Anisotropic Bianchi type V perfect fluid cosmological models in Lyra’s geometry

The law of variation for mean Hubble’s parameter with average scale factor, in an anisotropic Bianchi type V cosmological space–time, is discussed within the frame work of Lyra’s manifold. The variation of Hubble’s parameter, which gives a constant value of deceleration parameter, generates two types of solutions for the average scale factor; one is the power-law and the other one is of exponential form. Using these two forms, new classes of exact solutions of the field equations have been found for a Bianchi type V space–time filled with perfect fluid in Lyra’s geometry by considering a time-dependent displacement field. The physical and kinematical behaviors of the singular and non-singular models of the universe are examined. Exact expressions for look-back time, luminosity distance and event horizon versus redshift are also derived and their significance are discussed in detail. It has been observed that the solutions are compatible with the results of recent observations.     

Spéculation sur la cosmologie quantique primordiale

An old-fashioned axiomatic formalism for the quantization of the gravitational field is adapted to a recently introduced notion of cosmological gravitational wave. Dynamical equations for the quantum field are proposed. An outline for the primordial cosmological scenario is suggested.

     

Cosmological principle and primordial spinor fields

An exact solution of Dirac's equation in an open Robertson-Walker universe is constructed such that the corresponding energy-momentum densityT _µv obeys the cosmological principle. However, in anopen universe, this principlemust always be violated by the other physical densities of the cosmological solution (e.g. pseudoscalar, (axial-) current and polarization). If the current densityj _µ = isrequired to obey the cosmological principle, then the universe must beflat.     

Gravitational waves without gravitons

The radiation connection induced on an isotropic hypersurface of a Lorentz manifold is described. Consequences for the energy tensor in Einstein field equation are analyzed. A cosmological interpretation is proposed.     

Back-reaction equations for isotropic cosmologies when nonconformal particles are created

A model proposed some years ago by Hartle to study the back reaction in a cosmological model due to the creation of massless non-conformally coupled particles is reexamined. The model consists of a spatially flat FRW spacetime with a classical source made of two perfect fluids one a radiative fluid and the other a baryonic fluid with the equation of state of dust, and it is assumed that the ratio of baryons to photons is small. The back-reaction equations for the cosmological scale factor are derived using a CTP (closed time path) effective action method. Making use of the connection, in the semiclassical context, between the CTP effective action and the influence functional in quantum statistical mechanics, improved back-reaction equations are derived which take into account the fluctuations of the stress-energy tensor of the quantum field. These new dynamical equations are real and causal and predict stochastic fluctuations for the cosmological scale factor.     

Matching stationary spacetimes

Using the quasi-Maxwell formalism, we derive the necessary and sufficient conditions for the matching of two stationary spacetimes along a stationary time-like hypersurface, expressed in terms of the gravitational and gravitomagnetic fields and the 2-dimensional matching surface on the space manifold. We prove existence and uniqueness results to the matching problem for stationary perfect fluid spacetimes with spherical, planar, hyperbolic and cylindrical symmetry. Finally, we find an explicit interior for the cylindrical analogue of the NUT spacetime.     

Casimir effect in the Hořava–Lifshitz gravity with a cosmological constant

We calculate the Casimir energy of a massless scalar field confined between two nearby parallel plates formed by ideal uncharged conductors, placed tangentially to the surface of a sphere with mass M$M$ and radius R$R$. To this end, we take into account a static and spherically symmetric solution of Ho?ava–Lifshitz (HL) gravity, with a cosmological constant term, in lower orders of approximation, considering both weak-field and infrared limits. We show that the Casimir energy, just in the second order weak-field approximation, is modified due to the parameter of the HL gravity as well as to the cosmological constant.     

A class of new LRS Bianchi type-I perfect fluid universes with decaying vacuum energy density Λ

A class of new LRS Bianchi type-I cosmological models with a variable cosmological term is investigated in presence of perfect fluid. A procedure to generate new exact solutions to Einstein’s field equations is applied to LRS Bianchi type-I space-time. Starting from some known solutions a class of new perfect fluid solutions of LRS Bianchi type-I are obtained. The cosmological constant Λ is found to be positive and a decreasing function of time which is supported by results from recent supernovae Ia observations. The physical and geometric properties of spatially homogeneous and anisotropic cosmological models are discussed.     

Exact solutions of the Klein–Gordon equation in the Kerr–Newman background and Hawking radiation

This work considers the influence of the gravitational field produced by a charged and rotating black hole (Kerr–Newman spacetime) on a charged massive scalar field. We obtain exact solutions of both angular and radial parts of the Klein–Gordon equation in this spacetime, which are given in terms of the confluent Heun functions. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation of charged massive scalar particles.     

Meron and elliptic solutions in conformally flat space-time

The idea recently advanced by the author that particles arise as distortions of a riemannian background is pursued further. Such distortions represent conformally flat solutions of Einstein's “cosmological” equations extremely large “cosmological” constant. It is shown in particular that merons can be generated by perfect fluid or neutral superfluid distributions of energy and momentum. Perfect fluids can also generate elliptic plane waves of the type discussed by Petiau.     

