A non-parametric reconstruction of the deceleration parameter $q$ is carried out. The observational datasets are so chosen that they are model independent as much as possible. The present acceleration and the epoch at which the cosmic acceleration se
ts in is quite as expected, but beyond a certain redshift ($z sim 2$), a negative value of $q$ appears to be in the allowed region. A survey of existing literature is given and compared with the results obtained in the present work.
The cosmological jerk parameter $j$ is reconstructed in a non-parametric way from observational data independent of a fiducial cosmological model. From this kinematical quantity, the equation of state parameter for composite matter distribution is al
so found out. The result shows that there is a deviation from the $Lambda$CDM model close to $z=1.5$, at the $3sigma$ confidence level.
Thawing and freezing quintessence models are compared thermodynamically. Both of them are found to disobey the Generalized Second Law of Thermodynamics. However, for freezing models, there is still a scope as this breakdown occurs in the past, deep i
nside the radiation dominated era, when a standard scalar field model with a pressureless matter is not a correct description of the matter content. The thawing model has a pathological breakdown in terms of thermodynamics in a finite future.
In the present work we investigate the stability of the k-essence models allowing upto quadratic terms of the kinetic energy. The system of field equations is written as an autonomous system in terms of dimensionless variables and the stability crite
ria of the equilibria have been extensively investigated. The results strongly indicate that cosmologically consistent models dynamically evolve towards the quintessence model, a stable solution with a canonical form of the dark energy.
A comparative study of thawing and tracking models of dark energy is carried out with the help of a dynamical systems analysis. It is found that both of them have stable solutions which are consistent with the requirement of a dark energy. So none of
them is actually favored from the consideration of stability. The trackers have the interesting possibility that the present acceleration is a transient phenomenon.
The quasinormal modes of charged and uncharged massive scalar fields and also of charged Dirac fields against the background of a charged spherical black hole endowed with a scalar hair have been investigated. Special emphasis has been given to the c
ase where negative scalar charge dominates over the electric charge of the black hole which mimics an Einstein-Rosen bridge. Except for the complete monotonic behaviour of the damping (imaginary part of the quasinormal mode) against the charge of the black hole as opposed to the existence of a peak for the pure RN case, the qualitative behaviour does not appreciably change due to the presence of scalar hair.
In this work we have used the recent cosmic chronometers data along with the latest estimation of the local Hubble parameter value, $H_0$ at 2.4% precision as well as the standard dark energy probes, such as the Supernovae Type Ia, baryon acoustic os
cillation distance measurements, and cosmic microwave background measurements (PlanckTT $+$ lowP) to constrain a dark energy model where the dark energy is allowed to interact with the dark matter. A general equation of state of dark energy parametrized by a dimensionless parameter `$beta$ is utilized. From our analysis, we find that the interaction is compatible with zero within the 1$sigma$ confidence limit. We also show that the same evolution history can be reproduced by a small pressure of the dark matter.
We present a simple exact solution for the interior of a rotating star. The interpretation of the stress energy tensor as that of a fluid requires the existence of a high viscosity, which is quite expected for a rotating fluid. In spite of the negati
ve stresses, energy conditions are in fact all satisfied.
It is shown that the Jordan frame and its conformally transformed version, the Einstein frame of nonminimally coupled theories of gravity, are actually equivalent at the quantum level. The example of the theory taken up is the Brans-Dicke theory, and
the wave packet calculations are done for a homogeneous and isotropic cosmological model in the purest form of the theory, i.e., in the absence of any additional matter sector. The calculations are clean and exact, and the result obtained are unambiguous.
The present work investigates the gravitational collapse of a perfect fluid in $f(R)$ gravity models. For a general $f(R)$ theory, it is shown analytically that a collapse is quite possible. The singularity formed as a result of the collapse is found
to be a curvature singularity of shell focusing type. The possibility of the formation of an apparent horizon hiding the central singularity depends on the initial conditions.
