Narrow Results

We consider a five-dimensional Ricci flat Bouncing cosmology and assume that the four-dimensional universe is permeated smoothly by three minimally coupled matter components: CDM + baryons ρ_m, radiation ρ_r and dark energy ρ_x. Evolutions of these three components are studied and it is found that dark energy dominates before the bounce, and pulls the universe contracting. In this process, dark energy decreases while radiation and the matter increases. After the bounce, the radiation and matter dominates alternatively and then decreases with the expansion of the universe. At present, the dark energy dominates again and pushes the universe accelerating. In this model, we also obtain that the equation of state (EOS) of dark energy at present time is w_x0≈-1.05 and the redshift of the transition from decelerated expansion to accelerated expansion is z_T≈0.37, which are compatible with the current observations.

We consider a five-dimensional Ricci flat bouncing cosmological model in which the four-dimensional induced matter contains two components at late times — the cold dark matter (CDM) + baryons and dark energy. We find that the arbitrary function f(z) contained in the solution plays a similar role as the potential V(ϕ) in quintessence and phantom dark energy models. To resolve the coincidence problem, it is generally believed that there is a scaling stage in the evolution of the universe. We analyze the condition for this stage and show that a hyperbolic form of the function f(z) can work well in this property. We find that during the scaling stage (before z ≈ 2), the dark energy behaves like (but not identical to) a cold dark matter with an adiabatic sound speed and p_x ≈ 0. After z ≈ 2, the pressure of the dark energy becomes negative. The transition from deceleration to acceleration happens at z_T ≈ 0.8 which, as well as other predictions of the 5D model, agrees with current observations.

Torsion is a geometrical object, required by quantum mechanics in curved spacetime, which may naturally solve fundamental problems of general theory of relativity and cosmology. The black-hole cosmology, resulting from torsion, could be a scenario uniting the ideas of the big bounce and inflation, which were the subject of a recent debate of renowned cosmologists.

In quantum cosmology, it is expected that the Big Bang singularity is resolved and the universe undergoes a bounce. We find that for Gaussian initial states, matter-gravity entanglement entropy rises rapidly during the bounce, declines, and then approaches a steady-state value following the bounce. These observations suggest that matter-gravity entanglement is a feature of the macroscopic universe and that there is no Second Law of entanglement entropy.

A brief summary of the application of coherent states in the examination of quantum dynamics of cosmological models is given. We discuss quantization maps, phase space probability distributions and semiclassical phase spaces. The implementation of coherent states based on the affine group resolves the hardest singularities, renders self-adjoint Hamiltonians without boundary conditions and provides a completely consistent semiclassical description of the involved quantum dynamics. We consider three examples: the closed Friedmann model, the anisotropic Bianchi Type I model and the deep quantum domain of the Bianchi Type IX model.

The four-fermion gravitational interaction is induced by torsion. It gets dominating below the Planck scale. The regular, axial-axial part of this interaction by itself does not stop the gravitational compression. However, the anomalous, vector-vector interaction results in a natural way both in big bounce and in inflation.

If torsion exists, it generates gravitational four-fermion interaction (GFFI), essential on the Planck scale. We analyze the influence of this interaction on the Friedmann-Lemaitre-Robertson-Walker cosmology. Explicit analytical solution is derived for the problem where both the energy-momentum tensor generated by GFFI and the common ultrarelativistic energy-momentum tensor are included. We demonstrate that gravitational four-fermion interaction does not result in Big Bounce.