Abstract
In the present study, a new model of the universe, based on using a generalized form of the linearly varying deceleration parameter, is presented. This model is an oscillating expansion form and simultaneously a contraction form at different stages. It behaves normally as a conventional Big Bang model till the first half-age i.e. at a Big Rip (It represents the maximum value of the expansion of the universe). Then, it reverses its behavior up to the Big Crunch. Such a model has the same physical behavior at its beginning and ending stages. During its first half-age and second half-age, it begins with a singular stage and ends with a non-singular one. Yet, in the first half-age, the model covers a linearly varying deceleration parameter model. Furthermore, it covers the law of Berman and corresponds to the periodic universe of the varying deceleration parameter of the second degree in the Riemannian geometry. The effect of the constant terms in the proposed deceleration parameter is examined and discussed. Also, this article introduces a new model to explain the evolution of the universe by using the Riemannian geometry, together with a constant boundary connecting the two scaling parameters which have some quantum properties. The proposed model predicts the future of the universe after the Big Rip. The results obtained match the recent cosmological observations at the present moment. Finally, the relationship between the spin tensor and the redshift is obtained and discussed.