In this work we have investigated the dynamics of a recent modification to the general theory of relativity, the energy-momentum squared gravity model f (R, T 2 ), where R represents the scalar curvature and T 2 the square of the energy-momentum tensor. By using dynamical system analysis for various types of gravity functions f (R, T 2 ), we have studied the structure of the phase space and the physical implications of the energy-momentum squared coupling. In the first case of functional where f (R, T 2 ) = f0R n (T 2 ) m , with f0 constant, we have shown that the phase space structure has a reduced complexity, with a high sensitivity to the values of the m and n parameters. Depending on the values of the m and n parameters, the model exhibits various cosmological epochs, corresponding to matter eras, solutions associated to an accelerated expansion, or decelerated periods. The second model studied corresponds to the f (R, T 2 ) = αR n + β(T 2 ) m form with α, β constant parameters.In this case it is obtained a richer phase space structure which can recover different cosmological scenarios, associated to matter eras, de-Sitter solutions, and dark energy epochs. Hence, this model represent an interesting cosmological model which can explain the current evolution of the Universe and the emergence of the accelerated expansion as a geometrical consequence.The second approach aims at modifying the geometry of spacetime, i.e. the Einstein's gravity in the general theory of relativity (GR) at large distances, specifically beyond our Solar System to produce accelerating cosmological solutions [5][6][7]. This has given rise to the concept of "modified gravity". There are numerous such theories available in literature, such as Brans-Dicke theory [8], Einstein-Cartan theory [9], Brane gravity theory [10-13], Rosen's Bimetric theory of gravity [14][15][16], Kaluza-Klein theory [17][18][19][20][21], Hořava-Lifshitz theory [22,23], etc. Extensive reviews in modified gravity theories can be found in the Refs. [24,25]. All these have their own share of merits and de-merits. Many of the theories of modified gravity aims at modifying the linear function of scalar curvature, R responsible for the Einstein tensor in the Einstein equations of GR. So it is obvious that the alterations are brought about in such a way so as to generalize the gravitational Lagrangian which takes a special form L GR = R in case of GR. An extensively studied theory in this context is the f (R) gravity where the gravitational Lagrangian L GR = R is replaced by an analytic function of R, i.e., L f (R) = f (R). Via this generalization, we can explore the non-linear effects of the scalar curvature R in the evolution of the universe by choosing a suitable function for f (R). Extensive reviews on this theory is available in the Refs. [26,27].The cosmological viability of f (R) dark energy models have been studied in [28]. In this paper the authors ruled out the f (R) theories where a power of R is dominant at large or small R. Conditions for the cosmological via...

Within this work, we propose a new generalised quintom dark energy model in the teleparallel alternative of general relativity theory, by considering a non-minimal coupling between the scalar fields of a quintom model with the scalar torsion component T and the boundary term B. In the teleparallel alternative of general relativity theory, the boundary term represents the divergence of the torsion vector, B = 2∇µT µ , and is related to the Ricci scalar R and the torsion scalar T , by the fundamental relation: R = −T + B. We have investigated the dynamical properties of the present quintom scenario in the teleparallel alternative of general relativity theory by performing a dynamical system analysis in the case of decomposable exponential potentials. The study analysed the structure of the phase space, revealing the fundamental dynamical effects of the scalar torsion and boundary couplings in the case of a more general quintom scenario. Additionally, a numerical approach to the model is presented to analyse the cosmological evolution of the system.

In this work, we have assumed the generalized Vaidya solution in Lovelock theory of gravity in (n + 2)-dimensions. It has been shown that Gauss-Bonnet gravity, dimensionally continued Lovelock gravity and pure Lovelock gravity can be constructed by suitable choice of parameters. We have investigated the occurrence of singularities formed by the gravitational collapse in above three particular forms of Lovelock theory of gravity. The dependence of the nature of singularity on the existence of radial null geodesic for Vaidya space-time has been specially considered. In all the three models, we have shown that the nature of singularities (naked singularity or black hole) completely depend on the parameters. Choices of various parameters are shown in tabular form. In Gauss-Bonnet gravity theory, it can be concluded that the possibility of naked singularity increases with increase in dimensions. In dimensionally continued Lovelock gravity, the naked singularity is possible for odd dimensions for several values of parameters. In pure Lovelock gravity, only black hole forms due to the gravitational collapse for any values of parameters. It has been shown that when accretion is taking place on a collapsing object, it is highly unlikely to get a black hole. Finally on considering the phantom era in the expanding P. Rudra · U. Debnath ( ) universe it is observed that there is no possibility of formation of a black hole if we are in the Gauss-Bonnet gravity considering the accreting procedure upon a collapsing object.

In this work we investigate the background dynamics when dark energy is coupled to dark matter with a suitable interaction in the universe described by brane cosmology. Here DGP and the RSII brane models have been considered separately. Dark energy in the form of modified Chaplygin gas is considered. A suitable interaction between dark energy and dark matter is considered in order to at least alleviate (if not solve) the cosmic coincidence problem. The dynamical system of equations is solved numerically and a stable scaling solution is obtained. A significant attempt towards the solution of the cosmic coincidence problem is taken. The statefinder parameters are also calculated to classify the dark energy models. Graphs and phase diagrams are drawn to study the variations of these parameters. It is also seen that the background dynamics of modified Chaplygin gas is completely consistent with the notion of an accelerated expansion in the late universe. Finally, it has been shown that the universe in both the models follows the power law form of expansion around the critical point, which is consistent with the known results.

In this paper, we analyze Vaidya spacetime with an energy dependent metric in Galileon gravity's rainbow. This will be done using the rainbow functions which are motivated from the results obtained in loop quantum gravity approach and noncommutative geometry. We will investigate the Gravitational collapse in this Galileon gravity's rainbow. We will discuss the behavior of singularities formed from the gravitational collapse in this rainbow deformed Galileon