Interacting Quintessence, Cosmic Acceleration and the Coincidence Problem

Abstract

Faced by recent evidence for a flat universe dominated by dark energy, cosmologists grapple with deep cosmic enigmas such as the cosmological constant problem, extreme fine-tuning and the cosmic coincidence problem. The extent to which we observe the dimming of distant supernovae suggests that the cosmic acceleration is as least as severe as in cosmological constant models. Extrapolating this to our cosmic future implies terrifying visions of either a cold and empty universe or an explosive demise in a ``Big Rip.'' We construct a class of dynamical scalar field models of dark energy and dark matter. Within this class we can explain why supernovae imply a cosmic equation of state $w\lesssim-1$, address fine tuning issues, protect the universe from premature acceleration and predict a constant fraction of dark energy to dark matter in the future (thus solving the coincidence problem), satisfy the dominant energy condition, and ensure that gravitationally bound objects remain so forever (avoid a Big Rip). This is achieved with a string theory inspired Lagrangian containing standard kinetic terms, exponential potentials and couplings, and parameters of order unity.

Figures (3)

• Figure 1: The dashed line represents the $\phi$ self-interaction potential, the dot-dashed line the effective potential from the interaction with iCDM (which decays with expansion), and the solid the sum. At early times $\phi$ tracks down either side (either $A_1$ or $A_2$), coming to and then slowly rolling with the minimum (B).
• Figure 2: The fraction of the energy density in radiation, matter and quintessence as a function of the natural log of the scale factor N. The thin dashed line is the tracking attractor, while the thin dotted line represents the minimum of the effective potential. Note $\phi$ follows the former until it crosses the latter. For this numerical example $\alpha =5$,$\beta =15$, $\Omega _{Q0}=0.6$. Note that in the future, the ratio of the dark matter and dark energy densities approaches the constant $\alpha/\beta$.
• Figure 3: Luminosity distance--redshift ($d_L(z)$) curves for $\Lambda$CDM, a "Big Rip" equation of state $w_{Q}=-1.4$ (allowed by current SNIa data SCP2003) and iQCDM ($\alpha =5$,$\beta =15$,$\Omega _{Q0}=0.6$). The inset shows the percentage difference from the $\Lambda$CDM curve. Also shown in the inset (dot-dashed) is the curve one would obtain if the quintessence and iCDM were both treated as fluids with equations of state given by their decay rate: $w=-\beta /\left(\alpha +\beta \right)= 0.75$.