Non-local scalar field on deSitter and its infrared behaviour

Abstract

We investigate free non-local massless and massive scalar field on deSitter (dS) space-time. We compute the propagator for the non-local scalar field for the corresponding theories on flat and deSitter space-times. It is seen that for the non-local theory, the massless limit of massive propagator is smooth for both flat and deSitter. Moreover, this limit matches exactly with the massless propagator of the non-local scalar field for both flat and deSitter space-time. The propagator is seen to respect dS invariance. Furthermore, investigations of the non-local Green's function on deSitter for large time-like separation shows that the propagator has no infrared divergences. The dangerous infrared log-divergent contributions which arise is local massless theories are absent in the corresponding non-local version. Lack of infrared divergences in the propagator hints at the strong role non-localities may play in the dS infrared physics. This study suggest that non-locality can cure IR issues in deSitter. *

Non-locality effect on the entanglement entropy in de Sitter

“…The residual action describes the behaviour of the massive non-local scalar field. This non-local theory has recently been investigated in various contexts [5,17,18]. The purpose is to understand the effect of such infrared non-locality on the low-energy physics.…”

“…The purpose is to understand the effect of such infrared non-locality on the low-energy physics. Interestingly it is seen in [18] (see the references therein for the IR problem of the dS propagator) that the presence of the nonlocality offers a well-behaved infrared finite de Sitter propagator of the scalar field theory which decays at large time scale. DeSitter propagator of massless local scalar field has been a long standing problem where the propagator gets IR divergences and the massless limit of massive propagator is not well-defined.…”

“…DeSitter propagator of massless local scalar field has been a long standing problem where the propagator gets IR divergences and the massless limit of massive propagator is not well-defined. It was found in [18] that the presence of non-locality helps in overcoming these issues very elegantly thereby advocating the importance of nonlocal effects in the IR physics. Motivated by this we then investigated the effect of such non-locality on the behaviour of entanglement entropy on AdS [5] where the universal finite part was seen to have a characteristic oscillating feature due to the presence of non-locality.…”

“…( 4.4) being non-local in nature causes some complications. However, an interesting observation leads to simplification [5,17,18], as the operator can be factored. We will exploit this feature again to obtain mode-functions for the case presented here.…”