Cosmological solution to the gravitational field equations in the generalized Randall-Sundrum model for an anisotropic brane with Bianchi I geometry and perfect fluid as matter sources has been considered. The matter on the brane is described by a tachyonic field. The solution admits inflationary era and at a later epoch the anisotropy of the universe washes out. We obtain two classes of cosmological scenario, in the first case universe evolves from singularity and in the second case universe expands without singularity.

It was first observed at the end of the last century that the universe is presently accelerating. Ever since, there have been several attempts to explain this observation theoretically. There are two possible approaches. The more conventional one is to modify the matter part of the Einstein Field Equations and the second one is to modify the geometry part. We shall consider two phenomenological models based on the former, more conventional approach within the context of General Relativity. The phenomenological models in this paper consider a Λ term as a function of a a and ρ where a and ρ are the scale factor and matter-energy density respectively. Constraining the free parameters of the models with latest observational data gives satisfactory values of parameters as considered by us initially. Without any field-theoretic interpretation, we explain the recent observations with a dynamical cosmological constant.

In this paper, we study anisotropic universes with Modified Chaplygin gas (MCG) in the context of Randall Sundrum-2 (RS2) braneworld model. The cosmological solutions for Kantowski–Sachs (KS) and Bianchi-I universes with MCG are obtained on the RS2 braneworld. The solutions are found to be dependent on MCG parameters but are modified from the GR solutions due to the braneworld correction term arising from high-energy effects. The anisotropy and deceleration parameters are obtained for each solution and the possibility of occurrence of future singularities is considered. Interestingly, we find that one drawback of the relativistic picture can be overcome in this model giving a universe close to the presently observed state.

In Einstein’s Field Equation (EFE), the geometry of the spacetime is connected with the matter distribution. The geometry or the gravitational sector deals with classical macroscopic objects involving gravitational units while the matter sector can be better described by quantum theory involving atomic units. It has been argued by Bisabr [ arXiv:gr-qc/1904.09336 ] that there exists an epoch-dependent conversion factor between these two unit systems present in two different conformal frames, i.e. the conformal factor is epoch-dependent. We argue that the conformal transformation (CT) is a dynamical degree of freedom describing it’s possible relevance in inflation in context to the graceful exit problem, dynamics of the cosmological constant [Formula: see text] and justify the argument in the light of consequences of Dirac’s Large Number hypothesis (LNH).