Chiellini-Integrable Cosmologies with Phantom Divide Crossing

TL;DR

This paper presents exact analytical solutions for scalar field cosmologies that can describe late-time acceleration and phantom divide crossing without instabilities, potentially reducing the Hubble tension.

Contribution

It introduces a novel class of Chiellini-integrable scalar cosmologies with analytical solutions capable of modeling cosmic acceleration and phantom crossing.

Findings

Analytical solutions exhibit phantom divide crossing without instabilities.

Reconstructed Hubble parameter aligns with observations, reducing Hubble tension.

Models provide a robust framework for late-time cosmic acceleration.

Abstract

We investigate exact cosmological solutions with a massive scalar field minimally coupled to the Einstein-Hilbert action in General Relativity. For an extended Higgs-like scalar self-interaction, we find that the resulting field equations belong to the damped Ermakov-Painlev\'e II class and construct novel analytical solutions within the framework of the Chiellini integrability condition. We analyze whether the expanding branch of the solutions can describe a late-time cosmic acceleration, using a combined statistical analysis of BAO, CMB, cosmic chronometer and Pantheon+SHOES supernova datasets. A crucial outcome of this exercise is the analytical emergence of a smooth phantom divide crossing in the dark energy equation of state, achieved without introducing any pathological instabilities. The reconstruction yields a present-day Hubble parameter $H_0 \gtrsim 70 \,\mathrm{km\,s^{-1}\,Mpc^{-1}}$, with a reduced tension relative to the $\Lambda$CDM cosmology. The results indicate that Chiellini-integrable scalar cosmologies are capable of providing a robust and analytically controlled framework for modeling late-time cosmic acceleration and phantom divide crossing, offering a viable alternative to phenomenological dark-energy parametrizations.