arXiv subjects

Abhik Kumar Sanyal

Publications and source records attributed to Abhik Kumar Sanyal.

At least 55 records · Page 3Linked to original sources

arXiv2018

Early Universe with modified scalar-tensor theory of gravity

Scalar-tensor theory of gravity with non-minimal coupling is a fairly good candidate for dark energy, required to explain late-time cosmic evolution. Here we study the very early stage of evolution of the universe with a modified version of the theory, which includes scalar curvature squared term. One of the key aspects of the present study is that, the quantum dynamics of the action under consideration ends up generically with de-Sitter expansion under semiclassical approximation, rather than power-law. This justifies the analysis of inflationary regime with de-Sitter expansion. The other key aspect is that, while studying gravitational perturbation, the perturbed generalized scalar field equation obtained from the perturbed action, when matched with the perturbed form of the background scalar field equation, relates the coupling parameter and the potential exactly in the same manner as the solution of classical field equations does, assuming de-Sitter expansion. The study also reveals that the quantum theory is well behaved, inflationary parameters fall well within the observational limit and quantum perturbation analysis shows that the power-spectrum does not deviate considerably from the standard one obtained from minimally coupled theory.

hep-th↗

arXiv2017

Thermodynamics of irreversible particle creation phenomena and its cosmological consequence

The study of particle creation phenomena at the expense of the gravitational field is of great research interest. It might solve the cosmological puzzle single-handedly, without the need for either dark energy or the modified theory of gravity. In the early universe, following graceful exit from inflationary phase, it serves the purpose of reheating the cold universe, which gave way to the hot Big-Bang model. In the late universe, it led to late time cosmic acceleration, without affecting stand-ard Big-Bang-Nucleosynthesis (BBN), Cosmic Microwave Background Radiation (CMBR), or Structure Formation. In this chapter, we briefly review the present status of cosmic evolution, develop the thermodynamics for irreversible particle creation phenomena and study its consequences at the early as well as in the late universe.

gr-qc↗

arXiv2017

On the equivalence between different canonical forms of F(R) theory of gravity

Classical equivalence between Jordan's and Einstein's frame counterparts of F(R) theory of gravity has recently been questioned, since the two produce different Noether symmetries, which couldn't be translated back and forth using transformation relations. Here we add the Hamiltonian constraint equation, which is essentially the time-time component of Einstein's equation, through a Lagrange multiplier to the existence condition for Noether symmetry to show that all the three different canonical structures of F(R) theory of gravity, including the one which follows from Lagrange multiplier technique, admit each and every available symmetry independently. This establishes classical equivalence amongst all the three.

gr-qc↗

arXiv2017

Why scalar-tensor equivalent theories are not physically equivalent?

Whether Jordan's and Einstein's frame descriptions of F(R) theory of gravity are physically equivalent, is a long standing debate. However, practically none questioned on true mathematical equivalence, since classical field equations may be translated from one frame to the other following a transformation relation. Here we show that neither Noether symmetries, Noether equations, nor may quantum equations be translated from one to the other. The reason being, - conformal transformation results in a completely different system, with a different Lagrangian. Field equations match only due to the presence of diffeomorphic invariance. Unless a symmetry generator is found which involves Hamiltonian constraint equation, the mathematical equivalence between the two frames appears to be vulnerable. In any case, in quantum domain Mathematical and therefore physical equivalence can't be established.

gr-qc↗

arXiv2017

Semiclassical gravity with a nonminimally coupled scalar field

Semiclassical approximation to the Wheeler-DeWitt equation which corresponds to gravity with a minimally coupled scalar field has been performed. To the leading order, vacuum Einstein's equation along with the functional Schrodinger equation for the matter field, propagating in the background of classical curved space are obtained. The Schrodinger equation is solved for a quartic potential. It is observed that the wave-functional admits the wormhole boundary condition even for large negative values of the coupling constant epsilon. For conformal coupling epsilon = 1/6, the Hawking-Page wormhole solution is recovered.

gr-qc↗

arXiv2017

Extended Inflation - a quantum cosmological survey

This paper considers Einstein-Brans-Dicke action being coupled with a Higgs sector. It is shown that classically graceful exit from inflation is not possible in principle, rejecting the claim of La and Steinhardt. Further, wormhole solutions with and without conserved charges are explored. Finally, the wavefunction of the universe in this model is constructed with the boundary condition, as proposed by Vilenkin. The interesting feature of the wavefunction is that it has been constructed for an arbitrary factor-ordering index.

