Abstract
We present a method to compute the two-point functions for an $O(N)$ scalar field model in de Sitter spacetime, avoiding the well known infrared problems for massless fields. The method is based on an exact treatment of the Euclidean zero modes and a perturbative one of the nonzero modes, and involves a partial resummation of the leading secular terms. This resummation, crucial to obtain a decay of the correlation functions, is implemented along with a double expansion in an effective coupling constant $\sqrt\lambda$ and in $1/N$. The results reduce to those known in the leading infrared approximation and coincide with the ones obtained directly in Lorentzian de Sitter spacetime in the large $N$ limit. The new method allows for a systematic calculation of higher order corrections both in $\sqrt\lambda$ and in $1/N$.
Highlights
The analysis of interacting quantum fields in de Sitter spacetime is relevant to understand different aspects in cosmology, both in the early universe and in the present period of accelerated expansion
It is worth to note that the free UV propagators that build up the expressions of the two-point functions of the UV modes, Eq (15), are massless
In this work we considered an interacting O(N) scalar field model in d-dimensional Euclidean de Sitter space, paying particular attention to the IR problems that appear for massless and light fields
Summary
The analysis of interacting quantum fields in de Sitter (dS) spacetime is relevant to understand different aspects in cosmology, both in the early universe and in the present period of accelerated expansion. As this is a compact space, the modes of a quantum field are discrete, and the origin of the IR problems can be traced back to the zero mode [8]: the IR behavior improves if the zero mode is treated exactly while the nonzero modes (UV modes in what follows) are treated perturbatively Using this idea, it has been shown that in the massless λφ th√eory one obtains a dynamical squared mass for the field that in the leading IR limit is proportional to λH2. Up to quadratic order it can be shown that This is an exact property of the Euclidean theory valid for all N and λ, which shows that the dynamical mass mdyn, defined by the above equation, is related to the inverse of the variance of the zero modes.
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