Interacting quintessence from a variational approach Part II: derivative couplings

TL;DR

This work extends the variational approach to interacting quintessence by introducing derivative couplings between a canonical scalar field and a relativistic fluid, implemented via a term $f(n,s,\phi) J^\mu \partial_\mu \phi$ in Brown's fluid action. The resulting covariant field equations feature an energy-exchange current $Q_\nu= n^2 (\partial f/\partial n) \nabla_\lambda U^\lambda \nabla_\nu \phi$, with the interacting part of the stress-energy tensor orthogonal to the fluid flow and the background Friedmann equation remaining unchanged. Cosmological dynamics are explored through two models: Model A, a 2D autonomous system from a power-law derivative coupling, and Model B, a 3D system from a $1/n$-type coupling; both yield late-time acceleration and, in certain regimes, DM–DE transitions, with Model B admitting de Sitter attractors for either sign of the coupling parameter. A brief perturbation analysis in Newtonian gauge shows the derivative coupling alters only non-00, non-0i perturbations and that sub-horizon evolution remains ΛCDM-like, pointing to potential large-scale signatures and screening mechanisms to be investigated further.

Abstract

We consider an original variational approach for building new models of quintessence interacting with dark or baryonic matter. The coupling is introduced at the Lagrangian level using a variational formulation for relativistic fluids, where the interacting term generally depends on both the dynamical degrees of freedom of the theory and their spacetime derivatives. After deriving the field equations from the action, we consider applications in the context of cosmology. Two simple models are studied using dynamical system techniques showing the interesting phenomenology arising in this framework. We find that these models contain dark energy dominated late time attractors with early time matter dominated epochs and also obtain a possible dynamical crossing of the phantom barrier. The formulation and results presented here complete and expand the analysis exposed in the first part of this work, where only algebraic couplings, without spacetime derivatives, were considered.

Figures (6)

• Figure 1: Phase space for the dynamical system when $\xi=-1$ and $\lambda=4$. The shaded region indicates where acceleration is present.
• Figure 2: Phase space for the dynamical system when $\xi=1$ and $\lambda=2$. The shaded region indicates where acceleration is present.
• Figure 3: Phase space for the dynamical system when $\xi=-1.5$ and $\lambda=1$. The shaded region indicates where acceleration is present.
• Figure 4: Phase space of model B of the dynamical system with values $w=0$, $\lambda=2$, $\xi=-1$.
• Figure 5: Phase space of model B of the dynamical system with values $w=0$, $\lambda=2$, $\xi=1$.