Interacting quintessence from a variational approach Part I: algebraic couplings

TL;DR

This work develops a variational framework to model quintessence interacting with matter by introducing a single algebraic coupling $f(n,s,\phi)$ at the Lagrangian level, derived from Brown's relativistic-fluid formulation. The resulting field equations couple the scalar field to the fluid, yielding a fifth force and a chameleon-type screening mechanism via an environment-dependent effective potential $V_{\rm eff}=V(\phi)+f(n,s,\phi)$. On cosmological scales, the background dynamics are analyzed with dynamical systems techniques, producing two concrete models with rich late-time behavior, including acceleration and scaling solutions, and a mapping to the standard interacting dark energy framework through a covariant derivation of the coupling $Q=-\partial\rho_{\rm int}/\partial\phi\,\dot{\phi}$. The framework also accommodates small-scale phenomenology and screening, suggesting viable Solar System tests and possible galactic-scale effects, while indicating promising avenues for perturbation analysis and broader couplings in future work.

Abstract

We present a new approach to build models of quintessence interacting with dark or baryonic matter. We use a variational approach for relativistic fluids to realize an effective description of matter fields at the Lagrangian level. The coupling is introduced directly in the action by considering a single function mixing the dynamical degrees of freedom of the theory. The resulting gravitational field equations are derived by variations with respect to the independent variables. New interesting phenomenology can be obtained at both small scales, where new screening mechanisms for scalar fields can be realized, and large scales, where one finds an original and rich class of interacting quintessence models. The background cosmology of two of these models is studied in detail using dynamical system techniques. We find a variety of interesting results: for instance, these models contain dark energy dominated late time attractors and scaling solutions, both with early time matter dominated epochs and a possible inflationary origin. In general this new approach provides the starting point for future in depth studies on new interacting quintessence models.

Figures (12)

• Figure 1: Qualitative behaviour of the interacting potential (\ref{['042']}) for different values of $\rho$. On Earth ($\rho_{\rm E}$) the scalar field is highly massive, while for galactic densities ($\rho_{\rm gal}$) the mass is lower. At cosmological scales ($\rho_c$) the mass is so low that the potential effectively becomes a cosmological constant.
• Figure 2: $\beta$-$\lambda$ parameter space indicating the region where the critical points $B,C$ and $F$ are stable.
• Figure 3: Phase space showing trajectories of the dynamical system (\ref{['071']})-(\ref{['073']}) when $\alpha=1,\beta=1,\lambda=2$ and $w=0$. Point $B$ is the global attractor where the universe behaves as though it were completely matter dominated.
• Figure 4: Phase space showing trajectories of the dynamical system (\ref{['071']})-(\ref{['073']}) when $\alpha=1,\beta=-5,\lambda=2$ and $w=0$. Point $F$ is the global attractor, and for this choice of parameters it corresponds to a solution with $w_{\rm eff}=-5/6$.
• Figure 5: $\beta$-$\lambda$ parameter space indicating the different regions where the critical points $B,C,D$ and $F$ are stable.