Cosmological Dynamics of Modified Gravity With a Non-minimal Curvature-matter Coupling

Abstract

We perform a phase space analysis of a non-minimally coupled modified gravity theory with the Lagrangian density of the form $\frac{1}{2}{f}_1(R)+[1+\lambda f_2(R)]{\mathcal{L}}_m$, where $f_1(R)$ and $f_2(R)$ are arbitrary functions of the curvature scalar $R$ and ${\mathcal{L}}_m$ is the matter Lagrangian density. We apply the dynamical system approach to this scenario in two particular models. In the first model we assume $f_1(R)=2R$ with a general form for $f_2(R)$ and set favorable values for effective equation of state parameter which is related to the several epochs of the cosmic evolution and study the critical points and their stability in each cosmic eras. In the second case, we allow the $f_1(R)$ to be an arbitrary function of $R$ and set $f_2(R)=2R$. We find the late time attractor solution for the model and show that this model has a late time accelerating epoch and an acceptable matter era.

13 pages, 5 figures

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• Dynamical analysis of nonminimal coupled theories
• Big-bang nucleosynthesis and cosmic microwave background constraints on non-minimally coupled theories of gravity
• Lagrangian description of cosmic fluids: mapping dark energy into unified dark energy
• Dynamical analysis of modified gravity with nonminimal gravitational coupling to matter
• Particle creation and decay in nonminimally coupled models of gravity
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• Dynamical system approach to scalar-vector-tensor cosmology
• Analysing Ultra High Energy Cosmic Rays' Anisotropy in $\mathbf{f}(\mathbf{R},\mathbf{T})$ Gravity Theory