Related papers: Geodesic Completeness in General Cosmological Scen…
Models of inflation with super-Planckian excursion seem well in agreement with the recent observations of B- mode polarization in the cosmic microwave background (CMB) radiation by the BICEP2 data. In this note, we highlight the challenges…
We use the Gauss-Bonnet theorem and the triangle comparison theorems of Rauch and Toponogov to show that on compact Riemann surfaces of negative curvature period integrals of eigenfunctions $e_\lambda$ over geodesics go to zero at the rate…
We investigate an index theorem for a Bogoliubov-de Gennes Hamiltonian (BdGH) describing a topological superconductor with Yang-Mills-Higgs couplings in arbitrary dimensions. We find that the index of the BdGH is determined solely by the…
We investigate how various inflationary and bouncing cosmologies can be realized by imperfect fluids with a generalized equation of state, in the context of both classical and loop quantum cosmology. With regards to the inflationary…
We show that inflationary cosmology may be used to test the statistical predictions of quantum theory at very short distances and at very early times. Hidden-variables theories, such as the pilot-wave theory of de Broglie and Bohm, allow…
In the framework of Born-Infeld inspired gravity theories, which deviates from General Relativity (GR) in the high curvature regime, we discuss the viability of Cosmic Inflation without scalar fields. For energy densities higher than the…
According to previous work, topological defects expand exponentially without an end if the vacuum expectation value of the Higgs field is of the order of the Planck mass. We extend the study of inflating topological defects to the…
A semiclassical description of quantum systems is applied to probe the dynamics of the cosmological model of an inflationary universe with quadratic inflaton potential, described in a quantum framework of geometrodynamics. The systematic…
A finite duration of cosmic inflation can result in features $\mathcal{P}_{\mathcal{R}}(k) = |\alpha_k-\beta_k\,\mathrm{e}^{\mathrm{i}\delta_k}|^2 \,\mathcal{P}_{\mathcal{R}}^{(0)}(k)$ in the primordial power spectrum that carry information…
The physical mechanism responsible for the emergence of primordial cosmic seeds from a perfect isotropic and homogeneous Universe has not been fully addressed in standard cosmic inflation. To handle this shortcoming, D. Sudarsky et al have…
Starting with the Lagrangian formulation of General Relativity, we will conduct an investigation into the production of spacetime waves, due to a geometric boundary term of a closed extended manifold, within the tensor and scalar sectors.…
Friedrich's proofs for the global existence results of de Sitter-like space-times and of semi-global existence of Minkowski-like space-times [Comm. Math. Phys. \textbf{107}, 587 (1986)] are re-examined and discussed, making use of the…
A model of inflation is proposed in which compact extra dimensions allow a graceful exit without recourse to flat potentials or super-Planckian field values. Though bubbles of true vacuum are too sparse to uniformly reheat the Universe by…
The geodesic deviation equation (`GDE') provides an elegant tool to investigate the timelike, null and spacelike structure of spacetime geometries. Here we employ the GDE to review these structures within the…
An improved version of the well-known Peebles-Vilenkin model unifying early inflationary era to current cosmic acceleration, is introduced in order to match with the theoretical values of the spectral quantities provided by it with the…
We investigate the initiation of cosmic inflation, in full numerical relativity, from pre-inflationary scenarios with large tensor and vector fluctuations in the metric. These settings are characterized by having large values in the Weyl…
In this paper, we construct a class of collapsing spacetimes in vacuum without any symmetries. The spacetime contains a black hole region which is bounded from the past by the future event horizon. It possesses a Cauchy hypersurface with…
Using computer simulations we study the geometry of a typical quantum universe, i.e. the geometry one might expect before a possible period of inflation. We display it using coordinates defined by means of four classical scalar fields…
Regular black holes are often geodesically incomplete when their extensions to negative values of the radial coordinate are considered. Here, we propose to use the Simpson-Visser method of regularising a singular spacetime, and apply it to…
We give a combinatorial proof, using the hyperbolicity of the curve graphs, of the bounded geodesic image theorem of Masur and Minsky. Recently it has been shown that curve graphs are uniformly hyperbolic, thus a universal bound can be…