Dirac procedure and the Hamiltonian formalism for cosmological perturbations in a Bianchi I universe

We apply the Dirac procedure for constrained systems to the Arnowitt-Deser-Misner formalism linearized around the Bianchi I universe. We discuss and employ basic concepts such as Dirac observables, Dirac brackets, gauge-fixing conditions, reduced phase space, physical Hamiltonian, canonical isomorphism between different gauge-fixing surfaces and spacetime reconstruction. We relate this approach to the gauge-fixing procedure for non-perturbative canonical relativity. We discuss the issue of propagating a basis for the scalar-vector-tensor decomposition as, in an anisotropic universe, the wavefronts of plane waves undergo a non-trivial evolution. We show that the definition of a gravitational wave as a traceless-transverse mode of the metric perturbation needs to be revised. Moreover there exist coordinate systems in which a polarization mode of the gravitational wave is given entirely in terms of a scalar metric perturbation. We first develop the formalism for the universe with a single minimally coupled scalar field and then extend it to the multi-field case. The obtained fully canonical formalism will serve as a starting point for a complete quantization of the cosmological perturbations and the cosmological background.

Consistency Conditions of f(R,G)-Gravity Field Equations for Bianchi-Type III Metric

In this paper, we study the -gravitation theory under the assumption that the standard matter-energy content of the universe is a perfect fluid with linear barotropic equation of state within the framework of Bianchi-Type III model from the class of homogeneous and anisotropic universe models. However, whether such a restriction lead to any contradictions or inconsistencies in the field equations will create an issue that needs to be examined. Under the effective fluid approach, we will be concerned mainly the field equations in an orthonormal tetrad framework with an equimolar and examined the situation of establishing the functional form of together with the scale factors, which are their solutions. Unlike similar studies, which are very few in the literature, instead of assuming preliminary solutions, we determined the consistency conditions of the field equations by assuming the matter energy content of the universe as an isotropic perfect fluid for Bianchi-Type III.

Anisotropic Universe with Manimally Interacting Matter and Holographic Dark Energy

The holographic dark energy (HDE), a form of dark energy, has been a useful tool in explaining the recent phase transition of the universe. In this paper, we study the anisotropic and homogeneous Bianchi type-III model of the universe filled with minimally interacting matter and holographic dark energy under the framework of the Brans-Dicke (BD) scalar tensor theory of gravitation. Considering two physically plausible conditions such as, (i) the special law of variation for Hubble parameter and (ii) the scalar expansion proportional to the shear scalar, we propose two new models namely, exponential expansion model and power law expansion model. We also show the dynamics of these models fit with existing observational data and literature thereof. The transit behavior of the equation of state parameter for dark energy has been analyzed graphically. The jerk parameter is also studied for both of the models describing cosmological evolution. The Chittagong Univ. J. Sci. 42(1): 39-57, 2020

Interacting generalized anisotropic scalar field models

This paper is devoted to investigate the interacting generalized ghost pilgrim dark energy model in the background of anisotropic universe in general relativity. We analyze the two parameters i.e., hubble parameter and equation of state parameter to explore the cosmological evolution of the Bianchi type universe. We study scalar field dark energy models i.e., quintessence, dilaton, K-essence and tachyon to check the consistency of the current universe with their scalar field and corresponding potentials. Further, we check the compatibility of fractional density of matter and dark energy with recent observations of Plank along with their graphical analysis. It is remarkable to conclude that that both fractional densities admits consistency with Plank data 2018 in all cases of Bainchi type universe.

Final fate of Kantowski–Sachs gravitational collapse

Although it is not a fundamental question, determining exact and general solutions for a given theory has advantages over a numerical integration in many specific cases. Of course, respecting the peculiarities of the problem. Revisiting the integration of the General Relativity Theory field equations for the Kantowski–Sachs spacetime describes a homogeneous but anisotropic universe whose spatial section has the topology of [Formula: see text], we integrate the equations for arbitrary curvature parameter and write the solutions considering the process of gravitational collapse. We took the opportunity and made some comments involving some features of the model such as energy density, shear, viscosity and the production of gravitational waves via Petrov classification.

Bianchi-I cosmology within f(T): Reconstruction method and dynamical study

This paper is fundamentally devoted to the cosmological reconstruction and dynamic studying in homogeneous BIANCHI-I space-time under the [Formula: see text] background. Its content is supported by the fact that in the General Relativity description of the standard cosmological paradigm, the evolution from an anisotropic universe into an Friedmann–Lemaitre–Robertson–Walker (FLRW) one can be achieved by a period of inflationary expansion. Nowadays, modified gravity theories like [Formula: see text] are widely accepted to provide a real description of some universe evolution phases like inflation era, matter-dominated era, etc. So, we aim to examine here what [Formula: see text] gravity model can accommodate with an anisotropic universe, an expanding universe and even the transition between both evolutions. To reach this goal, we use a reconstruction method based on dynamic equations in Bianchi-I space-time by assuming a particular form for the metric anisotropy and by specifying some time functions describing average scale factor. Most of the obtained models are consistent with certain known results in the literature but other add new results in this work. In the second part of this work, the dynamical behaviors of the Bianchi-I space-time are addressed through the reconstruction of an autonomous dynamical system. For an aleatory choice of anisotropic fluid, the numerical analysis of the system shows that the metric anisotropy decreases with expansion. Then, an attractor point is reached and becomes unstable by the end of inflation. Such interesting properties found in this work on Bianchi-I space-time are often interpreted as graceful exit from inflation which doesn’t occur in ordinary FLRW space-time.

On Spacetime Duality and Bounce Cosmology of a Dual Universe

Precise astronomical measurements of the fine structure constant and universe expansion rate have revealed that they vary over specific directions, demonstrating an anisotropic universe. The curvature in complex spacetime can be interpreted as spatial warping evolution along with its travel through the imaginary time dimension. Complex spacetime worldlines of the universe spatial factor evolution through imaginary time are utilised to model universe anisotropy. The worldlines of a positively curved universe revealed both positive and negative solutions, which imply that matter and antimatter could be evolving in opposite directions as distinct sides of the universe, theoretically corroborating the axis of the cosmic microwave background and observed anisotropy. The model indicates that a nascent hyperbolic expansion is followed by a first phase of decelerating spatial expansion during the first 9 Gyr, and then, a second phase of accelerating expansion. The model potentially resolves the tension in Hubble parameter measurements, with a predicted density at the phase transition of 1.12>1. In addition, it predicts a final time-reversal phase of rapid spatial contraction leading to the Big Crunch, signalling a cyclic universe. On spacetime quantum duality, the simulations of the spacetime continuum flux through its travel along with its predicted worldlines demonstrated the fast-orbital speed of stars resulting from an external momentum exerted on galaxies via the spatial curvature through the imaginary time dimension. These findings indicate that antimatter could exist as a distinct side, which influences the universe evolution; physically explaining the effects attributed to dark matter and dark energy.