Particle production in higher derivative theory

The effect of particle production on the evolution of the spatially flat Friedmann-Lemaitre-Robertson-Walker cosmological model during the early stages of the universe is analysed in the framework of higher derivative theory. The universe has been considered as an open thermodynamic system where particle production gives rise to a supplementary negative creation pressure in addition to the thermodynamic pressure. The dynamical behaviour of both exponential as well as power law solutions have been discussed.     

Pre-inflationary homogenization of scalar field cosmologies

We consider the evolution of covariant and gauge invariant linear density perturbations of scalar field cosmologies using a dynamical systems? approach. We find conditions for which the perturbations decay in time, so that the spacetime approaches a homogeneous solution which inflates, for quadratic and exponential potentials. This pre-inflationary homogenization is found to be stable in the potentials? parameter spaces. Furthermore, in each case, we determine the minimum size of the resultant homogeneous patch and show that, for quadratic potentials, the resulting inflationary solutions include those with the necessary number of e-folds.     

Noether symmetry in the higher order gravity theory

Noether symmetry for scalar tensor theory including curvature quadratic term has been explored, with the introduction of an auxiliary variable. Introduction of an auxiliary variable in the action facilitates in transforming the fourth order field equations to the second order field equations. Introduction of Noether symmetry in the action yield the coupling function () and the potential V(). The application of Noether symmetry further turned out to be powerful tool to find the solution of the field equations. A few physically reasonable solutions like power law inflation are presented.     

An isotropic cosmological model in general scalar tensor theory

An isotropic homogeneous cosmological model with Robertson-Walker line element is studied in general scalar tensor theory where the parameterω is a function of the scalar field. The model consists of perfect fluid with the equation of statep=ερ. Exact solutions are obtained in Dicke’s conformally transformed units forε=1 andε=1/3 assuming a functional relationship betweenω and the scalar fieldφ. The properties are compared with vacuum models in this theory.     

Diagrammar in classical scalar field theory

In this paper we analyze perturbatively a g?⁴classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that a universal supersymmetry present in the classical path-integral mentioned above is responsible for the cancelation of various diagrams. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplify the calculations and make the classical perturbative calculations almost “identical” formally to the quantum ones. Using the super-diagrams technique, we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem.     

Accelerating cosmology in modified gravity with scalar field

The modified gravity with 1/R term (R being the scalar curvature) and the Einstein-Hilbert term is studied by incorporating the phantom scalar field. A number of cosmological solutions are derived in the presence of the phantom field in the perfect fluid background. It is shown: the current inflation obtained in the modified gravity is affected by the existence of the phantom field.     

Exact solutions for the massless plane symmetric scalar field in general relativity,with cosmological constant

The Klein–Gordon equations are solved for the case of a plane-symmetric static massless scalar field in general relativity with cosmological constant, generalizing the solutions found by Taub, Novotny and Horsky, and Singh. A separate class of solutions is obtained in which the metrics reduce to flat space in the limit that .The static solutions can be used to generate time-dependent cosmological solutions, one of which exhibits rapid inflation followed by continued exponential expansion at all later times.     

Inflationary solutions in general scalar tensor theory of gravitation

Extended inflation solution in Brans-Dicke theory given by Mathiazhagan and Johri (MJ) is shown as the unique solution only if the scale factor is assumed to be a power function of the scalar field. Only the consistent solution amongst the set of solutions given by Patra, Roy and Ray is found identical to the MJ solution. Both exponential inflation and power function inflation are studied in general scalar tensor theory where the parameter to is a function of the scalar, field. It is noted that exponential inflation is forbidden in Brans-Dicke theory wherew is a constant.     

Model for a Universe described by a non-minimally coupled scalar field and interacting dark matter

In this work the evolution of a Universe model is investigated where a scalar field, non-minimally coupled to space-time curvature, plays the role of quintessence and drives the Universe to a present accelerated expansion. A non-relativistic dark matter constituent that interacts directly with dark energy is also considered, where the dark matter particle mass is assumed to be proportional to the value of the scalar field. Two models for dark matter pressure are considered: the usual one, pressureless, and another that comes from a thermodynamic theory and relates the pressure with the coupling between the scalar field and the curvature scalar. Although the model has a strong dependence on the initial conditions, it is shown that the mixture consisted of dark components plus baryonic matter and radiation can reproduce the expected red-shift behavior of the deceleration parameter, density parameters and luminosity distance.     

