We will demonstrate how recent advances combined with old ideas are pointing to a surprising picture of the evolution of the universe.

Abstract: In four dimensional General Relativity the properties of gravitational waves emitted in BH-BH mergers have been extensively studied using numerical relativity, largely in astrophysical settings. Understanding higher dimensional BH-BH collisions is an important goal for numerical relativity, firstly in order to observe the behaviour of the theory in its most extreme, non-linear regime, and also due to its applications to areas of high energy physics such as TeV gravity theories. In this work we present for the first time full non-linear simulations of head-on BH-BH collisions in up to 10 dimensions and present an analysis of the gravitational radiation emitted. We use a new method for analysis of the radiation, analogous to the well known Weyl scalar method based on the Newman-Penrose formalism in 4D. We find that as the number of dimensions is increased, the energy emitted in gravitational radiation is suppressed. We also present a comparison of our numerical data with point particle calculations.

I will review the idea behind the matter bounce scenario as an alternative to inflation and highlight two of its problems: its instability with respect to anisotropies and its large tensor-to-scalar ratio. I will present two tentative resolutions to the latter in which curvature perturbations are effectively enhanced, but I will argue that these approaches are not viable because they always lead to the production of large non-Gaussianities. I will then show that a more robust resolution (to both problems) would be to consider a theory in which the graviton has a non-trivial mass, but I will also discuss the limitations of such a theory.

I will discuss the dynamics of a collapsing (homogeneous and isotropic) universe, and show that torsion induced interactions can prevent the universe from reaching a singularity, but lead to a regular bounce. This dynamic can be understood as the formation of fermionic condensate(s), which lowers the energy density of the fermions effectively slowing down the gravitational collapse. Before a singularity is reached, in fact, the null energy condition gets violated, and the energy density of the fermionic field reaches zero. At this point all the initial energy has been converted in a negative pressure, which causes the universe to re-expand. This process is possible because the energy density lost by the fermionic field is simply converted in the more energetically favourable condensate state, and will eventually come back as the universe cools down and gets bigger. I will discuss both classical and semi-classical treatment of this problem.

Our recent numerical simulations demonstrated that in higher dimensions even asymptotically flat black holes can break and give rise to naked singularities. This shows that if cosmic censorship were to hold in our universe, it would be a special property of four dimensional spacetimes. I will describe these results and outline other applications of the same numerical relativity code to cosmology, astrophysics, and AdS/CFT.