Speaker
Description
We investigate a family of $k$-essence cosmological models selected by the requirement that the field equations admit nontrivial variational symmetry. For the $k$-essence theory with Lagrangian function $F(R,X,\phi)=f_{1}R+f_{2}(X,\phi)$ and $f_{2}(\phi,X)=\alpha X+\beta \exp\left((n-1)\phi\right)X^{n}$, the existence of the symmetry constrains the kinetic terms and introduces a conservation law. We explore the structure of the phase-space for the cosmological field equations by performing dynamical systems analysis, in the absence and presence of a pressureless matter source. We employ the Hubble-normalized variables and the Poincar\'{e} compactification, such that to determine the asymptotic behavior of the model and identify all admissible cosmological epochs, from early-time to late-time behavior. We discuss in detail the existence and stability conditions of each fixed point as functions of the free parameters $n$ and $k$, and characterize the full asymptotic structure of the cosmological history as provided by this symmetry-driven $k$-essence model.