Related papers: Evolving extrinsic curvature and the cosmological …
We introduce a novel concept of coarse extrinsic curvature for Riemannian submanifolds, inspired by Ollivier's notion of coarse Ricci curvature. This curvature is derived from the Wasserstein 1-distance between probability measures…
Scalar curvature invariants are studied in type N solutions of vacuum Einstein's equations with in general non-vanishing cosmological constant Lambda. Zero-order invariants which include only the metric and Weyl (Riemann) tensor either…
An accelerated universe should naturally have a vacuum energy density determined by its dynamical curvature. The cosmological constant is most likely a temporary description of a dynamical variable that has been drastically evolving from…
In this thesis the cosmological constant is investigated from two points of view. First, we study the influence of a time-dependent cosmological constant on the late-time expansion of the universe. Thereby, we consider several combinations…
Multidimensional cosmological model with static internal spaces describing the evolution of an Einstein space of non-zero curvature and n internal spaces is considered. The action contains several dilatonic scalar fields and antisymmetric…
We discuss the linearization of Einstein equations in the presence of a cosmological constant, by expanding the solution for the metric around a flat Minkowski space-time. We demonstrate that one can find consistent solutions to the…
We start with a brief account of the latest analysis of the Oklo phenomenon providing the still most stringent constraint on time-variability of the fine- structure constant $\alpha$. Comparing this with the recent result from the…
In this paper we perform a systematic classification of the regimes of cosmological dynamics in Einstein-Gauss-Bonnet gravity with generic values of the coupling constants. We consider a manifold which is a warped product of a four…
General relativity postulates the Minkowski space-time to be the standard flat geometry against which we compare all curved space-times and the gravitational ground state where particles, quantum fields and their vacuum states are primarily…
There is sufficient amount of internal evidence in the nature of gravitational theories to indicate that gravity is an emergent phenomenon like, e.g, elasticity. Such an emergent nature is most apparent in the structure of gravitational…
We solve Einstein's equation with Robertson-Walker metric as an initial-value problem, using as the source of gravity a Halpern-Huang real scalar field, which was derived from renormalization-group analysis, with a potential that exhibits…
For general number of spatial dimensions we investigate the cosmological dynamics driven by a cosmological constant and by a source with barotropic equation of state. It is assumed that for both those sources the energy density can be…
A scalar self-interacting theory non-linearly coupled with some power of the curvature have a possibility to explain the current smallness of the cosmological constant. Here one concentrate on a massless scalar field in the four-dimensional…
Seiberg-Witten theory leads to a delicate interplay between Riemannian geometry and smooth topology in dimension four. In particular, the scalar curvature of any metric must satisfy certain non-trivial estimates if the manifold in question…
A phenomenological model is proposed to explain the recent observed cosmological variation of the fine structure constant as an effect of the quantum vacuum, assuming a flat universe with cosmological constant $\Lambda$ in the cases…
In this essay we offer a comprehensible overview of the gravitational aether scenario. This is a possible extension of Einstein's theory of relativity to the quantum regime via an effective approach. Quantization of gravity usually faces…
Recently the global variation of the Planck mass in the General Relativistic Einstein-Hilbert action was proposed as a self-tuning mechanism of the cosmological constant preventing vacuum energy from freely gravitating. We show that this…
We study a cosmological model based on the canonical Hamiltonian transformation theory. Using a linear-quadratic approach for the free gravitational De Donder-Weyl Hamiltonian $H_\mathrm{Gr}$, the model contains terms describing a…
We consider a dynamical approach to the cosmological constant. There is a scalar field with a potential whose minimum occurs at a generic, but negative, value for the vacuum energy, and it has a non-standard kinetic term whose coefficient…
It is suggested that the exact value of the cosmological constant could be derived from first principles, based on entanglement of the Standard Model field vacuum with emergent holographic quantum geometry. For the observed value of the…