Infrared stability of de Sitter space: Loop corrections to scalar propagators

Abstract

We compute 1-loop corrections to Lorentz-signature de Sitter-invariant 2-point functions defined by the interacting Euclidean vacuum for massive scalar quantum fields with cubic and quartic interactions. Our results apply to all masses for which the free Euclidean de Sitter vacuum is well-defined, including values in both the complimentary and the principal series of SO(D, 1). In dimensions where the interactions are renormalizeable we provide absolutely convergent integral representations of the corrections. These representations suffice to analytically extract the leading behavior of the 2-point functions at large separations and may also be used for numerical computations. The interacting propagators decay at long distances at least as fast as one would naively expect, suggesting that such interacting de Sitter invariant vacuua are well-defined and are wellbehaved in the IR. In fact, in some cases the interacting propagators decay faster than any free propagator with any value of M 2 > 0.and define representations of the (connected) de Sitter group SO 0 (D, 1). It is useful to define the dimensionless mass parameter σ by −σ(σ + d) := M 2 2 . Throughout most of our work, the ambiguity σ → −(σ + d) will be a redundancy of our description, and symmetry σ → −(σ + d) will provide a useful check on our calculations. However, for the moment   J + 2α, J − L + α, J − M + α, J − N + α J + α + 1, J − L + 1, J − M + 1, J − N + 1   , (A10) when J := (L+M +N )/2 ∈ N 0 , and L, M , and N satisfy the triangle inequalities; otherwise D(α, L, M, N ) = 0.

Loop Corrections to Standard Model fields in inflation

“…In that case the zero mode partition function is simple enough to be solved exactly, and the result shows that the zero mode acquire an effective mass m 2 eff ∝ √ λH 2 [33,34]. This result can also be viewed as a supporting argument for massless scalar in dS because it was proved that the correlation functions calculated in Euclidean dS (namely a sphere) and in the Poincaré patch of dS using in-in formalism are equivalent [35][36][37] (see however [38][39][40] for different perspectives).…”

“…Now so long as we are concerned with the late-time divergence, we can expand the integrand of τ -integral as, 35) so that all neglected O(τ 2 ) contribute no divergent terms as the late-time cutoff τ is sent to zero. On the other hand, we should note that the condition |kτ |, |pτ |, |qτ | 1 that we have assumed in doing expansion is not valid for all τ τ .…”

“…where a 1 , · · · , a n = ± denote two types of mass insertions and G ±± is the propagator for the scalar field of mass m. The above formula is most easily proved in Euclidean de Sitter space, and we refer the readers to [35] for details. Here we apply (5.5) to a massless scalar propagator and keep the leading divergence in τ only, then we have the following result, massless propagator with n mass insertions = 2H 2 k 3…”

de Sitter space is unstable in quantum gravity

“…Multiple analyses using multiple approaches e.g. Euclidean continuation [14][15][16][17][18], the stochastic formalism [19][20][21], the dynamical RG [22,23], truncated Schwinger-Dyson equations [24][25][26][27][28][29] and others [30][31][32][33][34][35] have conclusively resolved the physics of a massless scalar in de Sitter space. The scalar develops a dynamical mass; for example, an apparently massless scalar with a λφ 4 interaction develops a dynamical mass proportional to √ λ.…”

Quantum cosmology near two dimensions

“…There is considerable divergence in the literature about the final result [38][39][40][41][42][43][44] and more generally about infrared effects in nearly de Sitter spacetime [45][46][47][48][49][50][51][52][53][54][55]. The advantage of our two-dimensional model is that the important quantum effects can be computed explicitly with relative ease and without ambiguities to all orders in perturbation theory.…”