Beta Function Quintessence Cosmological Parameters and Fundamental Constants II: Exponential and Logarithmic Dark Energy Potentials

Abstract

This paper uses the beta function formalism to extend the analysis of quintessence cosmological parameters to the logarithmic and exponential dark energy potentials. The previous paper (Thompson 2018) demonstrated the formalism using power and inverse power potentials. The essentially identical evolution of the Hubble parameter for all of the quintessence cases and LambdaCDM is attributed to the flatness of the quintessence dark energy potentials in the dark energy dominated era. The Hubble parameter is therefore incapable of discriminating between static and dynamic dark energy. Unlike the other three potentials considered in the two papers the logarithmic dark energy potential requires a numerical integration in the formula for the superpotential rather than being an analytic function. The dark energy equation of state and the fundamental constants continue to be good discriminators between static and dynamical dark energy. A new analysis of quintessence with all four of the potentials relative the swampland conjectures indicates that the conjecture on the change in the scalar field is satisfied but that the conjecture on the change of the potential is not.

Accepted for publication in the MNRAS,

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• Constraints on dark energy models from the Horndeski theory
• Constraints on the electron-to-proton mass ratio variation at the epoch of reionization
• From Swampland to Phenomenology and Back
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Testing bound dark energy with cosmological parameter and fundamental constant evolution
• Hamilton-Jacobi formalism for Generalized Chaplygin Gas models