arXiv subjects

Abhik Kumar Sanyal

Publications and source records attributed to Abhik Kumar Sanyal.

72 records · Page 4Linked to original sources

arXiv2013

Euclidean wormholes with minimally coupled scalar fields

A detailed study of quantum and semiclassical Euclidean wormholes for Einstein's theory with a minimally coupled scalar field has been performed for a class of potentials. Massless, constant, massive (quadratic in the scalar field) and inverse (linear) potentials admit Hawking and Page wormhole boundary condition both in the classically forbidden and allowed regions. Inverse quartic potential has been found to exhibit semiclassical wormhole configuration. Classical wormholes under suitable back-reaction leading to a finite radius of the throat, where strong energy condition is satisfied, have been found for the zero, constant, quadratic and exponential potentials. Treating such classical Euclidean wormholes as initial condition, late stage of cosmological evolution has been found to remain unaltered from standard Friedmann cosmology, except for the constant potential which under back-reaction produces a term like negative cosmological constant.

gr-qc↗

arXiv2013

Why Noether symmetry of F(R) theory yields three-half power law?

Noether symmetry of F(R) theory of gravity in vacuum or in matter dominated era yields three-half power law of R. We show that this particular curvature invariant term is very special in the context of isotropic and homogeneous cosmological model as it makes the first fundamental form cyclic. As a result, it allows a unique power law solution, typical for this particular fourth order theory of gravity, both in the vacuum and in the matter dominated era. This power law solution has been found to be quite good to explain the early stage but not so special and useful to explain the late stage of cosmological evolution. The usefulness of Palatini variational technique in this regard has also been discussed.

astro-ph.CO↗

arXiv2013

Revisiting conserved currents in F(R) theory of gravity via Noether symmetry

Noether symmetry of F(R) theory of gravity in vacuum and in the presence of pressureless dust yields F(R) \propto R^{3/2} along with the conserved current \frac{d}{dt}(a\sqrt R) in Robertson-Walker metric and nothing else. Still some authors recently claimed to have obtained four conserved currents setting F(R) \propto R^{3/2} a-priori, taking time translation along with a gauge term. We show that the first one of these does not satisfy the field equations and the second one is the Hamiltonian which is constrained to vanish in gravity and thus a part and parcel of the field equations. We also show that the other two conserved currents, which do not contain time translation are the same in disguise and identical to the one mentioned above. Thus the claim is wrong.

astro-ph.CO↗

arXiv2012

Canonical formulation of curvature squared action in the presence of lapse function

Lapse function appears as Lagrange multiplier in Einstein-Hilbert action and its variation leads to the (0 0) equation of Einstein, which corresponds to the Hamiltonian constraint equation. In higher order theory of gravity the situation is not that simple. Here, we take up the curvature squared (R^2) action being supplemented by an appropriate boundary term in the background of Robertson-Walker minisuperspace metric, and show how to identify the constraint equation and formulate the Hamiltonian without detailed constraint analysis. The action is finally expressed in the canonical form $A = \int(\dot h_{ij} π^{ij} + \dot K_{ij}Π^{ij} - N{\mathcal H})dt \sim d^3 x$, where, the lapse function appears as Lagrange multiplier, once again. Canonical quantization yields Schrödinger like equation, with nice features. To show that our result is not an artifact of having reduced the theory to a measure zero subset of its configuration space, the role of the lapse function as Lagrangian multiplier has also been investigated in Bianchi-I, Kantowski-Sachs and Bianchi-III minisuperspace metrics. Classical and semiclassical solutions have finally been presented.

gr-qc↗

arXiv2012

Revisiting Noether gauge symmetry for F(R) theory of gravity

Noether gauge symmetry for F(R) theory of gravity has been explored recently. The fallacy is that, even after setting gauge to vanish, the form of F(R) \propto R^n (where n \neq 1, is arbitrary) obtained in the process, has been claimed to be an outcome of gauge Noether symmetry. On the contrary, earlier works proved that any nonlinear form other than F(R) \propto R^3/2 is obscure. Here, we show that, setting gauge term zero, Noether equations are satisfied only for n = 2, which again does not satisfy the field equations. Thus, as noticed earlier, the only admissible form that Noether symmetry is F(R) \propto R^3/2 . Noether symmetry with non-zero gauge has also been studied explicitly here, to show that it does not produce anything new.

astro-ph.CO↗

arXiv2011

Can particle creation phenomena replace dark energy?

