Particle Production by Time-Varying Dark Energy and the End of Cosmic Expansion

TL;DR

This paper analyzes how time-varying dark energy modeled by a quintessence field, whose energy partially converts into a thermal bath, modifies cosmic expansion via thermal friction. It compares a steep, eternal-pushing potential (V_I) and a steep-to-negative potential (V_II) under two particle-production channels: a constant (temperature-independent) and a temperature-dependent friction. Key findings include that thermal friction generally extends periods of accelerated expansion and can induce a notable bump in the quintessence equation of state, while also generating a potentially detectable dark-radiation background, including a neutrino component. The work highlights observational avenues beyond standard cosmology tests, such as dark radiation signatures, and discusses implications for swampland constraints and cyclic cosmologies.

Abstract

We consider various possible consequences of time-varying dark energy due to a quintessence scalar field whose energy density is partially converted to particles as the field evolves down its potential. This particle production acts as a source of thermal friction on the field that can make it difficult to distinguish whether dark energy is due to a radiating field rolling down a steep potential, a purely self-interacting field moving down a flatter potential, or a cosmological constant. By reducing the acceleration of the scalar field, thermal friction increases the amount of accelerated expansion and can cause a sizable bump in the quintessence equation of state. We take special interest in the case where a steep potential rapidly changes from positive to negative as the field evolves, resulting in the end of cosmic expansion and the beginning of contraction. Even in this case, we find that thermal friction lengthens the period of accelerated expansion and consequently delays the end of cosmic expansion, making it challenging to detect the impending transition to contraction using conventional cosmological tests. However, particle production can also provide alternative avenues for detection by generating a background of thermal dark radiation, partly comprised of neutrinos or other particles, whose energy density exceeds the remnant photon energy density.

Figures (8)

• Figure 1: Quintessence equation of state $w_\varphi$ for a simple quintessence scalar field as a function of FRW time $t$, where $t=0$ corresponds to the end of cosmic expansion and the beginning of contraction. The two divergences show the two points when $\rho_\varphi=0$. During expansion, $\rho_\varphi$ transitions from positive to negative, and afterwards during contraction, $\rho_\varphi$ transition back from negative to positive. A similar sequence of divergences is shown in phantommatters for the dark energy density of a scalar field coupled to matter.
• Figure 2: Quintessence equation of state $w_\varphi$ as a function of redshift $z$ with exponential potential $V_\text{I}$ for the temperature-independent (left panel) and temperature-dependent (right panel) particle production mechanisms. Both plots compare the case of simple quintessence ($\beta =\gamma =0$) against cases where $\beta$ (unitless) and $\gamma$ (in units of $H_0^{-1/4}M_{\text{Pl}}^{-3/4}$) are non-zero. As seen in the right panel, there can be a sizable bump in the quintessence equation of state when the combined Hubble and thermal friction sufficiently decelerate the scalar field, which only occurs before present day for the temperature-dependent mechanism.
• Figure 3: Combined quintessence and dark radiation equation of state $w_\text{DER}$ as a function of redshift $z$ with exponential potential $V_\text{I}$ for the temperature-independent (left panel) and temperature-dependent (right panel) particle production mechanisms. Both plots compare the case of simple quintessence ($\beta =\gamma =0$) against cases where $\beta$ (unitless) and $\gamma$ (in units of $H_0^{-1/4}M_{\text{Pl}}^{-3/4}$) are non-zero. For both mechanisms, $w_\text{DER}$ can resemble $\Lambda$CDM predictions if $\beta$ or $\gamma$ is large enough.
• Figure 4: Total equation of state $w_\text{TOT}$ as a function of $N$$e$-folds relative to present day ($N=0$) with exponential potential $V_\text{I}$ for the temperature-independent (left panel) and temperature-dependent (right panel) particle production mechanisms. Both plots compare the case of simple quintessence ($\beta=\gamma=0$) against cases where $\beta$ (unitless) and $\gamma$ (in units of $H_0^{-1/4}M_{\text{Pl}}^{-3/4}$) are non-zero, and the right panel includes a curve for $\Lambda$CDM. When a curve is in the shaded region $\left(w_\text{TOT} < -\frac{1}{3}\right)$, the universe is undergoing accelerated expansion. For the temperature-independent mechanism (left panel), the present phase of accelerated expansion may end for a finite period in some cases, as shown for $\beta=0.01$ and $\beta=0.1$, but for all non-zero $\beta$, $w_\text{TOT}$ approaches $-1$ once thermal friction becomes significant relative to Hubble friction, resulting in eternal accelerated expansion. For the temperature-dependent mechanism (right panel), thermal friction increases the amount of accelerated expansion, but accelerated expansion always ends.
• Figure 5: Present-day dark radiation fractional density $\Omega_\text{DR,0}$ with exponential potential $V_\text{I}$ for the temperature-independent (left panel) and temperature-dependent (right panel) particle production mechanisms. The rate of dark radiation production $\Upsilon\dot\varphi^2$ is affected by $\beta$ and $\gamma$ through $\Upsilon$ directly and $\dot\varphi$ indirectly via thermal friction, so $\Omega_\text{DR,0}$ does not increase monotonically with $\beta$ and $\gamma$.