No abstract

Unimodular gravity provides a theoretical framework that allows for non-conservation of energy-momentum, with possible implications for the cosmological constant problem. It is then important to study the predictions of unimodular gravity in other gravitational regimes. In this work we study stellar dynamics under the assumption of non-conserved energymomentum. We find that constant density objects can be as compact as Schwarzschild black holes. For polytropic objects, we find modifications due to the non-conservation of energy-momentum that lead to sizeable effects that could be constrained with observational data. Additionally, we revisit and clarify the Reissner-Nordström solution in unimodular gravity. We also study gravitational collapse and discuss possible implications for the growth of structure.

The presence of phantom dark energy in brane world cosmology generates important new effects, causing a premature Big Rip singularity when we increase the presence of extra dimension and considerably competing with the other components of our Universe. The idea is based first, in only considering a field with the characteristic equation ω < −1 and after that, consider the explicit form of the scalar field with a potential with a maximum (with the aim of avoid a Big Rip singularity). In both cases we study the dynamic in a robust form through the dynamical analysis theory, detailing in parameters like the deceleration q and the vector field associated to the dynamical system. Results are discussed with the purpose of deeming the cosmology with a phantom field as dark energy in a Randall-Sundrum scenario.

In this work, we find the asymptotic behavior for a commutative and noncommutative Mixmaster model in a Quantum Cosmology (QC) and semiclassical scenario, showing explicitly the calculus and applying the asymptotically equivalent functions that allow us to analyze the equivalence between Bianchi IX and Bianchi II models.