hep-th↗

arXiv2017

History of cosmic evolution with modified Gauss-Bonnet-dilatonic coupled term

Gauss-Bonnet-dilatonic coupling in four dimension plays an important role to explain late time cosmic evolution. However, this term is an outcome of low energy string effective action and thus ought to be important in the early universe too. Unfortunately, phase-space formulation of such a theory does not exist in the literature due to branching. We therefore consider a modified theory of gravity, which contains a nonminimally coupled scalar-tensor sector in addition to higher order scalar curvature invariant term with Gauss-Bonnet-dilatonic coupling. Such an action unifies early inflation with late-time cosmic acceleration. Quantum version of the theory is also well-behaved.

gr-qc↗

arXiv2016

Enlightening the dark universe

Lot of avenues, the black hole, the wormhole, the dark matter, the dark energy etc. have been opened since the advent of General Theory of Relativity in 1915. Cosmology, the physics of creation and evolution of the universe, which was once thought to be beyond human perseverance, has now become a rich science of highest importance. However, the theory of gravitation, the oldest known interaction, is still not well understood. In the process of unveiling the evolutionary history of the universe, we shall explore some facts that suggest General Theory of Relativity is not the complete theory of gravitation.

gr-qc↗

arXiv2016

Unified cosmology with Non-minimally coupled scalar-tensor theory of gravity

Unlike Noether symmetry, a metric independent general conserved current exits for non-minimally coupled scalar-tensor theory of gravity, if the trace of the energy momentum tensor vanishes. Thus, in the context of cosmology, a symmetry exists both in the early vacuum and radiation dominated era. For slow roll, symmetry is sacrificed, but at the end of early inflation, such a symmetry leads to a Friedmann-like radiation era. Late time cosmic acceleration in the matter dominated era is realized in the absence of symmetry, in view of the same decayed and red-shifted scalar field. Thus, unification of early inflation with late time cosmic acceleration with a single scalar field, may be realized.

gr-qc↗

arXiv2016

Canonical formulation of Pais-Ulhenbeck action and resolving the issue of branched Hamiltonian

Shortcomings of Dirac's constrained analysis in the context of fourth order Pais-Uhlenbeck oscillator action and the appearance of badly affected phase-space Hamiltonian for a generalized fourth order oscillator action, following Ostrogradski, Dirac and Horowitz's formalism, require a viable canonical formulation. This is achieved only after fixing appropriate variables at the end points and taking care of the counter surface terms obtained from variational principle. In the process a one-to-one correspondence between different higher order theories has been established. On the other hand the issue of branched Hamiltonian appearing in the presence of velocities with degree higher than two in the Lagrangian, has not been resolved uniquely as yet. However, often such terms appear with higher order theory, gravity in particular. Here we show that canonical formulation of higher order theory takes care of the issue elegantly.

hep-th↗

arXiv2016

Resolving the issue of branched Hamiltonian in modified Lanczos-Lovelock gravity

The Hamiltonian constraint Hc = NH = 0, defines a diffeomorphic structure on spatial manifolds by the lapse function N in general theory of relativity. However, it is not manifest in Lanczos-Lovelock gravity, since the expression for velocity in terms of the momentum is multivalued. Thus the Hamiltonian is a branch function of momentum. Here we propose an extended theory of Lanczos-Lovelock gravity to construct a unique Hamiltonian in its minisuperspace version, which results in manifest diffeomorphic invariance and canonical quantization.

hep-th↗

arXiv2015

Validating variational principle for higher order theory of gravity

Metric variation of higher order theory of gravity requires to fix the Ricci scalar in addition to the metric tensor at the boundary. Fixing Ricci scalar at the boundary implies that the classical solutions are fixed once and forever to the de-Sitter or anti de-Sitter solutions. Here, we justify such requirement from the standpoint of Noether Symmetry.

gr-qc↗

arXiv2014

Partition function of massless scalar field in Schwarzschild background

Using thermal value of zeta function instead of zero temperature, the partition function of quantized fields in arbitrary stationary backgrounds was found to be independent of undetermined regularization constant in even-dimension and the long drawn problem associated with the trace anomaly effect had been removed. Here, we explicitly calculate the expression for the coincidence limit so that the technique may be applied in some specific problems. A particular problem dealt with here is to calculate the partition function of massless scalar field in Schwarzschild background.

