IR finite correlation functions in de Sitter space, a smooth massless limit, and an autonomous equation

Kamenshchik, Alexander; Petriakova, Polina

IR finite correlation functions in de Sitter space, a smooth massless limit, and an autonomous equation

Alexander Kamenshchik
(
- Bologna U. and
- INFN, Bologna
)
,
Polina Petriakova
(
- Bologna U. and
- INFN, Bologna
)

Oct 21, 2024

37 pages

e-Print:

2410.16226 [hep-th]

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Abstract: (arXiv)

We explore two-point and four-point correlation functions of a massive scalar field on the flat de Sitter background in the long-wavelength approximation. By employing the Yang-Feldman-type equation, we compute the two-point correlation function up to the three-loop level and the four-point correlation function up to the two-loop one. In contrast to the standard theory of a massive scalar field based on the de Sitter-invariant vacuum, we develop the vacuum-independent reasoning that may not possess de Sitter invariance but results in a smooth massless limit of the correlation function's infrared part. Our elaboration affords to calculate correlation functions of a free massive scalar field and to proceed with quantum corrections, relying only on the known two-point correlation function's infrared part of a free massless one. Remarkably, the two-point correlation function of a free massive scalar field coincides with the Ornstein-Uhlenbeck stochastic process's one and has a clear physical interpretation. We compared our results with those obtained with the Schwinger-Keldysh diagrammatic technique, Starobinsky's stochastic approach, and the Hartree-Fock approximation. At last, we have constructed a renormalization group-inspired autonomous equation for the two-point correlation function. Integrating its approximate version, one obtains the non-analytic expression with respect to a self-interaction coupling constant

\lambda

. That solution reproduces the correct perturbative series up to the two-loop level. At the late-time limit, it almost coincides with the result of Starobinsky's stochastic approach in the whole interval of a new dimensionless parameter

0 \leq \tfrac{\pi^2 m^4}{3\lambda H^4} < \infty

.

Note:

A few typos in outcomes are corrected in v2

References(32)

Figures(0)

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