Effective potentials in the Lifshitz scalar field theory

We study the one-loop effective potentials of the four-dimensional Lifshitz scalar field theory with the particular anisotropic scaling z=2, and the mass and the coupling constants renormalization are performed whereas the finite counterterm is just needed for the highest order of the coupling because of the mild UV divergence. Finally, we investigate whether the critical temperature for the symmetry breaking can exist or not in this approximation.     

The nature of singularities in plane symmetric scalar field cosmologies

The nature of the initial singularity in spatially compact plane symmetric scalar field cosmologies is investigated. It is shown that this singularity is crushing and velocity dominated and that the Kretschmann scalar diverges uniformly as it is approached. The last fact means in particular that a maximal globally hyperbolic spacetime in this class cannot be extended towards the past through a Cauchy horizon. A subclass of these spacetimes is identified for which the singularity is isotropic.     

Nonequilibrium dynamics of scalar fields in a thermal bath

We study the approach to equilibrium for a scalar field which is coupled to a large thermal bath. Our analysis of the initial value problem is based on Kadanoff-Baym equations which are shown to be equivalent to a stochastic Langevin equation. The interaction with the thermal bath generates a temperature-dependent spectral density, either through decay and inverse decay processes or via Landau damping. In equilibrium, energy density and pressure are determined by the Bose-Einstein distribution function evaluated at a complex quasi-particle pole. The time evolution of the statistical propagator is compared with solutions of the Boltzmann equations for particles as well as quasi-particles. The dependence on initial conditions and the range of validity of the Boltzmann approximation are determined.     

Generalized scalar tensor theory in four and higher dimensional spherically symmetric space-time

In this paper, we have studied generalized scalar tensor theory for spherically symmetric models, both in four and higher dimensions with a bulk viscous fluid. We have considered both exponential and power law solutions with some assumptions among the physical parameters and solutions have been discussed.     

Exact solutions for the spherically symmetric vacuum field in the general scalar tensor theory

A conformai technique is given for the generation of exact solutions for the spherically symmetric vacuum field in the general Bergmann-Wagoner-Nordtvedt scalar-tensory theory with vanishing cosmological constant. We discuss in particular the solution for Schwinger's theory and for models with ⁿ coupling or with curvature coupling. It appears that all theories with vanishing cosmological term lead to the presence of naked singularities.     

Dynamic field theory and equations of motion in cosmology

We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein’s equations in the form of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast δρ/ρ≤1$\delta \rho /\rho \le 1$. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits δρ/ρ?1$\delta \rho /\rho ?1$. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of these equations with the bare stress–energy tensor of the baryonic matter. We explicitly work out the covariant field equations of the successive post-Friedmannian approximations of Einstein’s equations in cosmology and derive equations of motion of large and small scale inhomogeneities of dark matter and dark energy. We apply these equations to derive the post-Friedmannian equations of motion of baryonic matter comprising stars, galaxies and their clusters.     

Three-dimensional massive scalar field theory and the derivative expansion of the renormalization group

We show that non-perturbative fixed points of the exact renormalization group, their perturbations and corresponding massive field theories can all be determined directly in the continuum — without using bare actions or any tuning procedure. As an example, we estimate the universal couplings of the non-perturbative three-dimensional one-component massive scalar field theory in the Ising model universality class, by using a derivative expansion (and no other approximation). These are compared to the recent results from other methods. At order derivative-squared approximation, the four-point coupling at zero momentum is better determined by other methods, but factoring this out appropriately, all our other results are in very close agreement with the most powerful of these methods. In addition we provide for the first time, estimates of the n-point couplings at zero momentum, with n = 12, 14, and the order momentum-squared parts with n = 2,…, 10.