Quintessence, Cosmic Coincidence, and the Cosmological Constant

Abstract

Recent observations suggest that a large fraction of the energy density of the universe has negative pressure. One explanation is vacuum energy density; another is quintessence in the form of a scalar field slowly evolving down a potential. In either case, a key problem is to explain why the energy density nearly coincides with the matter density today. The densities decrease at different rates as the universe expands, so coincidence today appears to require that their ratio be set to a specific, infinitessimal value in the early universe. In this paper, we introduce the notion of a "tracker field", a form of quintessence, and show how it may explain the coincidence, adding new motivation for the quintessence scenario.

Figures (4)

• Figure 1: The evolution of the energy densities for a quintessence component with $V(Q)= M^4 \, [{\rm exp} (M_p/Q)-1]$ potential. The solid line is where $\rho_Q$ is initially comparable to the radiation density and immediately evolves according to tracker solution. The dot-dashed curve is if, for some reason, $\rho_Q$ begins at a much smaller value. The field is frozen and $\rho_Q$ is constant until the dot-dashed curve runs into tracker solution, leading to the same cosmology today: $\Omega_m=0.4$ and $w_Q=-0.65$.
• Figure 2: $w_Q$ vs. $z$ for the model in Figure 1. During the radiation-dominated epoch (large $z$), $w_Q \approx 1/3$ and the $Q$-energy density tracks the radiation background. During the matter-dominated epoch, $w_Q$ becomes somewhat negative (dipping down to $w_Q \approx -0.2$ beginning at $z=10^4$) until $\rho_Q$ overtakes the matter density; then, $w_Q$ plummets towards -1 and the universe begins to accelerate.
• Figure 3: The linear mass power spectrum for the model in Figure 1 assuming Hubble parameter $H_0=65$ km/sec/Mpc, compared to the Automatic Plate Measuring (APM) galaxy survey.
• Figure 4: The cosmic microwave background anisotropy power spectrum for the model in Figure 1 compared to the standard cold dark matter model and recent data.CMBdata