Einstein's field equations are considered for a locally rotationally symmetric Bianchi Type-II space–time in the presence of a massless scalar field with a scalar potential. Exact solutions of scale factors and other physical parameters are obtained by using a special law of variation for Hubble's parameter that yields a constant value of deceleration parameter. To get inflationary solutions, a flat region is considered in which the scalar potential is constant. Power-law and exponential cases are studied and in both solutions there is an anisotropic expansion of the cosmic fluid, but the fluid has vanishing vorticity. A detailed study of geometrical and kinematical properties of solutions has been carried out.

The effect of bulk viscosity on the early evolution of Universe for a spatially homogeneous and isotropic Robertson-Walker model is considered. Einstein's field equations are solved by using `gamma-law' equation of state $p = (\gamma - 1)\rho$, where the adiabatic parameter gamma $(\gamma)$ depends on the scale factor of the model. The `gamma' function is defined in such a way that it describes a unified solution of early evolution of the Universe for inflationary and radiation-dominated phases. The fluid has only bulk viscous term and the coefficient of bulk viscosity is taken to be proportional to some power function of the energy density. The complete general solutions have been given through three cases. For flat space, power-law as well as exponential solutions are found. The problem of how the introduction of viscosity affects the appearance of singularity, is briefly discussed in particular solutions. The deceleration parameter has a freedom to vary with the scale factor of the model, which describes the accelerating expansion of the Universe.

In this paper we discuss the variation law for Hubble's parameter with average scale factor in a spatially homogeneous and anisotropic Bianchi type-V space-time model, which yields constant value of the deceleration parameter. We derive two laws of variation of the average scale factor with cosmic time, one is of power-law type and the other is of exponential form. Exact solutions of Einstein field equations with perfect fluid and heat conduction are obtained for Bianchi type-V space-time in these two types of cosmologies. In the cosmology with the power-law, the solutions correspond to a cosmological model which starts expanding from the singular state with positive deceleration parameter. In the case of exponential cosmology, we present an accelerating non-singular model of the Universe. We find that the constant value of deceleration parameter is reasonable for the present day Universe and gives an appropriate description of evolution of Universe. We have also discussed different types of physical and kinematical behaviour of the models in these two types of cosmologies.

A spatially homogeneous locally-rotationally-symmetric (LRS) Bianchi type-V cosmological model is considered with a perfect fluid in general relativity. We present two types of cosmologies (power-law and exponential forms) by using a law of variation for the mean Hubble parameter that yields a constant value for the deceleration parameter. We discuss the physical properties of the non-flat and flat models in each cosmology. Exact solutions that correspond to singular and non-singular models are presented. In a generic situation, models can be interpolated between different phases of the Universe. We find that a constant value for the deceleration parameter is reasonable for a description of different phases of the Universe. We arrive at the conclusion that the Universe decelerates when the value of the deceleration parameter is positive whereas it accelerates when the value is negative. The dynamical behaviours of the solutions and kinematical parameters like expansion, shear and the anisotropy parameter are discussed in detail in each section. Exact expressions for look-back time, luminosity distance and event horizon vs. redshift are derived and their significances are discussed in some detail. It has been observed that the solutions are compatible with the results of recent observations.

In this paper we present a spatially homogeneous locally-rotationally-symmetric (LRS) Bianchi type-V cosmological model with perfect fluid and heat flow. A general approach is introduced to solve Einstein’s field equations using a law of variation for the mean Hubble parameter, which is related to average scale factor of the model that yields a constant value for the deceleration parameter. Exact solutions that correspond to singular and non-singular models are found with heat flow. The physical constraints on the solution and, in particular, the thermodynamical laws that govern such solutions are discussed in some detail.

Nonlinear optical studies in semiconductor-doped glasses (SDGs) are performed under femtosecond laser pulse excitation. Z-scan experiments with 800 nm wave- length pulses are used to excite SDG samples in the resonance and non-resonance regimes. Schott colour glass filter OG 515 shows stronger two-photon absorption than GG 420 and both the samples exhibit positive nonlinearity. However, in resonantly excited RG 850 the intensity-dependent Z-scan shows transition from saturable to reverse saturable absorption behaviour with the increase in intensity.

In this paper, we study anisotropic Bianchi-V Universe with magnetic field and bulk viscous fluid in string cosmology. Exact solutions of the field equations are obtained by using the equation of state (EoS) for a cloud of strings, and a relationship between bulk viscous coefficient and scalar expansion. The bulk viscous coefficient is assumed to be inversely proportional to the expansion scalar. It is interesting to examine the effects of magnetized bulk viscous string model in early and late stages of evolution of the Universe. This paper presents different string models like geometrical (Nambu string), Takabayasi (p-string) and Reddy string models by taking certain physical conditions. We discuss the nature of classical potential for viscous fluid with and without magnetic field. The presence of bulk viscosity stops the Universe from becoming empty in its future evolution. It is observed that the Universe expands with decelerated rate in the presence of viscous fluid with magnetic field whereas, it expands with marginal inflation in the presence of viscous fluid without magnetic field. The other physical and geometrical aspects of each string model are discussed in detail.