Massive Spin Zero Fields in Cosmology and the Tail-Free Property

Valerio Faraoni

doi:10.3390/sym11010036

Abstract

Fields of spin s ≥ 1 / 2 satisfying wave equations in a curved space obey the Huygens principle under certain conditions clarified by a known theorem. Here, this theorem is generalized to spin zero and applied to an inflaton field in de Sitter-like space, showing that tails of scalar radiation are an unavoidable physical feature. Requiring the absence of tails, on the contrary, necessarily implies an unnatural tuning between cosmological constant, scalar field mass, and coupling constant to the curvature.

Highlights

There is a long history of studies of massive fields of arbitrary spin which satisfy wave equations in curved space
Let us begin by considering massive fields of spin s ≥ 1/2 on a curved spacetime
We have restricted our considerations to the mathematical aspects of the propagation of a scalar field in a curved space

Summary

Introduction

There is a long history of studies of massive fields of arbitrary spin which satisfy wave equations in curved space. These studies have approached the subject from both the mathematical and the physical (classical and quantum) sides. Let us begin by considering massive fields of spin s ≥ 1/2 on a curved spacetime This situation was analyzed long ago in Ref. A solution of the homogeneous wave equation for a massive field of spin s ≥ 1/2 on the spacetime (M, gab ) obeys the Huygens principle if and only if (M, gab ) has constant curvature and the Ricci scalar is given by. Some order was brought to this area of research by the detailed discussion of the relations between the several characterizations of wave tails given in Ref. [12]

Spin Zero Fields

Conclusions