Particle creation at the expense of gravitational field might be sufficient to explain the cosmic evolution history, without the need of dark energy at all. This phenomena has been investigated in a recent work by Lima et-al, assuming particle creation at the cost of gravitational energy in the late Universe. However, the model does not satisfy the WMAP constraint on matter-radiation equality. Here, we have suggested a model, in the same framework, which fits perfectly with SNIa data at low redshift as well as early Integrated Sachs-Wolfe effect on matter-radiation equality determined by WMAP at high redshift. Such a model, requires the presence of nearly 26% primeval matter in the form of baryons and CDM.

astro-ph.CO↗

arXiv2011

Noether symmetry for Gauss-Bonnet dilatonic gravity

Noether symmetry for Gauss-Bonnet-Dilatonic interaction exists for a constant dilatonic scalar potential and a linear functional dependence of the coupling parameter on the scalar field. The symmetry with the same form of the potential and coupling parameter exists all in the vacuum, radiation and matter dominated era. The late time acceleration is driven by the effective cos- mological constant rather than the Gauss-Bonnet term, while the later compensates for the large value of the effective cosmological constant giving a plausible answer to the well-known coincidence problem.

astro-ph.CO↗

arXiv2009

Study of symmetry in F(R) theory of gravity

An action in which the Ricci scalar is nonminimally coupled with a scalar field and contains higher order curvature invariant terms carries a conserved current under certain conditions that decouples geometric part from the scalar field. The conserved current relates the pair of arbitrary coupling parameters $f(ϕ)$ and $ω(ϕ)$ with the gravitational field variable, where $ω(ϕ)$ is the Brans-Dicke coupling parameter. The existence of such conserved current may be helpful to sketch the cosmological evolution from its early age till date in a single frame.

astro-ph.CO↗

arXiv2009

Quantum cosmology of a classically constrained nonsingular Universe

The quantum cosmological version of a nonsingular Universe presented by Mukhanov and Brandenberger in the early nineties has been developed and the Hamilton Jacobi equation has been found under semiclassical (WKB) approximation. It has been pointed out that, parameterization of classical trajectories with semiclassical time parameter, for such a classically constrained system, is a nontrivial task and requires Lagrangian formulation rather than the Hamiltonian formalism.

gr-qc↗

arXiv2007

Transient Crossing of Phantom divide line $w_Λ=-1$ under Gauss-Bonnet interaction

Smooth double crossing of the phantom barrier $w_Λ = -1$ has been found possible in cosmological model with Gauss-Bonnet-scalar interaction, in the presence of background cold dark matter. Such crossing has been observed to be a sufficiently late time phenomena and independent of the sign of Gauss-Bonnet-scalar interaction. The luminosity distance versus redshift curve shows a perfect fit with the $ΛCDM$ model up to $z=3.5$.

astro-ph↗

arXiv2007

Intermediate inflation or late time acceleration?

The expansion rate of `Intermediate inflation' lies between the exponential and power law expansion but corresponding accelerated expansion does not start at the onset of cosmological evolution. Present study of `Intermediate inflation' reveals that it admits scaling solution and has got a natural exit form it at a later epoch of cosmic evolution, leading to late time acceleration. The corresponding scalar field responsible for such feature is also found to be a tracker field for both gravity with canonical and some non-canonical form of kinetic term. Thus the so called Intermediate inflation should be considered as yet another dark energy model with asymptotic de-Sitter expansion.

astro-ph↗

arXiv2006

If Gauss-Bonnet interaction plays the role of dark energy

Gauss-Bonnet-scalar interaction has been found to play a crucial role from the beginning till the late time of cosmological evolution. A cosmological model has been constructed where the Universe starts with exponential expansion but with infinite deceleration (q), and infinite equation of state (w) parameters. During evolution it passes through the stiff fluid era, q=2, w=1, the radiation dominated era, q=1, w=1/3 and the matter dominated era, q=1/2, w=0. Finally, deceleration halts, q=0, w=-1/3, and it then encounters a transition to the accelerating phase. Asymptotically the Universe reaches yet another inflationary phase as q and w go over to -1. Such evolution is independent of the form of the potential and the sign of the kinetic energy term ie., even a noncanonical kinetic energy is unable to phantomize (w<-1) the model.

