Expanding cosmology with back reaction term caused by quantum particle creation

Abstract

An extended Standard cosmological Model is considered with a time dependent cosmological term of the form λ0( ˙ R/dt)/R, R(t) the cosmic scale factor. Such term, that is proportional to the number of quantum particles created by Universe expansion, is introduced to take into account the back reaction to particle creation. The model is first studied when the equation of state p = wρ holds between the energy density ρ and pressure p of the Universe. Exact solutions are determined in the flat space-time case for arbitrary w. The curved space-time cases are solved for w = −1, −1/3. The solutions show the existence of a large variety of possible dynamics of the Universe. The model is studied also when the energy density has the sufficiently general form ρ = ρ0(R/R0) −α . Solutions are given by quadrature. In the flat spacetime case case the quadrature is performed exactly. This shows the existence of an inflationary big-bang at time t = 0 and an accelerated expansion for large t with corresponding particle production. Moreover a numerical determination of the particle creation parameter Ωcr is obtained. In the matter dominated case the value of Ωcr is near to the value of ΩΛ while in the radiation dominated case Ωcr is near to ΩΛ+ΩC where ΩΛ, ΩC are the numerical values of the experimental dark energy and cold dark matter parameters at present time. The model is solved also for ρ =0 ,p � 0. For such unusual situation the value of the ”radius of the Universe” at the present time is calculated