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

## Abstract

**:**

## 1. Introduction

## 2. Spin $\mathit{s}\mathbf{\ge}\mathbf{1}/\mathbf{2}$

**Theorem**

**1.**

## 3. Spin Zero Fields

**Theorem**

**2.**

## 4. Conclusions

- The presence of a mass term ($m\ne 0$) or of a potential $V\left(\varphi \right)$ in the wave equation (here we restrict the potential to a mass term $V={m}^{2}{\varphi}^{2}/2$ that keeps the Klein-Gordon equation linear). As an example, the wave-like solutions of the Klein-Gordon Equation (2) in four-dimensional flat spacetime $\left({\mathbb{R}}^{4},{\eta}_{ab}\right)$ exhibit tails whenever $m\ne 0$.
- Scattering of the waves off the background spacetime curvature—this is the situation in which the most interesting physics appears.

## Funding

## Acknowledgments

## Conflicts of Interest

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Faraoni, V.
Massive Spin Zero Fields in Cosmology and the Tail-Free Property. *Symmetry* **2019**, *11*, 36.
https://doi.org/10.3390/sym11010036

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Faraoni V.
Massive Spin Zero Fields in Cosmology and the Tail-Free Property. *Symmetry*. 2019; 11(1):36.
https://doi.org/10.3390/sym11010036

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Faraoni, Valerio.
2019. "Massive Spin Zero Fields in Cosmology and the Tail-Free Property" *Symmetry* 11, no. 1: 36.
https://doi.org/10.3390/sym11010036