De Sitter space and eternity

Abstract

This paper explores infrared quantum effects in the de Sitter space. The notion of "eternal manifolds" is introduced and it is shown that in most cases the de Sitter space doesn't belong to this class. It is unstable under small perturbations which may cause a breakdown of the de Sitter symmetry. The de Sitter string sigma model is discussed. It is argued that the gauge theory at the complex coupling is dual to the matrix elements of vertex operators in the de Sitter space, taken between the Bunch -Davies vacuum and the "out" state without particles. The described infrared effects are likely to screen away the cosmological constant.

Comments on the vacuum energy decay

“…The aim of the present work is to point out, following the logic of [1] and the previous section that generically owing to lacking of translation invariance, the matter vacuum is unstable (that is, it can decay to physical particles with a certain computable width) so that by unitarity the vacuum energy must have a unambiguous finite imaginary part. Assuming analyticity in the coupling constants, this in turn puts restrictions on the possible real part of the cosmological constant through the dispersion relations as a consequence of Cauchy's theorem.…”

“…Indeed, in [1] some arguments are given for finiteness (after substraction) of the massive contribution to the imaginary part of the effective action, and in [3][5] it is similarly argued for the finiteness of the forbidden decay width, which is, as is has been already argued for, a closely related quantity through crossing symmetry.…”

“…where the Hadamard symmetric function G (1) and the Pauli-Jordan commutator function D are real, σ(x, y) is the sign of the time ordering of x and y, and D is antisymmetric and zero for causally disconnected points, i.e. has the form D(x, y) = σ(x, y)∆(x, y) with ∆(x, y) symmetric.…”

“…The imaginary part of the nth power of the propagator is then proportional to i∆(x, y) times asymmetric function (built with odd powers of G (1) and even powers of D), in such a way that the integrand depends only on z(x, x 0 ), and not on the sign of the time ordering, so the transformation X 0 → −X 0 leaves unaltered the value of the integral. This proves the unitarity relation.…”

“…A recent contribution to it is Polyakov's [1] claim that vacuum energy is unstable. This instability is supposed to be different from previous proposals in the sense that this is due to particle interactions in a de Sitter background, and consequently is only indirectly of gravitational origin.…”