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The time equation associated to the Dirac Equation (DE) is studied for the radiation-dominated Friedmann-Robertson-Walker (FRW) universe. The results are analysed for small and large values of time. We also incorporate the corrections of…
In this manuscript we investigate the intrinsically flat (space-flat) spacetimes as viable cosmological models. We show that they have a natural geometric structure which is suitable to describe inhomogeneous matter distributions forming a…
In this work we compile a few differential equations (ODEs) that arise from the relativistic equations in cosmological models that consider the ``constants'' as scalars functions dependent on time and they are described as perfect as well…
We discuss the effects of a (possibly) negative $(1+z)^6$ type contribution to the Friedmann equation. No definite answer can be given as to the presence and magnitude of a particular mechanism, because any test using the general relation…
Extending the approach developed by Ara\'ujo and Stoeger [1] and improved in Ara\'ujo {\it et al} [2], we have shown how to construct dust-filled $\Lambda \neq 0$ Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) cosmological models from FLRW…
A solution of codimension 2 brane is found for which 4 dimensional Friedmann cosmology is recovered on the brane with time dependent tension, in the Einstein frame. The effective parameter $p/\rho$ of equation of state on the brane can be…
We present a regular cubic lattice solution to Einstein field equations that is exact at second order in a small parameter. We show that this solution is kinematically equivalent to the Friedmann-Lema\^itre-Robertson-Walker (FLRW) solution…
In what follows, we investigate the relation between the Friedmann and thermodynamic pressure equations, through solving the Friedmann and thermodynamic pressure equations simultaneously. Our investigation shows that a perfect fluid, as a…
We investigate the conformal geometry of spherically symmetric spacetimes in general without specifying the form of the matter distribution. The general conformal Killing symmetry is obtained subject to a number of integrability conditions.…
We show that any measurable solution of the cohomological equation for a H\"older linear cocycle over a hyperbolic system coincides almost everywhere with a H\"older solution. More generally, we show that every measurable invariant…
In the macroscopic gravity approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We present exact cosmological solutions to the…
The evolution of spatially homogeneous and isotropic cosmological models containing a perfect fluid with equation of state p=w\rho\ and a cosmological constant \Lambda\ is investigated for arbitrary combinations of w and \Lambda, using…
We consider four dimensional heterotic string backgrounds for which supersymmetry is spontaneously broken via the Scherk-Schwarz mechanism on an internal spatial cycle and by finite temperature effects. We concentrate on initially flat…
Recent works by the second author and Maxwell et al. have shown that the Einstein-scalar field conformal constraint equations are highly complex and generally intractable, even in the vacuum case. In this article, to gain a clearer…
In this work we extend the first order formalism for cosmological models that present an interaction between a fermionic and a scalar field. Cosmological exact solutions describing universes filled with interacting dark energy and dark…
The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of…
This work examines a relativistic model for the observed inhomogeneities of the large scale structure where the hypothesis that this structure can be described as being a self-similar fractal system is advanced. The concept of hierarchical…
The approximate homogeneity of spatial sections of the Universe is well supported observationally, but the inhomogeneity of the spatial sections is even better supported. Here, we consider the implications of inhomogeneity in dust models…
A quantum-field model of the conformally flat space is formulated using a standard field-theoretical technique, a probability interpretation and a way to establish the classical limit. The starting point is the following: after conformal…
In this {\sl Letter} we construct the Hubble diagram (HD) for the standard Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmological model after enforcing it with the general relativistic energy conditions, heeding to investigate whether it…