Related papers: Gauge/frame invariant variables for the numerical …
We investigate the scalar sector of linear cosmological perturbations in quadratic gravity. Working in the Einstein frame, we derive the equations of motion in a gauge-independent manner and express them in terms of three sets of…
The gauge gravitation theory in the Riemann-Cartan space-time is investigated in order to solve the fundamental problems of the general relativity theory. The constraints for indefinite parameters of the theory under which solutions of…
There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has…
We investigate gauge invariant cosmological perturbations in a spatially flat Friedman-Robertson-Walker universe with scalar fields. It is well known that the evolution equation for the gauge invariant quantities has exact solutions in the…
For the study of cosmological backreacktion an avaragng procedure is required. In this work a covariant and gauge invariant averaging formalism for finite volumes will be developed. This averaging will be applied to the scalar parts of…
Gauge invariant treatments of the second order cosmological perturbation in a four dimensional homogeneous isotropic universe filled with the perfect fluid are completely formulated without any gauge fixing. We derive all components of the…
We review the study of inhomogeneous perturbations about a homogeneous and isotropic background cosmology. We adopt a coordinate based approach, but give geometrical interpretations of metric perturbations in terms of the expansion, shear…
Numerical relativity describes a discrete initial value problem for general relativity. A choice of gauge involves slicing space-time into space-like hypersurfaces. This introduces past and future gauge relative to the hypersurface of…
In "extended phase space" approach to quantum geometrodynamics numerical solutions to Schrodinger equation corresponding to various choice of gauge conditions are obtained for the simplest isotropic model. The "extended phase space"…
In contrast to electrodynamics, Einstein's gravitation equations are not invariant with respect to a wide class of the mapping of field variables which leave equations of motion of test particles in a given coordinate system invariant. It…
The issue of the physical equivalence between the different coordinate system in Einstein theory is revised. Gauge fixing influences results of measurements and physics are different in two different coordinate system. Spacetime metric…
We present a general formalism for the Hamiltonian description of perturbation theory around any spatially homogeneous spacetime. We employ and refine the Dirac method for constrained systems, which is very well-suited to cosmological…
The simplest variant of gauge gravitation theory in Riemann-Cartan spacetime leading to the solution of the problem of cosmological singularity and dark energy problem is investigated. It is shown that this theory by certain restrictions on…
The interpretations of solutions of Einstein field's equations led to the prediction and the observation of physical phenomena which confirm the important role of general relativity, as well as other relativistic theories in physics. In…
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…
Along the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. {\bf 110} (2003), 723; {\it ibid}, {\bf 113} (2005), 481.], we formulate the second order gauge invariant…
We present the results of a study of the gauge dependence of spacetime perturbations. In particular, we consider gauge invariance in general, we give a generating formula for gauge transformations to an arbitrary order n, and explicit…
In recent years there has been a lot of interest in discussing frame dependences/independences of the cosmological perturbations under the conformal transformations. This problem has previously been investigated in terms of the covariant…
We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second and higher order perturbations. We first derive some mathematical results…
The Hubble tension cast a blight on the standard cosmology. As a possible attitude to the problem, the local variation of the expansion rate in an inhomogeneous cosmology has been proposed where the spatial averaging over a finite domain…