Characters of different secular effects in various patches of de Sitter space

Abstract

There are at least three different types of secular effects in the two-point correlation functions in scalar quantum field theories in de Sitter space-time. The first one is specific to de Sitter massless and tachyonic minimally coupled scalar fields. The remaining two are generic and are encountered practically in any non-stationary situation in quantum field theory. Furthermore there are secular effects in the n-point correlation functions for low enough mass. They are also specific to de Sitter quantum field theory. In this paper we focus on the differences between the secular effects in two-point functions. We discuss also their character in different patches of de Sitter space-time -global, expanding and contracting Poincaré patches.

Quantization in background scalar fields

“…On the other hand, as we will see below the imaginary part of the Feynman effective action on the scalar field background is zero (see Appendix B). Hence, non-zero quantum expectation values indicate rather 4 Of course, one can obtain classical solutions with other values and signs of this constant via time shifts: t → t + δt =⇒ φ cl = Eδt + Et, or reversals: t → −t =⇒ φ cl = m λ − Et. E.g.…”

“…9). Note that in non-stationary situations in strong background fields vertexes potentially can also show a secular growth [4].…”

“…For instance, stationary approximation is violated in an expanding space-time (see e.g. [1][2][3][4][5]), in strong electric fields [6,7], during the gravitational collapse [8] and in a number of other non-trivial physical situations [9][10][11][12]. In such situations loop corrections to the tree-level correlation functions grow with time.…”

“…Such a resummation was performed only in a limited number of cases [2][3][4][5][6][7]. Moreover, even in these cases one can catch only the leading qualitative effects in the limit of long evolution period and small coupling constant.…”

Renormalization group inspired autonomous equations for secular effects in de Sitter space

“…An interesting example is the de Sitter spacetime represented in the system of coordinates with flat spatial sections (Poincaré patch). Here the infrared divergences are much stronger than in Minkowski spacetime and different kinds of secular effects arise [6,7]. For a massless minimally coupled scalar field there is a secular growth already present at the level of the free theory: the long-wavelength part of the expectation value hϕ 2 ð⃗ x; tÞi evaluated in the Bunch-Davies vacuum [8][9][10] grows linearly with time [11][12][13][14][15].…”