# Generalized scalar field models with the same energy density and linear stability

## TL;DR

This paper explores how scalar field models can be generalized with a field-dependent factor, affecting their energy density and stability, and identifies models sharing identical energy and stability properties.

## Contribution

It introduces a class of generalized scalar field models with identical energy density and stability, providing analytical insights into their properties.

## Key findings

- Models with the same energy density identified
- Linear stability potentials can be identical across different models
- Analytical expressions for energy and stability analyzed

## Abstract

We study how the properties of a Lagrangian density for a single real scalar field in flat spacetime change with inclusion of an overall factor depending only on the field. The focus of the paper is to obtain analytical results. So, we show that even though it is possible to perform a field redefinition to get an equivalent canonical model, it is not always feasible to write the canonical model in terms of elementary functions. Also, we investigate the behavior of the energy density and the linear stability of the solutions. Finally, we show that one can find a class of models that present the same energy density and the same stability potential.