Singularity formation in general relativistic dynamics of homogeneous scalar fields

Collapsing dynamics of a wide class of self-interacting, self-gravitating homogeneous scalar field models is analyzed. The assumptions made on the potential satisfy some general conditions allowing to show that the generic evolution is divergent in a finite time. Combining results shown here with the ones from [R. Giambó, F. Giannoni, G. Magli, J. Math. Phys. 49 (2008) 042504], dealing with sub-exponential growing potentials, allows us to obtain the same results of singularity formation for more general potentials. Moreover it turns out that these models can be completed to find radiating collapsing star models of the Vaidya type, where blackholes are generically formed.     

Relic Density of Asymmetric Dark Matter in Modified Cosmological Scenarios

We discuss the relic abundance of asymmetric Dark Matter particles in modified cosmological scenarios where the Hubble rate is changed with respect to the standard cosmological scenario. The modified Hubble rate leaves its imprint on the relic abundance of asymmetric Dark Matter particles if the asymmetric Dark Matter particles freeze-out in this era. For generality we parameterize the modification of the Hubble rate and then calculate the relic abundance of asymmetric Dark Matter particles and anti-particles. We find the abundances for the Dark Matter particles and anti-particles are enhanced in the modified cosmological models. The indirect detection signal is possible for the asymmetric Dark Matter particles due to the increased annihilation rate in the modified cosmological models. Applying Planck data, we find the constraints on the parameters of the modified cosmological models.     

Rotating viscous-fluid cosmologies with scalar field and heat flux

Rotating cosmological models under the influence of both shear and bulk viscosity, together with scalar field and heat flow, are studied. Exact solutions of the field equations are obtained. The solutions have nonzero expansion, shear, and rotation. The properties of the solutions are studied and the temperature distribution is also given explicitly.     

Physics of Dark Energy Particles

We consider the astrophysical and cosmological implications of the existence of a minimum density and mass due to the presence of the cosmological constant. If there is a minimum length in nature, then there is an absolute minimum mass corresponding to a hypothetical particle with radius of the order of the Planck length. On the other hand, quantum mechanical considerations suggest a different minimum mass. These particles associated with the dark energy can be interpreted as the “quanta” of the cosmological constant. We study the possibility that these particles can form stable stellar-type configurations through gravitational condensation, and their Jeans and Chandrasekhar masses are estimated. From the requirement of the energetic stability of the minimum density configuration on a macroscopic scale one obtains a mass of the order of 10⁵⁵ g, of the same order of magnitude as the mass of the universe. This mass can also be interpreted as the Jeans mass of the dark energy fluid. Furthermore we present a representation of the cosmological constant and of the total mass of the universe in terms of ‘classical’ fundamental constants.     

Imploding-exploding gravitational waves

A solution of Einstein's vacuum field equations is constructed describing an imploding spherical impulsive gravitational wave followed by an exploding similar wave. The two waves propagate in Minkowskian spacetime and the history of the process is the past and future sheets of the null-cone of an event (taken as origin) in the spacetime. The solution is a superposition of two of Penrose's impulsive wave solutions and is described in a single coordinate system in which the metric tensor components are continuous across the histories of the wave fronts.     

Soliton geometry and the vacuum gravitational field equations

A soliton geometry is introduced on manifolds with arbitrary dimensions. The usual soliton connection 1-form defined by Crampin et al. is recovered when the soldering form is a 0-form. It is shown that Einstein's vacuum field equations admit a soliton connection and a soldering 1-form. An associated linear equation with a spectral parameter of Einstein's vacuum field equations are found and some properties of this equation are explored. An example of a Bäcklund transformation is also given.     

Symmetries of the Einstein Hamiltonian

The vacuum Einstein equations for metrics that have two commuting spacelike Killing vector fields are studied from a Hamiltonian point of view using the Ashtekar variables. It is shown that the evolution equations are equivalent to those of a modified SL(2) principal chiral model with a time dependent coupling constant. This fact is used to extract an infinite set of symmetries of the Einstein Hamiltonian via a generalized zero-curvature formulation. These symmetries give evolving observables explicitly on the phase space, and may be viewed as providing an infinite set of solutions of the Hamiltonian Einstein equations. The possibility of quantization using these observables is briefly discussed.     

Spatially Homogeneous Bianchi Type-I Universes with Variable G and Λ

In this paper, we have studied the cosmological models of Bianchi type-I universes in a different basic form filled with bulk viscous fluid, in the presence of time-dependent gravitational as well as cosmological constants. A set of new exact cosmological solutions have been obtained in both full and truncated causal theories. These solutions are suitable for describing the evolution of the universe in its early stages. The physical and dynamical consequences have been discussed in detail.     

Anisotropic Cosmological Models with Variable G and Decaying Vacuum Energy

We present Bianchi type-I cosmological models with a perfect fluid source and time-dependent gravitational and cosmological constants based on new exact solutions of Einstein’s equations. The perfect fluid is chosen to obey a barotropic equation of state. The models obtained represent a radiation dominated phase and a dust era. In some of the models the expansion changes from a decelerating phase to an accelerating one and these models asymptotically tend to the de Sitter universe. The paper is dedicated to late Prof. S.R. Roy, Ex-Head, Department of Mathematics, Banaras Hindu University, Varanasi, India.