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.Comment: 14 pages in Quantum Stud.: Math. Found. (2014

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.Comment: 10 page

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.Comment: 7 pages,Late

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, $A=\beta\int \sqrt{-g} R^2 d^4 x$ should be supplemented by a boundary term in the form $\sigma=4\beta\int ^{3}R K \sqrt{h} d^{3}x$, 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.Comment: 15 pages, late