Searcharxiv⌕ Search

arXiv subjects

Abhik Kumar Sanyal

Publications and source records attributed to Abhik Kumar Sanyal.

At least 37 records · Page 2Linked to original sources
arXiv2021

Bianchi Type-II Cosmological Model with Viscous Fluid

A spatially homogeneous and locally rotationally symmetric Bianchi type-II cosmological model under the influence of both shear and bulk viscosity has been studied. Exact solutions are obtained with a barotropic equation of state between thermodynamics pressure and the energy density of the fluid, and considering the linear relationships amongst the energy density, the expansion scalar and the shear scalar. Special cases with vanishing bulk viscosity coefficients and with the perfect fluid in the absence of viscosity have also been studied. The formal appearance of the solutions is the same for both the viscous as well as the perfect fluids. The difference is only in choosing a constant parameter which appears in the solutions. In the cases of either a fluid with bulk viscosity alone or a perfect fluid, the barotropic equation of state is no longer an additional assumption to be imposed; rather it follows directly from the field equations.

gr-qc↗
arXiv2021

Bianchi type I cosmological model with a viscous fluid

Bianchi I cosmological models consisting of a fluid with both bulk and shear viscosity are studied. It is shown how the dynamical importance of the shear and the fluid density change in the course of evolution. Exact solutions with an equation of state $ρ= p$ for a stiff fluid are also obtained in several special cases, assuming the viscosity coefficients to be the power functions of the density. The results are, in some relevant cases, compared with those of Belinskii and Khalatnikov (1976) in the asymptotic limits and are seen to agree with them in that the models start with $ρ= 0$ at the beginning and evolve with the creation of matter by the gravitational field, finally approaching the Friedmann universe.

gr-qc↗
arXiv2021

Scalar meson field in a conformally flat space

Among several authors, who studied massive and massless scalar meson fields in general relativity, attempts to obtain a complete set of solutions for a conformally flat metric $e^ψ\left({dx^1}^2 + {dx^2}^2 + {dx^3}^2 - {dx^4}^2\right)$ were made by Ray for massive and massless mesons and Gursay for massless mesons. Both of them concluded that $ψ$ must be a function of $K_0\left({dx^1}^2 + {dx^2}^2 + {dx^3}^2 -{dx^4}^2\right) + K_1 x^1 + K_2 x^2 + K_3 x^3 + K_4 x^4$, where, where $K_0,~K_1,~ K_2,~K_3,~K_4$ are all constants. Both Ray and Gursay, however, overlooked an important particular case, which is studied here. As a by-product certain equations obtained by Auria and Regge in connection with "Gravitational theories with asymptotic flat Instantons," are solved under less restrictive assumptions.

gr-qc↗
arXiv2021

Hydrodynamic self-similar cosmological models

Hydrodynamic self-similar solutions, as obtained by Chi [J. Math. Phys. 24, 2532 (1983)] have been generalized by introducing new variables in place of the old space and time variables. A systematic procedure of obtaining a complete set of solutions has been suggested. The Newtonian analogs of all homogeneous isotropic Friedmann dust universes with spatial curvature $k = 0, \pm 1$ have been given.

gr-qc↗
arXiv2021

Early universe in view of a modified theory of gravity

We study the quantum evolution of the early universe, its semi-classical analogue together with inflationary regime, in view of a generalized modified theory of gravity. The action is built by supplementing the non-minimally coupled scalar-tensor theory of gravity with scalar curvature squared term and a Gauss-Bonnet-dilatonic coupled term. It is generalized, since all the parameters are treated as arbitrary functions of the scalar field. It is interesting to explore the fact that instead of considering additional flow parameters, an effective potential serves the purpose of finding inflationary parameters. The dilaton stabilization issue appears here as a problem with reheating. Addition of a cosmological constant term alleviates the problem, and inflation is effectively driven by the vacuum energy density. Thus Gauss-Bonnet term might play a significant role in describing late-time cosmic evolution.

