Cosmological dynamical systems of non-minimally coupled fluids and scalar fields

TL;DR

This work develops a covariant variational framework in which Brown-fluid matter and a canonical scalar field non-minimally couple to a geometric bulk term $\mathbf{G}$ via an algebraic coupling $f(n,\phi,\mathbf{G})$, yielding modified cosmological dynamics. By reducing to a 3D autonomous system in dimensionless variables $(x,y,z)$ with an exponential potential, the authors identify fixed points corresponding to matter domination, scalar-field domination, de Sitter phases, and early-time inflation, as well as novel behavior such as transient phantom crossing. Two primary coupling regimes are analyzed: energy-density coupling ($c_2=0$) producing an inflationary point $D$ and a late-time de Sitter/phantom structure in scalar-field couplings ($c_1=0$) that includes a saddle $E$ enabling phantom crossing; hybrid models with both couplings exhibit even richer phenomenology. The results illuminate how fundamental variational couplings to geometry can realize diverse cosmological histories, with potential links to teleparallel theories and clear prospects for confronting observations through background evolution and perturbations.

Abstract

We study the cosmological dynamics of non-minimally coupled matter models using the Brown's variational approach to relativistic fluids in General Relativity. After decomposing the Ricci scalar into a bulk and a boundary term, we construct new models by coupling the bulk term to the fluid variables and an external scalar field. Using dynamical systems techniques, we study models of this type and find that they can give rise to both early-time inflationary behaviour and late-time accelerated expansion. Moreover, these models also contain very interesting features that are rarely seen in this context. For example, we find dark energy models which exhibit phantom crossing in the recent past. Other possibilities include models that give a viable past evolution but terminate in a matter-dominated universe. The dynamical systems themselves display an array of mathematically interesting phenomena, including spirals, centres, and non-trivial bifurcations depending on the chosen parameter values.

Figures (7)

• Figure 1: Physical phase space and fixed points for the $c_2=0$ model, given by Eqs. \ref{['eq:gen1']}--\ref{['eq:gen3']}. The fixed point $D$ only exists for $c_1<0$.
• Figure 2: Parameter values are $\lambda=1$, $c_1 =-1$, $c_2=0$. As initial conditions we set the value of today's matter density parameter to $\Omega_{m} \approx 0.33$, indicated by the dashed line at $N=0$.
• Figure 3: Physical phase space and fixed points for the $c_1=0$ model, given by Eqs. \ref{['eq:gen1']}--\ref{['eq:gen3']}. The fixed point $E$ only exists for $c_2>0$.
• Figure 4: Here $w=0$, $c_1=0,c_2=1$ and $\lambda=1$, $k=1/2$. Today's value has been taken at $\Omega_m \approx 0.33$
• Figure 5: Here $w=0$, $c_1=0$, $c_2=94$ and $\lambda=2$.