Dynamical system analysis in multiscalar-torsion cosmology

Abstract

We explore the phase-space of a multiscalar-torsion gravitational theory within a cosmological framework characterized by a spatially flat Friedmann-Lemaître-Robertson-Walker model. Our investigation focuses on teleparallelism and involves a gravitational model featuring two scalar fields, where one scalar field is coupled to the torsion scalar. We consider coupling in the two scalar fields' kinetic and potential components. We employ exponential functions for the scalar field potentials and analyze the field equations' equilibrium points to reconstruct the cosmological evolution. Remarkably, we discover many equilibrium points in this multiscalar field model, capable of describing various eras of cosmological evolution. Hence, this model can be used to describe the early and late time acceleration phases of the universe and as a unification model for the elements of the dark sector of the universe.

Figures (16)

• Figure 1: Two-dimensional phase-space portrait of the dynamical system on the surface $y=0$. The left plot is for $\beta=1$ and $\omega=-2$, while the right plot is for $\beta=-1$ and $\omega=2$. With red lines are the family of points $P_{1}^{\pm}$. From the phase-space portrait, points $P_{1}^{\pm}$ define surfaces where the trajectories can move from the finite to the infinity regimes and vice versa.
• Figure 2: Region of existence of point $P_2$ where $v(P_2)= 0.$
• Figure 3: Region plot on the space of the free parameters $\lambda$ and $\omega$ where point $P_{2}$ is an attractor.
• Figure 4: Region for the free parameters $\lambda$ and $\omega$ where point $P_2$ describes an accelerated solution.
• Figure 5: Evolution of $w_{eff}$ and $q$ evaluated at a numerical solution of system \ref{['eq-a']}, \ref{['eq-b']} and \ref{['eq-c']} with initial conditions near $P_2$, i.e. $x(0)=\frac{\lambda +4}{\sqrt{3} \omega }+0.1,y(0)=\frac{\sqrt{(\lambda +4)^2+3 \omega }}{\sqrt{3} \sqrt{\omega }}+0.1,z(0)=0.1$ for different values of the parameters $\mu, \beta, \omega, \lambda.$ We see that for early time $w_{eff}>-\frac{1}{3}$ and $q>0$, meaning there is an early-time deceleration phase. Later, it enters a matter-dominated phase when $w_{eff}=0$ and $q=\frac{1}{2}$ but quickly after that, we see that the behaviour describes late time acceleration for $w_{eff}<-\frac{1}{3}$ and $q<0.$ We also see a transient de Sitter behaviour since both cross the value $w_{eff}=q=-1.$ Finally, they cross to the phantom regime $w_{eff}<-1$ and $q<-1$ with a transient damped oscillation in both parameters.