Quantum backreaction of O (N) -symmetric scalar fields and de Sitter spacetimes at the renormalization point: Renormalization schemes and the screening of the cosmological constant

Abstract

We consider a theory of N self-interacting quantum scalar fields with quartic O(N)-symmetric potential, with a coupling constant λ, in a generic curved spacetime. We analyze the renormalization process of the semiclassical Einstein equations at leading order in the 1/N expansion for different renormailzation schemes, namely: the traditional one that sets the geometry of the spacetime to be Minkowski at the renormalization point and other schemes (originally proposed in [1,2]) that set the geometry to be that of a fixed de Sitter spacetime. In particular, we study the quantum backreaction for fields in de Sitter spacetimes with masses much smaller than the expansion rate H. We find that the scheme that uses the classical de Sitter background solution at the renormalization point, stands out as the most convenient to study the quantum effects on de Sitter spacetimes. We obtain that the backreaction is suppressed by H2/Mpl2 with no logarithmic enhancement factor of lnλ, giving only a small screening of the classical cosmological constant due to the backreaction of such quantum fields. We point out the use of the new schemes can also be more convenient than the traditional one to study quantum effects in other spacetimes relevant for cosmology.