Cosmology for Scalar Fields with Negative Potentials and w <-1
Abstract
Description
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 "big crunch". In this picture we would still be living in the expanding universe.
LaTeX 15 pages, 14 figures. Minor changes. Accepted in IJMPD
LaTeX 15 pages, 14 figures. Minor changes. Accepted in IJMPD