hep-th↗

arXiv2014

Viability of Noether symmetry of F(R) theory of gravity

Canonization of F(R) theory of gravity to explore Noether symmetry is performed treating R - 6(\frac{\ddot a}{a} + \frac{\dot a^2}{a^2} + \frac{k}{a^2}) = 0 as a constraint of the theory in Robertson-Walker space-time, which implies that R is taken as an auxiliary variable. Although it yields correct field equations, Noether symmetry does not allow linear term in the action, and as such does not produce a viable cosmological model. Here, we show that this technique of exploring Noether symmetry does not allow even a non-linear form of F(R), if the configuration space is enlarged by including a scalar field in addition, or taking anisotropic models into account. Surprisingly enough, it does not reproduce the symmetry that already exists in the literature (A. K. Sanyal, B. Modak, C. Rubano and E. Piedipalumbo, Gen.Relativ.Grav.37, 407 (2005), arXiv:astro-ph/0310610) for scalar tensor theory of gravity in the presence of R^2 term. Thus, R can not be treated as an auxiliary variable and hence Noether symmetry of arbitrary form of F(R) theory of gravity remains obscure. However, there exists in general, a conserved current for F(R) theory of gravity in the presence of a non-minimally coupled scalar-tensor theory (A. K. Sanyal, Phys.Lett.B624, 81 (2005), arXiv:hep-th/0504021 and Mod.Phys.Lett.A25, 2667 (2010), arXiv:0910.2385 [astro-ph.CO]). Here, we briefly expatiate the non-Noether conserved current and cite an example to reveal its importance in finding cosmological solution for such an action, taking F(R) \propto R^{3/2}.

astro-ph.CO↗

arXiv2014

Canonical formulation of scalar curvature squared action in higher dimensions

Canonical formulation for an action containing scalar curvature squared term $(R^2)$ in arbitrary dimension has been performed in maximally symmetric space-time. The quantum dynamics does not alter significantly from the same in $4$-dimension. Classical solution is also at par with the one presented by Starobinsky. WKB approximation peaks around the classical solution.

hep-th↗

arXiv2014

Modified theory of gravity and the history of cosmic evolution

A continuous transition from early Friedmann-like radiation era through to late time cosmic acceleration passing through a long Friedmann-like matter dominated era followed by a second phase of radiation era has been realized in modified theory of gravity containing a combination of curvature squared term, a linear term, a three-half term and an ideal fluid. Thus the history of cosmic evolution is explained by modified theory of gravity singlehandedly. The second phase of radiation-like era might provide an explanation to the hydrogen and helium reionization at low redshift.

astro-ph.CO↗

arXiv2013

Revisiting Noether symmetry approach in F(R)-tachyon Model

Recently, some authors have made a falsifiable claim that Noether gauge symmetry for F(R) theory of gravity coupled to a tachyon field enforces gauge to vanish and leads to F(R) \propto R^2, with a tachyon potential V(ϕ) \propto ϕ^{-4}. Here, we show that the analysis is completely wrong since the conserved current does not satisfy the field equations. Earlier, it has been shown that F(R) theory of gravity in vacuum or in matter dominated era admits trivial Noether symmetry for F(R) \propto R^{3/2}, because z = a^2, a being the scale factor, becomes cyclic for F(R) \propto R^{3/2}. Further, it has already been noticed that F(R) does not admit Noether symmetry when coupled to a scalar sector, minimally or non-minimally. Finally, here we show that Noether symmetry is obscure even when F(R) is coupled to a tachyon field. However, Noether symmetry for R^2 gravity coupled to a scalar taking an auxiliary variable Q different from R exists in the literature and it is not recovered from F(R) gravity. Since, canonization of a general F(R) theory of gravity is only possible treating R as the auxiliary variable, so we conclude that in general Noether symmetry of F(R) theory of gravity is obscure.

astro-ph.CO↗

arXiv2013

Field independent cosmic evolution

It has been shown earlier that Noether symmetry does not admit a form of F(R) corresponding to an action in which F(R) is coupled to scalar-tensor action for gravity or even for pure F(R) gravity taking anisotropic model into account. Here, we prove that F(R) theory of gravity does not admit Noether symmetry even if it is coupled to Tachyonic field and considering a gauge in addition. To handle such a theory, a general conserved current has been constructed under a condition which decouples higher order curvature part from the field part. This condition in principle, solves for the scale factor, independently. Thus cosmological evolution remains independent of the form of the chosen field, whether it be a scalar or a tachyon.

gr-qc↗