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A new class of cylindrically symmetric inhomogeneous cosmological models for perfect fluid distribution with electromagnetic field is obtained in the context of Lyra's geometry. We have obtained solutions by considering the time dependent displacement field. The source of the magnetic field is due to an electric current produced along the

The inhomogeneous cosmological models play a significant role in understanding some essential features of the universe such as the formation of galaxies during the early stages of evolution and process of homogenization. The early attempts at the construction of such models have been done by Tolman [

The occurrence of magnetic field on galactic scale is a well-established fact today, and its importance for a variety of astrophysical phenomena is generally acknowledged as pointed out by Zeldovich et al. [

In 1917 Einstein introduced the cosmological constant into his field equations of general relativity in order to obtain a static cosmological model since, as is well known, without the cosmological term his field equations admit only nonstatic solutions. After the discovery of the red-shift of galaxies and explanation thereof Einstein regretted for the introduction of the cosmological constant. Recently, there has been much interest in the cosmological term in context of quantum field theories, quantum gravity, super-gravity theories, Kaluza-Klein theories and the inflationary-universe scenario. Shortly after Einstein's general theory of relativity Weyl [

In 1951 Lyra [

Halford [

Recently, Pradhan et al. [

We consider the cylindrically symmetric metric in the form

The coordinates are considered to be comoving so that

The field equations (in gravitational units

For the line-element (

The energy conservation equation

Equations (

To get determinate solution, we assume that the expansion

From (

After using suitable transformation of the coordinates, the model (

Equation (

The reality conditions (Ellis [

The dominant energy conditions (Hawking and Ellis [

The expressions for the expansion

The rate of expansion

In absence of magnetic field, the field (

Therefore, in absence of magnetic field, we have

After using suitable transformation of the coordinates, the metric (

With the use of (

Using (

The reality conditions (Ellis [

The expressions for the expansion

The rate of expansion

In this paper, we have obtained a new class of exact solutions of Einstein's modified field equations for cylindrically symmetric space-time with perfect fluid distribution within the framework of Lyra's geometry both in presence and absence of magnetic field. The solutions are obtained using the functional separability of the metric coefficients. The source of the magnetic field is due to an electric current produced along the

It is possible to discuss entropy in our universe. In thermodynamics the expression for entropy is given by

In spite of homogeneity at large scale, our universe is inhomogeneous at small scale, so physical quantities being position-dependent are more natural in our observable universe if we do not go to super high scale. This result shows this kind of physical importance. It is observed that the displacement vector

The authors would like to thank the Harish-Chandra Research Institute, Allahabad, India for local hospitality where this work is done. The authors also thank the referee for his fruitful comments.