hep-th↗
arXiv2020

Self-Similar Magnetohydrodynamics

For the solution of the full set of magnetohydrodynamics (MHD) equations in the presence of gravity due to a central point-mass, a self-similar theory for a general polytrope has already suggested a set of exact time-dependent solutions by analytical methods for a, (gamma = 4\over3) polytrope, since (gamma = 4/3) is the simplest to treat. In the present paper while going for a complete set of self-similar solutions, we find that (gamma = 4/3) is the only physically-possible polytrope and that then, pressure is independent of the scalar function A, and depends on angle and time only. We also obtain a specific form of time-dependence for the self-similar variable.

physics.flu-dyn↗
arXiv2020

Canonical equivalence in anisotropic models for higher order theory of gravity

We show that as in the case of isotropic models, the `Dirac Algorithm' and `Modified Horowitz' Formalism' lead to identical phase-space structure of the Hamiltonian for the gravitational action with curvature squared terms, in anisotropic space-time, viz, Bianchi-I, Bianchi-III and Kantowski-Sachs models too.

hep-th↗
arXiv2020

Probing the early universe with a generalized action

Possibly, the most general action in the background of isotropic and homogeneous space-time has been considered to study the quantum evolution of the early universe, apart from a cosmological constant. The hermiticity of the effective Hamiltonian operator in the presence of curvature squared terms suggests unitary time evolution of the quantum states, assuring conservation of probability. The oscillatory behaviour of the semi-classical wavefunction around a de-Sitter solution signals that the theory is classically allowed, and the universe enters an inflationary regime just after Planck's era. In view of a hierarchy of Hubble flow parameters, and using a redefined effective potential, the complicated classical field equations in the presence of several coupling parameters, reduce to standard general-relativistic equations with a single scalar field. As a result, inflation has been studied without considering any additional flow parameters. Inflationary parameters lie very much within the presently available Planck's data, and the model admits graceful exit from inflation.

hep-th↗
arXiv2020

Analyzing Conserved Currents in F(R) theory of gravity

F(R) theory of gravity is claimed to admit a host of conserved currents under the imposition of Noether symmetry following various techniques. However, for a constrained system such as gravity, Noether symmetry is not on-shell. As a result, the symmetries do not necessarily satisfy the field equations in general, constraints in particular, unless the generator is modified to incorporate the constraints. In the present manuscript, we apply the first theorem of Poisson to unveil the fact that not all the conserved currents appearing in the literature for F(R) theory of gravity, satisfy the field equations. We also provide a list of available forms of F(R) along with associated conserved currents, and construct a generalized action, which might address the cosmic puzzle, elegantly.

gr-qc↗
arXiv2020

Inflation with scalar-tensor theory of gravity

The latest released data from Planck in 2018, put up tighter constraints on inflationary parameters. In the present article, the in-built symmetry of the non-minimally coupled scalar-tensor theory of gravity is used to fix the coupling parameter, the functional Brans-Dicke parameter, and the potential of the theory. It is found that all the three different power-law potentials and one exponential, pass these constraints comfortably, and also gracefully exit from inflation.

astro-ph.CO↗
arXiv2019

Irrotational Bianchi V Viscous Fluid Cosmology with Heat Flux

The irrotational Bianchi V cosmological model under the influence of both shear and bulk viscosity, together with heat flux, has been studied. Exact solutions for the model are obtained with three physically viable assumptions. The first two relate the matter density, shear scalar, and expansion scalar and the third is a barotropic equation of state, connecting the matter density and thermodynamic pressure. The properties of the solutions are studied and the temperature distribution is also presented explicitly. It has been observed that along with the viscosity, heat flux further adds to the rate of entropy increase.

gr-qc↗
arXiv2019

Stability of a scalar potential under gravity

In the present note we show that the thin-wall approximation is not an assumption rather a necessary condition for satisfying Boucher's criteria for gravitational stability of the scalar potential.

