The transient acceleration from time-dependent interacting dark energy models

TL;DR

The paper investigates whether the current cosmic acceleration could be transient rather than eternal by introducing time-dependent interactions between dark energy and dark matter. It develops analytic solutions for density evolutions and the Hubble parameter under simple and extended coupling forms, notably $Q = 3 \beta(a) H \rho_{de}$ with $\beta(a)=\beta_0 a^\xi$ and $Q = 3 \alpha(a) H \rho_{de} + \alpha(a) \dot{\rho}_{de}$ with $\alpha_0 a^\eta$, including special cases. The main result is that transient acceleration generically arises when energy is transferred from dark energy to dark matter with $\beta_0>0$ and $\xi>0$ (and similar conditions in the generalized model), while certain negative-parameter choices lead to permanent acceleration. These results provide a mechanism to ease the coincidence problem and have implications for late-time cosmology and the interpretation of cosmic acceleration in the presence of couplings between dark sectors.

Abstract

The transient acceleration which the current cosmic acceleration is not eternal is possible by introducing the interaction between dark matter and dark energy. If the energy transfer is from dark energy to dark matter, then it is possible to realize the transient acceleration. We study the possibility of transient acceleration by considering two time-dependent phenomenological interaction forms so that the energy transfer increases as the universe evolves. Starting from a simple and extending to a more complicated ansatz, we obtain analytical expressions for the evolutions of the deceleration and the various energy density parameters. We find the ranges of the parameters in the models for a transient acceleration.

Figures (2)

• Figure 1: The results for the simplest interacting model $Q=3\beta_0 a^\xi H \rho_{de}$. Upper left panel: The evolutions of the various density parameters for $\beta_0=-0.01$, $\xi=-3.1$ and $w_0=-0.98$. Upper right panel: The evolutions of the various density parameters for $\beta_0=0.01$, $\xi=1.0$ and $w_0=-1.02$. Lower left panel: The corresponding evolutions of the deceleration parameter $q$. Line (i) is for the parameters $\beta_0=-0.01$, $\xi=-3.1$ and $w_0=-0.98$ and line (ii) is for the parameters $\beta_0=0.01$, $\xi=1.0$ and $w_0=-1.02$. Lower right panel: the evolutions of the effective equation of state parameters for dark energy (lines (i) and (iii)) and dark matter (lines (ii) and (iv)). Lines (i) and (ii) are for the parameters $\beta_0=-0.01$, $\xi=-3.1$ and $w_0=-0.98$, and lines (iii) and (iv) are for the parameters $\beta_0=0.01$, $\xi=1.0$ and $w_0=-1.02$.
• Figure 2: The results for the general interacting model $Q= \alpha_{0} a^{\xi}(\dot{\rho}_{de}+3H \rho_{de})$. Upper left panel: The evolutions of the various density parameters for $\alpha_0=0.01$, $\xi=-0.5$ and $w_0=-0.98$. Upper right panel: The evolutions of the various density parameters for $\alpha_0=0.01$, $\xi=1.0$ and $w_0=-1.02$. Lower left panel: The corresponding evolutions of the deceleration parameter $q$. Line (i) is for the parameters $\alpha_0=0.01$, $\xi=-0.5$ and $w_0=-0.98$ and line (ii) is for the parameters $\alpha_0=0.01$, $\xi=1.0$ and $w_0=-1.02$. Lower right panel: the evolutions of the effective equation of state parameters for dark energy (lines (i) and (iii)) and dark matter (lines (ii) and (iv)). Lines (i) and (ii) are for the parameters $\alpha_0=0.01$, $\xi=-0.5$ and $w_0=-0.98$, and lines (iii) and (iv) are for the parameters $\alpha_0=0.01$, $\xi=1.0$ and $w_0=-1.02$.