astro-ph↗

arXiv2006

Inflation is the generic feature of phantom field-not the big-rip

A class of solutions for phantom field corresponding to a generalized k-essence lagrangian has been presented, employing a simple method which provides the scope to explore many such. All the solutions having dynamical state parameter are found to touch the magic line w = -1, asymptotically. The solutions with constant equation of state can represent phantom, quitessence or an ordinary scalar field cosmologies depending on the choice of a couple of parameters of the theory. For w approximately equal to -1, quintessence and phantom models are indistinguishable through the Hubble parameter. Finally, inflation rather than big-rip has been found to be the generic feature of phantom cosmology.

astro-ph↗

arXiv2005

Scalar tensor theory of gravity carrying a conserved current

A general scalar-tensor theory of gravity carries a conserved current for a trace free minimally coupled scalar field, under the condition that the potential $V(ϕ)$ of the nonminimally coupled scalar field is proportional to the square of the parameter $f(ϕ)$ that is coupled with the scalar curvature $R$. The conserved current relates the pair of arbitrary coupling parameters $f(ϕ)$ and $ω(ϕ)$, where the latter is the Brans-Dicke coupling parameter. Thus fixing up the two arbitrary parameters by hand, it is possible to explore the symmetries and the form of conserved currents corresponding to standard and many different nonstandard models of gravity.

hep-th↗

arXiv2004

Hamiltonian formulation of curvature squared action

It has been observed earlier that, in principle, it is possible to obtain a quantum mechanical interpretation of higher order quantum cosmological models in the spatially homogeneous and isotropic background, if auxiliary variable required for the Hamiltonian formulation of the theory is chosen properly. It was suggested that for such a choice, it is required to get rid of all the total derivative terms from the action containing higher order curvature invariant terms, prior to the introduction of auxiliary variable. Here, the earlier work has been modified and it is shown that the action, $A=β\int \sqrt{-g} R^2 d^4 x$ should be supplemented by a boundary term in the form $σ=4β\int ^{3}R K \sqrt{h} d^{3}x$, where, $^3 R$, $K$ and $h$ are the Ricci scalar for three-space, trace of the extrinsic curvature and determinant of the metric on the three space respectively. The result has been tested in the background of homogeneous and anisotropic models and thus confirmed.

hep-th↗

arXiv2003

Quantum Mechanical Formulation Of Quantum Cosmology For Brane-World Effective Action

Canonical quantization of the Brane-World effective action presented by Kanno and Soda containing higher order curvature invariant terms, has been performed. It requires introduction of an auxiliary variable. As observed in a series of publications by Sanyal and Modak, here again we infer that properly chosen auxiliary variable leads to a Schrodinger like equation where the kinetic part of a canonical variable disentangles from the rest of the variables giving a natural quantum mechanical flavour of time. Further, the effective Hamiltonian turns out to be hermitian, leading to the continuity ewuation. Thus, a quantum mechanical probability inter pretation is plausible. Finally, the extremization of the effective potential leads to Einstein's equation and a well behaved classical solution, which is a desirable feature of the gravitational action containing higher order curvature invariant terms.

gr-qc↗

arXiv2002

Quantum Mechanical Probability Interpretation In The Mini-superspace Model Of Higher Order Gravity Theory

It has been shown that inclusion of higher order curvature invariant terms in the Robertson-Walker minisuperspace model of the Einstein-Hilbert action leads to Schrodinger like equation, whose corresponding effective action is hermitian. Thus, it is possible to write the continuity equation in a straight forward manner, which reveals a quantum mechanical probability interpretation of the theory.

gr-qc↗

arXiv2001

Noether and some other dynamical symmetries in Kantowski-Sachs model

The forms of coupling of the scalar field with gravity, appearing in the induced theory of gravity, and the potential are found in the Kantowski-Sachs model under the assumption that the Lagrangian admits Noether symmetry. The form thus obtained makes the Lagrangian degenerate. The constrained dynamics thus evolved due to such degeneracy has been analysed and a solution has also been presented which is inflationary in behaviour. It has further been shown that there exists other technique to explore the dynamical symmetries of the Lagrangian and that is simply by inspecting the field equations. Through this method, Noether along with some other dynamical symmetries are found, which do not make the Lagrangian degenerate.

gr-qc↗