Cosmology for Scalar Fields with Negative Potentials and w <-1

Abstract

We study the cosmology of canonically normalized scalar fields that lead to an equation of state parameter of w_ϕ=p_ϕ/ρ_ϕ<-1 without violating the weak energy condition: rho=Σ_iρ_i \geq 0 and ρ_i+p_i\geq 0. This kind of behavior requires a negative scalar potential V, widely predicted in particle physics. We show that the energy density ρ_ϕ=E_k+V takes negative values with an equation of state with w_ϕ< -1. However, the net effect of the $ϕ$ field on the scale factor is to decelerate it giving a total equation of state parameter w=p/ρ> w_b=p_b/ρ_b, where ρ_b stands for any kind of energy density with -1\leq w_b \leq 1. The fact that ρ_ϕ<0 allows, at least in principle, to have a small cosmological constant or quintessence today as the cancellation of high energy scales such as the electroweak or susy breaking scale. While V is negative |ρ_ϕ| is smaller than the sum of all other energy densities regardless of the functional form of the potential V. We show that the existence of a negative potential leads, inevitable, to a collapsing universe, i.e. to a would be &#34;big crunch&#34;. In this picture we would still be living in the expanding universe.