also find the spectral index of curvature perturbation ($n_s$) and tensor to scalar ratio ($r$) in the present context, which match with the observational results based on the observations of $Planck$ $2015$.Comment: 10 pages, 5 figures. arXiv admin note: text overlap with arXiv:1701.0157

Fermion localization in higher curvature and scalar-tensor theories of gravity

It is well known that in a braneworld model, the localization of fermions on lower dimensional submanifold (say a TeV 3-brane) is governed by the gravity in the bulk which also determines the corresponding phenomenology on the brane. Here we consider a five dimensional warped spacetime where the bulk geometry is governed by higher curvature like F(R) gravity. In such a scenario, we explore the role of higher curvature terms on the localization of bulk fermions which in turn determines the effective radion-fermion coupling on the brane. Our result reveals that for appropriate choices of the higher curvature parameter, the profiles of the massless chiral modes of the fermions may get localized near TeV brane while that for massive Kaluza-Klein (KK) fermions localize towards the Planck brane. We also explore these features in the dual scalar-tensor model by appropriate transformations. The localization property turns out to be identical in both the models. This rules out the possibility of any signature of massive KK fermions in TeV scale collider experiments due to higher curvature gravity effects.Comment: 24 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1704.0611

Various notions of best approximation property in spaces of Bochner integrable functions

We show that a separable proximinal subspace of X , say Y is strongly proximinal (strongly ball proximinal) if and only if L p ( I, Y ) is strongly proximinal (strongly ball proximinal) in L p ( I, X ), for 1 ≤ p < ∞ . The p = ∞ case requires a stronger assumption, that of ’uniform proximinality’. Further, we show that Y is ball proximinal in X if and only if L p ( I, Y ) is ball proximinal in L p ( I, X ) for 1 ≤ p ≤ ∞ . We develop the notion of ’uniform proximinality’ of a closed convex set in a Banach space, rectifying one that was defined in a recent paper by P.-K Lin et al. [J. Approx. Theory 183 (2014), 72–81]. We also provide several examples viz. any U -subspace of a Banach space has this property. Recall the notion of 3 . 2 .I.P. by Joram Lindenstrauss, a Banach space X is said to have 3 . 2 .I.P. if any three closed balls which are pairwise intersecting actually intersect in X . It is proved the closed unit ball B X of a space with 3 . 2 .I.P and closed unit ball of any M-ideal of a space with 3 . 2 .I.P. are uniformly proximinal. A new class of examples are given having this property

Antisymmetric tensor fields in modified gravity: a summary

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.Comment: Invited review paper from Symmetry for special issue Feature Papers 2020, Symmetry Accepte