Effective field equation on m-brane embedded in n-dimensional bulk of Einstein and f(R) gravity

We have derived effective gravitational field equations on a lower dimensional hypersurface (known as a brane), placed in a higher dimensional bulk spacetime for both Einstein and $f(\mathcal{R})$ gravity theories. We have started our analysis on $n$-dimensional bulk from which the effective field equations on a $(n-1)$-dimensional brane has been obtained by imposing $Z_{2}$ symmetry. Subsequently, we have arrived at the effective equations in $(n-2)$-dimensions starting from the effective equations for $(n-1)$ dimensional brane. This analysis has been carried forward and is used to obtain the effective field equations in $(n-m)$-dimensional brane, embedded in a $n$-dimensional bulk. Having obtained the effective field equations in Einstein gravity, we have subsequently generalized the effective field equation in $(n-m)$-dimensional brane which is embedded the $n$-dimensional bulk spacetime endowed with $f(\mathcal{R})$ gravity. We have also presented applications of our results in the context of Einstein and $f(\mathcal{R})$ gravity. In both the cases we have discussed vacuum static spherically symmetric solutions as well as solutions in cosmological context. Implications are also discussed.Comment: v2, Revised, Accepted in EPJC, 35 pages, no figure

Kinematics of Radion field: A possible source of dark matter

The discrepancy between observed virial and baryonic mass in galaxy clusters have lead to the missing mass problem. To resolve this, a new, non-baryonic matter field, known as dark matter has been invoked. However, till date no possible constituents of the dark matter components are known. This has led to various models, by modifying gravity at large distances to explain the missing mass problem. The modification to gravity appears very naturally when effective field theory on a lower dimensional manifold, embedded in a higher dimensional spacetime is considered. It has been shown that in a scenario with two lower dimensional manifolds separated by a finite distance is capable to address the missing mass problem, which in turn determines the kinematics of the brane separation. Consequences for galactic rotation curves are also described.Comment: Title changed, revised, 25 pages, 4 figure

Lightest Kaluza-Klein graviton mode in a backreacted Randall-Sundrum scenario

In search of extra dimensions in the ongoing LHC experiments, signatures of Randall-Sundrum (RS) lightest KK graviton have been one of the main focus in recent years. The recent data from the dilepton decay channel at the LHC has determined the experimental lower bound on the mass of the RS lightest Kaluza-Klein (KK) graviton for different choices of underlying parameters of the theory. In this work we explore the effects of the backreaction of the bulk scalar field, which is employed to stabilise the RS model, in modifying the couplings of the lightest KK graviton with the standard model (SM) matter fields located on the visible brane. In such a modified background geometry we show that the coupling of the lightest KK graviton with the SM matter fields gets a significant suppression due to the inclusion of the backreaction of the bulk stabilising scalar field. This implies that the backreaction parameter weakens the signals from RS scenario in collider experiments which in turn explains the non-visibility of KK graviton in colliders. Thus we show that the modulus stabilisation plays a crucial role in the search of warped extra dimensions in collider experiments.Comment: 12 pages, 1 figur

Modulus stabilization in a non-flat warped braneworld scenario

The stability of the modular field in a warped brane world scenario has been a subject of interest for a long time. Goldberger \& Wise ( GW ) proposed a mechanism to achieve this by invoking a massive scalar field in the bulk space-time neglecting the back-reaction. In this work, we examine the possibility of stabilizing the modulus without bringing in any external scalar field. We show that instead of flat 3-branes as considered in Randall-Sundrum ( RS ) warped braneworld model, if one considers a more generalized version of warped geometry with de-Sitter 3-brane, then the brane vacuum energy automatically leads to a modulus potential with a metastable minimum. Our result further reveals that in this scenario the gauge hierarchy problem can also be resolved for appropriate choice of brane cosmological constant.Comment: 8 pages, 4 figure

A step towards exploring the features of Gravidilaton sector in Randall-Sundrum scenario via lightest Kaluza-Klein graviton mass

In this paper we study the role of the 5D Gauss-Bonnet corrections and two loop higher genus contribution to the gravity action in type IIB string theory inspired low energy supergravity theory in the light of gravidilatonic interactions on the lightest Kaluza-Klein graviton mass spectrum. From the latest constraints on the lightest Kaluza-Klein graviton mass as obtained from the ATLAS dilepton search in 7 TeV proton-proton collision, we have shown that due to the presence of Gauss-Bonnet and string loop corrections, the warping solution in an ${\bf AdS_{5}}$ bulk is quite distinct from Randall-Sundrum scenario. We discuss the constraints on the model parameters to fit with present ATLAS data.Comment: 11 pages, 4 figures, Revision accepted by European Physical Journal