# On Euclidean limit cycles in cosmological models based on scalar fields

## TL;DR

This paper investigates the behavior of phase trajectories in scalar field cosmological models, demonstrating the existence of Euclidean limit cycles near zero effective energy surfaces, which supports previous theoretical assumptions.

## Contribution

It provides a detailed analysis confirming the existence of Euclidean limit cycles in scalar field cosmological models with Higgs potential, expanding understanding of their phase space dynamics.

## Key findings

- Phase trajectories merge with free oscillations at zero energy
- Existence of Euclidean limit cycles confirmed in scalar field models
- Trajectories converge within finite time to zero-energy surfaces

## Abstract

A detailed analysis of the phase trajectories of cosmological models based on classical and scalar fields near surfaces of zero effective energy has been carried out. A study of the differential parameters of the convergence of phase trajectories to a zero-energy surface boundary shows that the phase trajectories merge within a finite time with the phase trajectories of free oscillations corresponding to zero effective energy. This confirms the assumption formulated in a number of previous works by one of the authors about the existence of Euclidean limit cycles in cosmological models based on scalar fields with a Higgs interaction potential.