Cosmological dynamics of mimetic gravity

TL;DR

The paper develops a comprehensive dynamical-systems framework to study the cosmological dynamics of mimetic gravity with a general scalar potential, identifying how the mimetic constraint and potential interplay to reproduce radiation, matter, and dark-energy eras. By introducing an autonomous system with variables $x$, $y$, $z$ and the function $\Gamma(z)$, it maps out fixed points and their stability for several potentials, including inverse-square, power-law, exponential, and a $(1+\beta\phi^2)^{-2}$ form. The inverse-square potential emerges as particularly compelling, yielding a unified description of dark matter and dark energy through a single scalar and a natural radiation–matter–acceleration sequence with a scaling attractor that can alleviate the coincidence problem. Depending on the potential, the model can also produce phantom or scaling accelerating phases and, in some cases, a future Big Rip, highlighting rich phenomenology at the background level and motivating future perturbative and data-fitting studies to assess viability.

Abstract

We present a detailed investigation of the dynamical behavior of mimetic gravity with a general potential for the mimetic scalar field. Performing a phase-space and stability analysis, we show that the scenario at hand can successfully describe the thermal history of the universe, namely the successive sequence of radiation, matter, and dark-energy eras. Additionally, at late times the universe can either approach a de Sitter solution, or a scaling accelerated attractor where the dark-matter and dark-energy density parameters are of the same order, thus offering an alleviation of the cosmic coincidence problem. Applying our general analysis to various specific potential choices, including the power-law and the exponential ones, we show that mimetic gravity can be brought into good agreement with the observed behavior of the universe. Moreover, with an inverse square potential we find that mimetic gravity offers an appealing unified cosmological scenario where both dark energy and dark matter are characterized by a single scalar field, and where the cosmic coincidence problem is alleviated.

Figures (7)

• Figure 1: Left graph: The shaded regions mark the stability region of point $A_{5+}$ in the $(w,z_*)$ plane, when $\Gamma_z(z_*)>0$. Right graph: The stability region of point $A_{5-}$ in the $(w,z_*)$ plane, when $\Gamma_z(z_*)<0$.
• Figure 2: The phase-space behavior of the system \ref{['eq:x']}-\ref{['eq:y']}, for the case of inverse square scalar-field potential $V=\alpha \phi^{-2}$, with the choice $\alpha=9/\kappa^2$, for $w=0$ (left graph) and $w=1/3$ (right graph), respectively. As we explain in the text, orbits with $y>0$ initially, i.e. expanding universes, will result to the (accelerating for this $\alpha$ value) scaling solution $A_{5+}$, while orbits with $y<0$ initially, i.e. contracting universes, will result to the contracting counterpart $A_{5-}$.
• Figure 3: The evolution of the density parameters $\Omega_m$, $\Omega_{\phi}$, $\Omega_\lambda$, as well as of the effective equation-of-state parameter $w_{\rm eff}$ , as functions of the redshift, for the case of inverse square scalar-field potential $V=\alpha \phi^{-2}$, with the choice $\alpha=9/\kappa^2$, for $w=0$ (left graph) and $w=1/3$ (right graph), respectively.
• Figure 4: The evolution of the density parameters $\Omega_m$, $\Omega_{\phi}$, $\Omega_\lambda$, as well as of the effective equation-of-state parameter $w_{\rm eff}$ , as functions of the redshift, for the case of power-law scalar-field potential $V(\phi) \propto \phi^n$, with the choice $n=3$, for $w=0$.
• Figure 5: The phase-space behavior of the system \ref{['eq:x']}-\ref{['eq:y']} projected on the $x=0$ plane, for the case of power-law scalar-field potential $V(\phi) \propto \phi^n$, with the choice $n=3$ and for $w=0$. The universe starts from the matter-dominated critical line $A_2$, resulting in the dark-energy dominated saddle de Sitter point $A_{3+}$.