In the context of the Randall-Sundrum braneworld, the minimal geometric deformation approach (MGD) is used to generate a new physically acceptable interior solution to Einstein's field equations for a spherically symmetric compact distribution. This new solution is used to elucidate the role of exterior Weyl stresses from bulk gravitons on compact stellar distributions. We found strong evidences showing that the exterior dark radiation U + always increases both the pressure and the compactness of stellar structures, and that the exterior "dark pressure" P + always reduces them. 1 theory like never before, but also leaves GR as the only reliable gravitational theory to be used in the analysis of phenomena occurred in the strong field regime. Likewise, the ability of observing increasingly distant objects deep in the universe, and thus with a great gravitational red shift, leads inevitably to the conclusion that only using GR we can obtain an adequate analysis of these phenomena [3], [4]. Furthemore, with the recent results shown by PLANCK [5], which improve greatly the previous by WMAP [6], we can assure that the cosmological models based in GR enjoys a well-deserved and well-earned prestige.Despite the above facts, there are some fundamental questions associated to the gravitational interaction which GR cannot answer satisfatory. This can be broadly grouped in two fundamental issues, which most likely are closely related: 1) The inability of GR to explain satisfactorily the dark matter [7] and dark energy problem without the need of introducing some kind of unknown matter-energy to reconcile what predicts GR with the observed, namely, galactic rotation curves and accelerated expansion of the universe. 2) The impossibility, so far, to reconcile GR with the Standard Model of particle physics, or equivalently, the inability to quantize GR. This has strongly motivated the searching of a gravitational theory beyond GR that helps to explain satisfactorily part of the problems described above. If the new theory is a consistent quantum theory, this should lead to a generalization of GR at low energy, being likely this extension of GR at low energy which could accounts for the dark matter and dark energy problems. If the new theory is not a consistent quantum theory for gravity, this should also contain GR in a suitable limit, and somehow show greater tolerance to its quantum description.Extra-dimensional theories, which are mostly inspired by String/M-theory, are among the theories that lead to modifications to GR. One of these extra-dimensional theories is the Braneworld (BW) proposed by Randall and Sundrum (RS) [8] which has been largely studied and which explains, so pretty straightforward, one of the fundamental problems of Physics, i.e. the hierarchy problem (see also the ADD model [9] and [10]). This theory reduces the fundamental scale to the weak scale by considering extra-dimensional effects, thus explaining the weakness of gravity relative to the other forces. Because of this, its study and impact on GR is full...

In this paper, we study two different models of dark energy based on the Chaplygin gas equation of state. The first model is the variable modified Chaplygin gas, while the second one is the extended Chaplygin gas. Both models are considered in the framework of higher order f (R) modified gravity. We also consider the case of time-varying gravitational constant G and for both models. We investigate some cosmological parameters such as the Hubble, the deceleration, and the equation of state parameters. Then we show that the model that we consider, the extended Chaplygin gas with time-dependent G and , is consistent with the observational data. Finally we conclude with the discussion of cosmological perturbations of our model.

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Among different candidates to play the role of Dark Energy (DE), modified gravity has emerged as offering a possible unification of Dark Matter (DM) and DE. The purpose of this work is to develop a reconstruction scheme for the modified gravity with f (T ) action using holographic energy density. In the framework of the said modified gravity we have considered the equation of state of the Holographic DE (HDE) density. Subsequently we have developed a reconstruction scheme for modified gravity with f (T ) action. Finally we have obtained a modified gravity action consistent with the HDE scenario. PACS numbers: 98.80.-k, 95.36.+x, 04.50.Kd I. INTRODUCTION Cosmological observations obtained with Supernovae Ia (SNeIa), the Cosmic Microwave Background (CMB) radiation anisotropies, the Large Scale Structure (LSS) and X-ray experiments have well established the accelerated expansion of our universe [1-7]. A missing energy component also known as Dark Energy (DE) with negative pressure is widely considered by scientists as responsible of this accelerated expansion. Recent analysis of cosmological observations indicates that the two-thirds of the total energy of the universe is been occupied by the DE whereas DM occupies almost the remaining part (the baryonic matter represents only a few percent of the total energy density of the universe) [8]. The contribution of the radiation is practically negligible.The nature of DE is still unknown and many candidates have been proposed in order to describe it [9][10][11][12][13][14][15][16]. The simplest one is represented by a tiny positive cosmological constant, with a negative constant equation of state (EoS) parameter ω, i.e. ω = −1. However, cosmologists know that the cosmological constant suffers from two well-known difficulties, the fine-tuning and the cosmic coincidence problems: the former asks why the vacuum energy density is so small (of the order of * Electronic address: surajit˙2008@yahoo.co.in, surajcha@iucaa.ernet.in † Electronic address: toto.pasqua@gmail.com

Motivated by the holographic principle, it has been suggested that the dark energy density may be inversely proportional to the area A of the event horizon of the universe. However, such a model would have a causality problem. In this work, we consider the entropy-corrected version of the holographic dark energy model in the non-flat FRW universe and we propose to replace the future event horizon area with the inverse of the Ricci scalar curvature. We obtain the equation of state (EoS) parameter ω , the deceleration parameter q and D in the presence of inter-A. Pasqua action between Dark Energy (DE) and Dark Matter (DM). Moreover, we reconstruct the potential and the dynamics of the tachyon, K-essence, dilaton and quintessence scalar field models according to the evolutionary behavior of the interacting entropy-corrected holographic dark energy model.