Related papers: Geodesic Completeness in General Cosmological Scen…
We wish to demonstrate how the presence of a dynamic cosmological parameter, plus a model of the universe as a quantum computer can be combined to give us a picture of early universe inflationary physics which is quite non linear, with a…
In this paper we prove a global existence theorem, in the direction of cosmological expansion, for sufficiently small perturbations of a family of spatially compact variants of the $k=-1$ Friedmann--Robertson--Walker vacuum spacetime. We…
Two theorems related to gravitational time delay are proven. Both theorems apply to spacetimes satisfying the null energy condition and the null generic condition. The first theorem states that if the spacetime is null geodesically…
We show that a general solution of the Einstein equations that describes approach to an inhomogeneous and anisotropic sudden spacetime singularity does not experience geodesic incompleteness. This generalises the result established for…
We extend to multidimensional cosmology Vilenkin's prescription of tunnelling from nothing for the quantum origin of the observable Universe. Our model consists of a $D+4$-dimensional spacetime of topology ${\cal R}\times {\cal S}^3…
We discuss applications of perturbative quantum gravity in the theory of very early quantum Universe and quantum cosmology. Consistency of the theoretical formalism for quantum effects of matter and correspondence with observational status…
Throughout the study of the geodesics of some popular spherically symmetric regular black holes, we hereby prove that the analytically extended Hayward black hole is geodetically incomplete. The simplest extension of the…
The previously proposed modification of the standard (flat) inflationary $\Lambda CDM$ model in which the inflaton field(s) and ``dark energy" are replaced by the vacum in expanding Friedmann-Lema\^itre-Robertson-Walker Universe is studied.…
Singularity theorems of general relativity utilize the notion of causal geodesic incompleteness as a criterion of the presence of a spacetime singularity. The incompleteness of a causal curve implies the end and/or beginning of the…
The vierbein (tetrad) fields for closed and open Friedmann-Robertson-Walker cosmologies are hard to work out in most of the theories featuring absolute parallelism. The difficulty is traced in the fact that these theories are not invariant…
I show that if a geodesic space has curvature bounded below locally in the sense of Alexandrov then its completion has the same lower curvature bound globally.
We find that general relativity can be naturally free of cosmological singularities. Several nonsingular models are currently available that either assume ad hoc matter contents, or are nonsingular only over a sector of solution space of…
Herein we shall argue for the utility of "spacetime geodesy", a point of view where one delays as long as possible worrying about dynamical equations, in favour of the maximal utilization of both symmetries and geometrical features. This…
In this paper a theorem is derived in order to provide a wide sufficient condition for an orthogonally transitive cylindrical spacetime to be singularity-free. The applicability of the theorem is tested on examples provided by the…
The dynamics of a preinflacionary phase of the universe, and its exit to inflation, is discussed. This phase is modeled by a closed Friedmann-Robertson-Walker geometry, the matter content of which is radiation plus a scalar field minimally…
Inflation has been the leading early universe scenario for two decades, and has become an accepted element of the successful `cosmic concordance' model. However, there are many puzzling features of the resulting theory. It requires both…
We study the geometrical properties of scale-invariant two-field models of inflation. In particular, we show that when the field-derivative space in the Einstein frame is maximally symmetric during inflation, the inflationary predictions…
We argue that the presence of an inflationary epoch is a natural, almost unavoidable, consequence of the existence of a sensible effective action involving an infinite tower of higher-curvature corrections to the Einstein-Hilbert action. No…
In this chapter we review the recent developments of realizing $R^2$-like inflation in the framework of a most general UV nonlocal extension of Einstein's general theory of relativity (GR). It is a well-motivated robust approach towards…
The classical singularity theorems of R. Penrose and S. Hawking from the 1960s show that, given a pointwise energy condition (and some causality as well as initial assumptions), spacetimes cannot be geodesically complete. Despite their…