The Limits of Quintessence

TL;DR

Evidence that the simplest particle-physics scalar-field models of dynamical dark energy can be separated into distinct behaviors based on the acceleration or deceleration of the field as it evolves down its potential towards a zero minimum is presented.

Abstract

We present evidence that the simplest particle-physics scalar-field models of dynamical dark energy can be separated into distinct behaviors based on the acceleration or deceleration of the field as it evolves down its potential towards a zero minimum. We show that these models occupy narrow regions in the phase-plane of w and w', the dark energy equation-of-state and its time-derivative in units of the Hubble time. Restricting an energy scale of the dark energy microphysics limits how closely a scalar field can resemble a cosmological constant. These results, indicating a desired measurement resolution of order σ(w')\approx (1+w), define firm targets for observational tests of the physics of dark energy.

Figures (2)

• Figure 1: The $w-w'$ phase space occupied by thawing and freezing fields is indicated by the shaded regions. No strong constraints on this range of dark energy properties exist at present. The fading at the top of the freezing region indicates the approximate nature of this boundary. Freezing models start above this line, but pass below it by a red shift $z \sim 1$. The short-dashed line shows the boundary between field evolution accelerating and decelerating down the potential. Future cosmological observations will aim to discriminate between these two fundamental scenarios.
• Figure 2: The evolutionary tracks in $w-w'$ phase space are shown for a variety of particle physics models of scalar fields. The two broad classes are clear: those that initially are frozen and look like a cosmological constant, starting at $w=-1$, $w'=0$, and then thaw and roll to $w'>0$, and those that initially roll and then slow to a creep as they come to dominate the Universe. The sample of thawing models shown have potentials $V\propto \phi^n$ for $n=1,\,2,\,4$ (short-, dot-, and long-dashed curves) and a PNGB with $V\propto \cos^2(\phi/2f)$ (solid curves). The right-most point of the tracks corresponds to the present. For variety, the $n=4$ model has $\Omega_{de}=0.6$, and the $n=1$ model ending at $w=-0.8$ has $\Omega_{de}=0.65$. All other models end with a fractional energy density $\Omega_{de}=0.7$. The sample of freezing models shown have potentials $V\propto \phi^{-n}, \, \phi^{-n}{\rm e}^{\alpha\phi^2}$ (solid and dashed curves). The line $w'=1.5w(1+w)$ indicated by the light, dotted line is a possible lower bound on the freezing models. The left-most point of the tracks corresponds to the present; the right-most point is at $z=1$. For variety, upper and lower close pairs of curves have $\Omega_{de}=0.7,\,0.8$ respectively. All other models end with a fractional energy density $\Omega_{de}=0.7$.