gr-qc↗
arXiv2019

Some aspects of modified theory of gravity in Palatini formalism unveiled

Under conformal transformation, f(R) theory of gravity in Palatini formalism leads to a Brans-Dicke type of scalar-tensor equivalent theory with a wrong sign in the effective kinetic energy term. This means, the effective scalar acts as the dark energy and so late-time cosmic acceleration in matter-dominated era is accountable. However, we unveil some aspects of Palatini formalism, which clearly reveals the fact that the formalism is not suitable to explain the cosmological evolution of the early universe with $f(\mathfrak{R})$ gravity alone. Additionally, it is noticed that some authors, in an attempt to explore Noether symmetry of the theory changed the sign of the kinetic term and hence obtained the wrong answer. Here, we make the correction and unmask a very interesting aspect of symmetry analysis.

gr-qc↗
arXiv2019

The role of cosmological constant in f(R, G) gravity

Einstein-Hilbert action is supplemented by Gauss-Bonnet squared term, its phase-space structure is constructed and canonical quantization is performed. Resolution of a contradiction that emerges in the process, requires the presence of other fields at least in the form of vacuum energy-density, commonly known as the cosmological constant. This reveals the very importance of the presence of other fields at least in the form of cosmological constant, in the very early universe.

gr-qc↗
arXiv2019

Degenerate Hamiltonian operator in higher-order canonical gravity -- the problem and a remedy

Different routes towards the canonical formulation of a classical theory result in different canonically equivalent Hamiltonians, while their quantum counterparts are related through appropriate unitary transformation. However, for higher-order theory of gravity, although two Hamiltonians emerging from the same action differing by total derivative terms are related through canonical transformation, the difference transpires while attempting canonical quantization, which is predominant in non-minimally coupled higher-order theory of gravity. We follow Dirac's constraint analysis to formulate phase-space structures, in the presence (case-I) and absence (case-II) of total derivative terms. While the coupling parameter plays no significant role as such for case-I, quantization depends on its form explicitly in case-II, and as a result, unitary transformation relating the two is not unique. We find certain mathematical inconsistency in case-I, for modified Gauss-Bonnet-Dilatonic coupled action, in particular. Thus, we conclude that total derivative terms indeed play a major role in the quantum domain and should be taken care of a-priori, for consistency.

gr-qc↗
arXiv2018

Cosmological Lorentzian Wormholes via Noether symmetry approach

Noether symmetry has been invoked to explore the forms of a couple of coupling parameters and the potential appearing in a general scalar-tensor theory of gravity in the background of Robertson-Walker space-time. Exact solutions of Einstein's field equations in the familiar Brans-Dicke, Induced gravity and a General non-minimally coupled scalar-tensor theories of gravity have been found using the conserved current and the energy equation, after being expressed in a set of new variables. Noticeably, the form of the scale factors remains unaltered in all the three cases and represents cosmological Lorentzian wormholes, analogous to the Euclidean ones. While classical Euclidean wormholes requires an imaginary scalar field, the Lorentzian wormhole do not, and the solutions satisfy the weak energy condition.

astro-ph.CO↗
arXiv2018

Equivalent and inequivalent canonical structures of higher order theories of gravity

Canonical formulation of higher order theory of gravity can only be accomplished associating additional degrees of freedom, which are extrinsic curvature tensor. Consequently, to match Cauchy data with the boundary data, terms in addition to the three-space metric, must also be fixed at the boundary. While, in all the three, viz. Ostrogradski's, Dirac's and Horowitz' formalisms, extrinsic curvature tensor is kept fixed at the boundary, a modified Horowitz' formalism fixes Ricci scalar, instead. It has been taken as granted that the Hamiltonian structure corresponding to all the formalisms with different end-point data are either the same or are canonically equivalent. In the present study, we show that indeed it is true, but only for a class of higher order theory. However, for more general higher order theories, e.g. dilatonic coupled Gauss-Bonnet gravity in the presence of curvature squared term, the Hamiltonian obtained following modified Horowitz' formalism is found to be different from the others, and is not related under canonical transformation. Further, it has also been demonstrated that although all the formalisms produce viable quantum description, the dynamics is different and not canonically related to modified Horowitz' formalism. Therefore it is not possible to choose the correct formalism which leads to degeneracy in Hamiltonian.

gr-qc↗