Related papers: Anisotropic geometrodynamics in cosmological probl…
Cosmological observations indicate that the Einstein equation may not be entirely correct to describe gravity. However, numerous modifications of these equations usually do not affect foundations of the theory. In this paper two important…
In the framework of the theory of scale relativity, we suggest a solution to the cosmological problem of the formation and evolution of gravitational structures on many scales. This approach is based on the giving up of the hypothesis of…
We construct an effective model for gravity of a central object at large scales. To leading order in the large radius expansion we find a cosmological constant, a Rindler acceleration, a term that sets the physical scales and subleading…
We propose several covariant models which may solve one of the problems in the cosmological constant. One of the model can be regarded as an extension of sequestering model. Other models could be regarded as extensions of the covariant…
The imposition of symmetries or special geometric properties on submanifolds is less restrictive than to impose them in the full space-time. Starting from this idea, in this paper we study irrotational dust cosmological models in which the…
Dynamical system methods are used in the study of the stability of spatially flat homogeneous cosmologies within a large class of generalized modified gravity models in the presence of a relativistic matter-radiation fluid. The present…
We briefly discuss new models of an `affine' theory of gravity in multidimensional space-times with symmetric connections. We use and generalize Einstein's proposal to specify the space-time geometry by use of the Hamilton principle to…
The axes of gyroscopes experimentally define non-rotating frames. But what physical cause governs the time-evolution of gyroscope axes? Starting from an unperturbed, spatially flat FRW cosmology, we consider cosmological vorticity…
This paper examines the issue of the existence and nature of time-like geodesics in asymptotically flat spacetimes and proposes a novel generalized topological criterion for the existence of time-like geodesics. Its validity is proved using…
Homogeneous isotropic spatial flat cosmological models with two torsion functions in vacuum are built and investigated in the framework of de Sitter gauge theory of gravity. It is shown that by certain choices of parameters of gravitational…
We revisit nonsingular cosmologies in which the limiting curvature hypothesis is realized. We study the cosmological perturbations of the theory and determine the general criteria for stability. For the simplest model, we find generic…
We study the geometric and physical foundations of Finsler gravity theories with metric compatible connections defined on tangent bundles, or (pseudo) Riemannian manifolds). There are analyzed alternatives to Einstein gravity (including…
It is widely believed that classical gravity breaks down and quantum gravity is needed to deal with a singularity. We show that there is a class of spacetime curvature singularities which can be resolved with metric and matter field…
In Chapter 1 I present the current picture of the universe and briefly review the cosmological constant problem and some of the theories proposed to solve it. The following Chapters essentially contain the published papers with some…
Cosmological constant problem (in its various versions) is arguably the deepest gap in our understanding of theoretical physics, the solution to which may very likely require revisiting the Einstein theory of gravity. In this letter, I…
We generalize the Hamiltonian picture of General Relativity coupled to classical matter, known as geometrodynamics, to the case where such matter is described by a Quantum Field Theory in Curved Spacetime, but gravity is still described by…
We investigate the evolution of cosmological perturbations in models of dark energy described by a time-like unit normalized vector field specified by a general function $\mathcal{F}(\mathcal{K})$, so-called Generalized Einstein-Aether…
We derive the Hamiltonian for spherically symmetric Lovelock gravity using the geometrodynamics approach pioneered by Kucha\v{r} in the context of four-dimensional general relativity. When written in terms of the areal radius, the…
Modelling structure formation across the full dynamical range of the Universe remains a major challenge in cosmology. This difficulty originates from a fundamental limitation of geodesics in general relativity: a one-parameter family of…
Singularities in general relativity such as the big bang and big crunch, and exotic singularities such as the big rip are the boundaries of the classical spacetimes. These events are marked by a divergence in the curvature invariants and…