The Quadratic Approximation for Quintessence with Arbitrary Initial Conditions

Abstract

We examine quintessence models for dark energy in which the scalar field, $\varphi$, evolves near the vicinity of a local maximum or minimum in the potential $V(\varphi )$, so that $V(\varphi )$ be approximated by a quadratic function of $\varphi$ with no linear term. We generalize previous studies of this type by allowing the initial value of $d\varphi /dt$ to be nonzero. We derive an analytic approximation for $w(a)$ and show that it is in excellent agreement with numerical simulations for a variety of scalar field potentials having local minima or maxima. We derive an upper bound on the present-day value of $w$ as a function of the other model parameters and present representative limits on these models from observational data. This work represents a final generalization of previous studies using linear or quadratic approximations for $V(\varphi )$.

arXiv comment16 pages, 12 figures, added discussion of observational constraints on these models

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Cited by in corpus (4)

• Kick it like DESI: PNGB quintessence with a dynamically generated initial velocity
• A new generic evolution for $k$-essence dark energy with $w\approx -1$
• Obtaining a scalar fifth force via a broken-symmetry couple between the scalar field and matter
• Constraints for the thawing and freezing potentials