Quintessence and Supergravity

Abstract

In the context of quintessence, the concept of tracking solutions allows to address the fine-tuning and coincidence problems. When the field is on tracks today, one has $Q\approx m_{\rm Pl}$ demonstrating that, generically, any realistic model of quintessence must be based on supergravity. We construct the most simple model for which the scalar potential is positive. The scalar potential deduced from the supergravity model has the form $V(Q)=\frac{Λ^{4+α}}{Q^α}e^{\fracκ{2}Q^2}$. We show that despite the appearence of positive powers of the field, the coincidence problem is still solved. If $α\ge 11$, the fine-tuning problem can be overcome. Moreover, due to the presence of the exponential term, the value of the equation of state, $ω_Q$, is pushed towards the value -1 in contrast to the usual case for which it is difficult to go beyond $ω_Q\approx -0.7$. For $Ω_{\rm m}\approx 0.3$, the model presented here predicts $ω_Q\approx -0.82$. Finally, we establish the $Ω_{\rm m}-ω_Q$ relation for this model.

Figures (4)

• Figure 1: Evolution of the different energy densities. The dashed-dotted line represents the energy density of radiation whereas the dashed line represents the energy density of matter. The solid line is the energy density of quintessence in the SUGRA model with $\alpha =11$. The dotted line is the energy density of quintessence for the potential $V(Q)=\Lambda ^{4+\alpha }Q^{-\alpha }$ with the same $\alpha$. The initial conditions are such that equipartition, i.e. $\Omega _{Qi}\approx 10^{-4}$, is realized just after inflation.
• Figure 2: The dotted line represents the evolution of $\omega _Q$ for the potential $V(Q)=\Lambda ^{4+\alpha }Q^{-\alpha }$ with $\alpha =11$. The dashed line represents the evolution of $\omega _Q$ in the SUGRA model for the same value of $\alpha$. In this case $\omega _Q\approx -0.82$ today.
• Figure 3: $\Omega _{\rm m}-\omega _Q$ relation for the SUGRA potential given by $V(Q)=\Lambda ^{4+\alpha }Q^{-\alpha }e^{\kappa Q^2/2}$ with $\alpha =11$.
• Figure 4: $\omega _Q-\alpha$ relation for the SUGRA potential.