Debashis Gangopadhyay

Evolution of primordial black holes in Jordan–Brans–Dicke cosmology

We consider the evolution of primordial black holes in a generalized Jordan-BransDicke cosmological model where both the Brans-Dicke scalar field and its coupling to gravity are dynamical functions determined from the evolution equations. The evaporation rate for the black holes is different from the case in standard cosmology. We show that the accretion of radiation can proceed effectively in the radiation dominated era. It follows that the black hole lifetime shortens for low initial mass, but increases considerably for larger initial mass, thus providing a mechanism for the survival of primordial black holes as candidates of dark matter. We derive a cut-off value for the initial black hole mass, below which primordial black holes evaporate out in the radiation dominated era, and above which they survive beyond the present era.

Probing the Leggett-Garg Inequality for Oscillating Neutral Kaons and Neutrinos

The Leggett-Garg inequality (LGI) as a temporal analogue of Bells inequality, derived using the notion of realism, is applied in a hitherto unexplored context involving the weak interaction induced two-state oscillations of decaying neutral kaons and neutrinos. The maximum violation of LGI obtained from the quantum mechanical results is significantly higher for the oscillating neutrinos compared to that for the kaons. Interestingly, the effect of CP non-invariance for the kaon oscillation is to enhance this violation while, for neutrinos, it is sensitive to the value of the mixing parameter.

The Hawking temperature in the context of dark energy

An emergent-gravity metric incorporating k-essence scalar fields ? having a Born-Infeld?type Lagrangian is mapped into a metric whose structure is similar to that of a blackhole of large mass M that has swallowed a global monopole. However, here the field is not that of a monopole but rather that of a k-essence scalar field. If ?emergent are the solutions of the emergent-gravity equations of motion under cosmological boundary conditions at ?, then for the rescaled field has exact correspondence with ? with ?(r,t)?=??1(r)?+??2(t). The Hawking temperature of this metric is , taking the speed of light c?=?1. Here is the kinetic energy of the k-essence field ? and K is always less than unity, kB is the Boltzmann constant. This is phenomenologically interesting in the context of Belgiorno et al.s gravitational analogue experiment.

Logarithm of the scale factor as a generalised coordinate in a Lagrangian for dark matter and dark energy

Abstract A Lagrangian for the k-essence field is set up with canonical kinetic terms and incorporating the scaling relation of [R.J. Scherrer, Phys. Rev. Lett. 93 (2004) 011301]. There are two degrees of freedom, viz., q ( t ) = ln a ( t ) ( a ( t ) is the scale factor) and the scalar field ϕ, and an interaction term involving ϕ and q ( t ) . The Euler–Lagrange equations are solved for q and ϕ. Using these solutions quantities of cosmological interest are determined. The energy density ρ has a constant component which we identify as dark energy and a component behaving as a −3 which we call dark matter. The pressure p is negative for time t → ∞ and the sound velocity c s 2 = ∂ p ∂ ρ ≪ 1 . When dark energy dominates, the deceleration parameter Q → − 1 while in the matter dominated era Q ∼ 1 / 2 . The equation of state parameter w = p / ρ is shown to be consistent with w = p / ρ ∼ − 1 for dark energy domination and during the matter dominated era we have w ∼ 0 . Bounds for the parameters of the theory are estimated from observational data.

The k -essence scalar field in the context of Supernova Ia observations

A k-essence scalar field model having (non-canonical) Lagrangian of the form L=−V(ϕ)F(X) where

Lorentz-preserving fields in Lorentz-violating theories

X=\frac{1}{2}g^{\mu\nu}\nabla_{\mu}\phi\nabla_{\nu}\phi

Estimating temperature fluctuations in the early universe

with constant V(ϕ) is shown to be consistent with luminosity distance–redshift data observed for type Ia Supernova. For constant V(ϕ), F(X) satisfies a scaling relation which is used to set up a differential equation involving the Hubble parameter H, the scale factor a and the k-essence field ϕ. H and a are extracted from SNe Ia data and using the differential equation the time dependence of the field ϕ is found to be: ϕ(t)∼λ0+λ1t+λ2t2. The constants λi have been determined. The time dependence is similar to that of the quintessence scalar field (having canonical kinetic energy) responsible for homogeneous inflation. Furthermore, the scaling relation and the obtained time dependence of the field ϕ are used to determine the X-dependence of the function F(X).

On a cosmological invariant as an observational probe in the early universe

We identify a fairly general class of field configurations (of spins 0, ½ and 1) which preserve Lorentz invariance in effective field theories of Lorentz violation characterized by a constant timelike vector. These fields concomitantly satisfy the equations of motion yielding cubic dispersion relations similar to those found earlier. They appear to have prospective applications in inflationary scenarios.

THE CNOT QUANTUM LOGIC GATE USING q-DEFORMED OSCILLATORS

AbstractA lagrangian for a k-essence field is constructed for a constant scalar potential, and its form is determined when the scale factor is very small as compared to the present epoch but very large as compared to the inflationary epoch. This means that one is already in an expanding and flat universe. The form is similar to that of an oscillator with time-dependent frequency. Expansion is naturally built into the theory with the existence of growing classical solutions of the scale factor. The formalism allows one to estimate the temperature fluctuations of the background radiation at these early stages (as compared to the present epoch) of the Universe. If the temperature is Ta at time ta and Tb at time tb (tb > ta), then, for small times, the probability evolution for the logarithm of the inverse temperature can be estimated as