相关论文: An extension theorem for conformal gauge singulari…
We discuss qualitative features of the conformal relation between certain classes of gravity theories and general relativity, common to different themes such as $f(R)$, Brans-Dicke-type, and string theories. We focus primarily on the frame…
The current standard cosmological model is constructed within the framework of general relativity with a cosmological constant $\Lambda$, which is often associated with dark energy, and phenomenologically explains the accelerated cosmic…
We present the general theory of curves in conformal geometry using tractor calculus. This primarily involves a tractorial determination of distinguished parametrizations and relative and absolute conformal invariants of generic curves. The…
Inflationary homogeneous isotropic cosmological models filled by scalar fields and ultrarelativistic matter are examined in the framework of gauge theories of gravitation. By using quadratic scalar field potential numerical analysis of…
In this paper, we want to give an exposition of our recent work on linear and nonlinear potential theory and their applications in conformal geometry. We use potential theory to study linear and quasilinear equations arising from conformal…
We present a method for constructing gauge-invariant cosmological perturbations which are gauge-invariant up to second order. As an example we give the gauge-invariant definition of the second-order curvature perturbation on uniform density…
We use a new, conformally-invariant method of analysis to test incomplete null geodesics approaching the singularity in a model of an evaporating black hole for the possibility of extensions of the conformal metric. In general, a local…
A theory of gravitation is constructed in which all homogeneous and isotropic solutions are nonsingular, and in which all curvature invariants are bounded. All solutions for which curvature invariants approach their limiting values approach…
In the present work some generalizations of the Hawking singularity theorems in the context of $f(R)$ theories are presented. The assumptions are of these generalized theorems is that the matter fields satisfy the conditions…
Much of the published work regarding the Isotropic Singularity is performed under the assumption that the matter source for the cosmological model is a barotropic perfect fluid, or even a perfect fluid with a $\gamma$-law equation of state.…
Homogeneous isotropic gravitating models are discussed in the framework of gauge approach to gravitation. Generalized cosmological Friedmann equations without specific solutions are deduced for models filled by scalar fields and usual…
We present a set of equations describing the evolution of the scalar-type cosmological perturbation in a gravity with general quadratic order curvature coupling terms. Equations are presented in a gauge ready form, thus are ready to…
We examine an extension of General Relativity with an explicit non-minimal coupling between matter and curvature. The purpose of this work is to present an overview of the implications of the latter to various contexts, ranging from…
As we shall briefly recall, Nordstr\"om's theory of gravity is observationally ruled out. It is however an interesting example of non-minimal coupling of matter to gravity and of the role of conformal transformations. We show in particular…
Problem of cosmological singularity of general relativity theory is discussed. The possible resolution of this problem in the framework of inflationary cosmology is proposed. Physical conditions leading to bouncing inflationary solutions in…
Quiescent cosmology and the Weyl curvature hypothesis possess a mathematical framework, namely the definition of an Isotropic Singularity, but only for the initial state of the universe. A complementary framework is necessary to also encode…
The construction of the cylinder at spatial infinity for stationary spacetimes is considered. Using a specific conformal gauge and frame, it is shown that the tensorial fields associated to the conformal Einstein field equations admit…
In the generalized matter-geometry coupling theory, we investigate the physical characteristics and causality of some new cosmological models for a flat, homogeneous, and isotropic spacetime filled with stiff, radiation, dust, and curvature…
We review and relate two recent complementary constructions of linear local gauge-invariant observables for cosmological perturbations in generic spatially flat single-field inflationary cosmologies. After briefly discussing their physical…
In this article we introduce local gauge conditions under which many curvature tensors appearing in conformal geometry, such as the Weyl, Cotton, Bach, and Fefferman-Graham obstruction tensors, become elliptic operators. The gauge…