# The cosmological constant and a scalar field coupled non minimally to gravity

## TL;DR

This paper demonstrates how combined minimal and non-minimal scalar field interactions with gravity can generate a cosmological constant and explores states that are influenced by gravity but do not produce it, challenging the action-reaction principle.

## Contribution

It introduces a novel mechanism for cosmological constant generation via scalar field coupling and identifies unique scalar field states that defy the usual action-reaction expectation.

## Key findings

- Combined scalar-gravity interactions can produce a cosmological constant.
- Existence of scalar field states influenced by gravity but not generating it.
- Explicit examples provided in a homogeneous, isotropic universe.

## Abstract

We show that the combined minimal and non minimal interaction with the gravitational field may produce the generation of a cosmological constant without self-interaction of the scalar field. In the same vein we analyze the existence of states of a scalar field that by a combined interaction of minimal and non minimal coupling with the gravitational field can exhibit an unexpected property, to wit, they are acted on by the gravitational field but do not generate gravitational field. In other words, states that seems to violate the action-reaction principle. We present explicit examples of this situation in the framework of a spatially isotropic and homogeneous universe.