# On a nonlinear model of the localized vacuum hypothesis, for solving the cosmological constant problem

## TL;DR

This paper introduces a nonlinear oscillator model involving a scalar field and relativistic effects, proposing a local vacuum concept that offers insights into the cosmological constant problem.

## Contribution

It presents a novel nonlinear Klein-Gordon based model with a local vacuum hypothesis to address the cosmological constant problem.

## Key findings

- Energy minimum at zero velocity is impossible for small rest mass particles.
- The field exhibits non-stationary behavior with emitted and absorbed waves.
- The local vacuum hypothesis aids in solving the cosmological constant problem.

## Abstract

A new model of oscillators was suggested, in which an oscillating particle in the minimum energy state has a nonzero velocity. A system consisting of a point material particle and a scalar field described by the nonlinear Klein-Gordon equation has been considered. It has been shown that, when taking into account relativistic effects, in the case of small rest masses of a particle an energy minimum at zero velocity is impossible for such a particle. It is showed that the behavior of a field in such a system is not stationary and is characterized by the presence of waves emitted and absorbed by the system in the minimum energy state. The system properties having being analyzed, a concept of the local vacuum was suggested; it was showed that the local vacuum hypothesis is useful in solving the cosmological constant problem.