## Anisotropic Bianchi type V perfect fluid cosmological models in Lyra’s geometry.(English)Zbl 1197.83128

Summary: The law of variation for the mean Hubble 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 are 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.

### MSC:

 83F05 Relativistic cosmology 83C15 Exact solutions to problems in general relativity and gravitational theory 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
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