Multi-fluid potential in the loop cosmology

TL;DR

This paper derives scalar field potentials with constant equation of state in loop cosmology, analyzes their behavior including phantom cases, and explores their perturbations and potential observational signatures.

Contribution

It introduces a class of scalar field potentials with constant w in loop cosmology and studies their analytical solutions, monotonicity, and perturbations, including phantom fields.

Findings

Scalar field can mimic various cosmic fluids with constant w

Scalar field is monotonic, serving as internal time in models

Non-Gaussian features in perturbations suggest observational constraints

Abstract

The scalar field can behave like a fluid with equation of state $p_{\phi}=w\rho_{\phi}$, where $w \in [-1,1]$. In this Letter we derive a class of the scalar field potentials for which $w=$ const. Scalar field with such a potential can mimic ordinary matter, radiation, cosmic strings, etc. We perform our calculations in the framework of the loop cosmology with holonomy corrections. We solve the model analytically for the whole parameter space. Subsequently, we perform similar consideration for the model with a phantom field ($w<-1$). We show that scalar field is monotonic function in both cases. This indicates that it can be treated as a well-defined internal time for these models. Moreover we perform preliminary studies of the scalar field perturbations with this potential. We indicate that non-Gaussian features are present admitting for the possible observational constraints of the model.