Some results in the general scalar tensor theory

Raychaudhuri-type equations are written for a cosmological model filled with a perfect fluid and obeying the equations of general scalar-tensor theory proposed by Nordtvedt. It is found that a non-rotating cosmological model may, in general, have a minimum volume. The Hawking-Penrose energy condition suggests that the singularity can be avoided in this theory.     

A dark energy model in a scalar tensor theory of gravitation

LRS Bianchi type-I dark energy model with variable equation of state (EoS) parameter is presented in the scalar-tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A 113:467, 1986). To get a determinate solution of the field equations we take the help of special law of variation for Hubble’s parameter presented by Bermann (Nuovo Cimento B 74:182, 1983) which yields a cosmological model with negative constant deceleration parameter. Some physical and kinematical properties of the model are also discussed.     

Axially symmetric cosmological models in a scalar tensor theory based on Lyra manifold

Axially symmetric cosmological models are obtained in a scalar tensor theory proposed by Sen (Z. Phys. 149:311, 1957) based on Lyra manifold with time dependent β in the presence of string source, perfect fluid distribution, dust distribution and thick domain walls. Some physical and geometrical properties of these models are discussed.     

A new scalar tensor theory for gravity and the flat rotation curves of spiral galaxies

In this paper we reproduce flat rotation curves of spiral galaxies by discussing a scalar tensor theory of gravity which includes the Higgs field as scalar field. The galaxy density distribution is assumed to be homogeneous or polytropic and in the galaxy core there exists a large concentrated mass.     

Bianchi type-VI0 vacuum model in the general scalar-tensor theory of gravitation

The spatially-homogeneous and anisotropic Bianchi type-VI₀ cosmological model is obtained in the Nordtvedt-Barker general scalar-tensor theories of gravitation. Exact solutions of the Nordtvedt-Barker field equations in vacuum are presented and studied.     

Bianchi Type-1 vacuum models in modified theory of general relativity

In this paper, the problem of spatially homogeneous and an isotropic Bianchi type-1 space time with perfect fluid distribution is considered in Barber's second theory of gravitation. To obtain determinate solutions, we have assumed the equation of statep= γρ, 0 ≤ γ ≤ 1. It is observed that the general fluid distribution degenerates isotropic vacuum model whenγ = 1 and Λ < 0. Further it is observed that the vacuum model obtained in case of γ = 0, ρ = 0 andΛ = 0, reduces to well known Kasner model in Einstein's theory. Some physical and geometrical aspects of the models together with singularities in the models are also discussed This revised version was published online in July 2006 with corrections to the Cover Date.     

LRS Bianchi type-II Universe with cosmic strings and bulk viscosity in a scalar tensor theory of gravitation

A spatially homogeneous and anisotropic Bianchi type-II cosmological model is obtained in a scalar tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A 130:467, 1986) when the source for energy momentum tensor is a bulk viscous fluid containing one-dimensional cosmic strings. Some physical and kinematical properties of the model are also discussed.     

Conformally-invariant scalar field with trace-free energy-momentum tensor in Robertson-Walker models

Exact solutions of Einstein's field equations for a conformally-invariant scalar field with trace-free energy-momentum tensor is presented for the Robertson-Walker models withK=+1, –1. The physical properties of the solution are also studied.     

The scalar, vector and tensor contributions of a stochastic background of magnetic fields to cosmic microwave background anisotropies

We study the contribution of a stochastic background (SB) of primordial magnetic fields (PMFs) on the anisotropies in temperature and polarization of the cosmic microwave background (CMB) radiation. A SB of PMF modelled as a fully inhomogeneous component induces non-Gaussian scalar, vector and tensor metric linear perturbations. We give the exact expressions for the Fourier spectra of the relevant energy–momentum components of such a SB, given a power-law dependence parametrized by a spectral index   n_B   for the magnetic field power spectrum cut at a damping scale k _D. For all the values of   n_B   considered here, the contribution to the CMB temperature pattern by such a SB is dominated by the scalar contribution and then by the vector one at higher multipoles. We also give an analytic estimate of the scalar contribution to the CMB temperature pattern.     

The conformal potential of the stationary axisymmetric vacuum

In a stationary axisymmetric vacuum gravitational field, the conformal structure of the 3-space is determined by the symmetric, trace free and divergence-less tensor Y_ir. Using the Killing vector Kⁱ of the axisymmetry, the conformal potential U can be defined by U,_i = _εijkKjY^krK_r. Conversely, the tensor Y_ik is given algebraically in terms of the gradient U,_i of the conformal potential. An attempt is made here to re-formulate the field equations R_λμ = 0 in terms of the conformal potential. Introducing the Ernst potential as a complex coordinate, the cylindrical radius can be eliminated from the field equations.     

Inhomogeneous cosmological models in the presence of massless scalar fields

Non-static inhomogeneous cosmological models are obtained in general relativity for the case of a plane symmetric massless scalar field with cosmological constant A,when the source of the gravitational field is a viscous fluid.Some physical and geometrical behaviors of the solutions are also discussed.     

Bianchi type-I universe in the presence of zero-mass scalar fields

An exact Bianchi type-I cosmological model in the presence of zero-mass scalar fields is obtained when the source of the gravitational field is a perfect fluid with pressure equal to energy density. Some properties of the model are discussed.     

A plane-symmetric universe in the presence of zero-mass scalar fields

A non-static plane-symmetric cosmological model in the presence of zero-mass scalar fields is obtained when the source of the gravitational field is a perfect fluid with pressure equal to energy density. Some properties of the model are discussed.     

Bianchi type-VI0 universe in the presence of zero-mass scalar fields

An exact Bianchi type-VI₀ cosmological model in the presence of zero-mass scalar fields is obtained when the source of the gravitational field is a perfect fluid with pressure equal to energy density. Some physical properties of the model are discussed.     

Bianchi type-III cosmological model in the presence of zero-mass scalar fields

An exact Bianchi type-III cosmological model in the presence of zero-mass scalar fields is obtained when the source of the gravitational field is a perfect fluid with pressure equal to energy density. Some properties of the model are also discussed.     

Bianchi type-II cosmological models in the presence of zero-mass scalar fields

The exact Bianchi type-II vacuum- and stiff-fluid cosmological models, in the presence of zero-mass scalar fields, are obtained. Some physical properties of the models are also discussed.     

Bianchi type-V cosmological model with perfect fluid using negative constant deceleration parameter in a scalar tensor theory based on Lyra Manifold

An exact Bianchi type-V perfect fluid cosmological model is obtained in a scalar tensor theory proposed by Sen (Z. Phys. 149:311, 1957) based on Lyra Manifold in case of β is a constant and it is shown that this cosmological model exists only in the case of Radiation Universe (ρ=3p) if β is a function of ‘t’ using negative constant deceleration parameter. Some physical and geometrical properties of these models are discussed.