Kaluza-Klein Type Cosmological Model with Ω–Dependent Cosmological Constant and Big Rip Singularity

Abstract

In this paper by using the modified EOS of the form p=– ρ–f(ρ) we investigate the evolution of the scale factor in Kaluza-Klein type cosmological model in which cosmological constant is given by the scalar arisen by the contraction of the scale energy tensor. It is shown that the big rip singularity occurs at finite time t = ts by violating null, weak, strong energy condition and satisfying the dominant energy condition for α > 0. For the general case f(ρ) = αρ(β+1/2), it is observed that for β= 1/2 >0,R(t), p(t) and H(t) → ∞ are reached at a finite time ts = 2/b0, where b0 is constant. So again take place big rip singularity at a finite time. However, for β < 0, singularity does not occurs at a finite time in the framework of Kaluza-Klein theory of gravitation.