Abstract:Bermann [ Nuovo Cimento B (1983), 74, 182 ] presented a law of variation of Hubble's parameter that yields constant deceleration parameter models of the Universe. In this paper, we study some cosmological models with negative constant deceleration parameter within the framework of Lyra geometry.PACS NOS: 98.80 cq , 04.20 jb , 04.50

Observations of high red shift supernovae indicate that the Universe is accelerating. Existence of Big-bang singularity is one of the basic failures of general theory of relativity. In this letter we show that within the framework of Lyra geometry, the space-time of the Universe is not only free of Big-bang singularity but also exhibits acceleration during its evolution.The two most important problems prevailing the present cosmological scenario beset the standard models based on Riemannian geometry are the existence of Big-bang singularity and the accelerating phase of the Universe (recently detected experimentally) (Gasperini et al., 2003). Ever since the beginning of the general theory of relativity, a multitude of efforts has been devoted to construct alternative theories of gravity. One of the most intriguing modifications of general relativity is that proposed by Lyra by introducing gauge functions in to the structure less manifold (Lyra, 1951;Sen and Dunn, 1971). On the basis of Lyra geometry (LG), Sen and Dunn (1971) constructed an analog of the Einstein field equations which in a normal gauge may be written as:where ϕ a is the displacement vector and other symbols have their usual meaning as in Riemannian geometry [a brief review is given in the appendix]. The analysis of Halford (1970) indicates that the present theory predicts the same effects within the observational limits, as well as the classical solar system tests are concerned, as well as tests based on the linearised form of the field equations.In the present work, we examine the above-mentioned cosmological problems by considering a homogeneous and isotropic cosmological model within the framework of LG.The observed location of the first acoustic peak of CMB temperature fluctuation corroborated by the latest BOOMERANG and MAXIMA data favors a spatially flat matter dominated Universe whose energy density is dominated by some missing