Quintessence as a run-away dilaton

TL;DR

This paper proposes that a run-away dilaton, driven toward $+ \infty$ in a strong-coupling limit of string/M-theory, can serve as a quintessence field causing late-time cosmic acceleration. By embedding non-universal dilaton couplings—negligible to ordinary matter but nontrivial to dark matter—the authors derive the string- and Einstein-frame cosmological equations, identify an accelerated attractor with fixed $\Omega_\phi$, and analyze early-time focusing and dragging when the potential is negligible. They illustrate the dynamics with numerical examples showing focusing before matter-radiation equality and dragging during matter domination, yielding $\Omega_\phi$ around $0.6$–$0.7$ and $w_\phi$ in the observationally viable range, while maintaining consistency with early-universe constraints. While acknowledging caveats and the need for detailed CMB/SN analysis, the work presents a concrete, string-theory–inspired pathway for quintessence that naturally links late-time acceleration to fundamental couplings and dark-matter interactions, with testable implications for cosmology and high-energy theory.

Abstract

We consider a late-time cosmological model based on a recent proposal that the infinite-bare-coupling limit of superstring/M-theory exists and has good phenomenological properties, including a vanishing cosmological constant, and a massless, decoupled dilaton. As it runs away to $+ \infty$, the dilaton can play the role of the quintessence field recently advocated to drive the late-time accelerated expansion of the Universe. If, as suggested by some string theory examples, appreciable deviations from General Relativity persist even today in the dark matter sector, the Universe may smoothly evolve from an initial "focusing" stage, lasting untill radiation--matter equality, to a "dragging" regime, which eventually gives rise to an accelerated expansion with frozen $Ω(\rm{dark energy})/Ω(\rm{dark matter})$.

Figures (5)

• Figure 1: The asymptotic configurations in the plane $\{\lambda\ ,q\}$. The full bold curves correspond to asymptotic solutions with fixed ratios $\rho_\phi /\rho_d$ and with the following values of $\Omega_\phi$: $1, \ 0.8, \ 0.7, \ 0.6, \ 0.5, \ 0.4$ . On the right vertical axis we have reported the corresponding $q$-dependent acceleration parameter, $\ddot{a} a/\dot{a}^2$. The thin dashed curves correspond to fixed asymptotic values of the dilatonic equation of state $w_\phi= p_\phi/\rho_\phi$, respectively $-0.4$, $-0.7$, $-0.9$ and $-0.95$.
• Figure 2: Time evolution of $\rho_\phi$ for $q=0$ (dash-dotted curve), $q=0.01$ (dashed curve) and $q=0.1$ (dotted curve). The initial scale is $a_i= 10^{-20} a_{\rm eq}$, and the epoch of matter-radiation equality corresponds to $\chi \simeq 46$. Left panel: the dilaton energy density is compared with the radiation (thin solid curve) and matter (bold solid curve) energy density. Right panel: the dilaton energy density (in critical units) is compared with the analytical estimates (\ref{['focusing']}), (\ref{['413']}), (\ref{['materia']}) for the focusing and dragging phases.
• Figure 3: Left panel: Late-time evolution of the dark matter (solid curve), barionic matter (dashed curve), radiation (dotted curve) and the dilaton (dash-dotted curve) energy densities, for the string cosmology model specified by eqs. (\ref{['54']}), (\ref{['55']}). The upper horizontal axis gives the $\log_{10}$ of the redshift parameter. Right panel: for the same model, the late-time evolution of $q$ (fine-dashed curve), $w_\phi$ (dash-dotted curve), $\Omega_\phi$ (solid curve) and of the acceleration parameter $\ddot{a}a/\dot{a}^2$ (dashed curve).
• Figure 4: Time evolution of the dilaton field, for different initial conditions $\phi_i=-4,-2,0,2$. All the other parameters are the same as in the example of Fig. 3. After the plateau associated with the focusing regime, and for a strong enough dilatonic charge, the solutions tend to converge to a common value of $\phi$. The subsequent running to $+ \infty$, driven by the potential, is thus completely independent from the initial value.
• Figure 5: Time evolution of $q(\phi)$, from eq. (\ref{['54']}), for three different values of the parameter $c$. All the other parameters are the same as in the example of Fig. 3. During the dragging phase the value of $q$ converges to the regime $q \ll 1$.