Abstract:
© 2019 Institute of Physics Publishing. All rights reserved. In this work we shall investigate the singularity structure of the phase space corresponding to an exponential quintessence dark-energy model recently related to swampland models. The dynamical system corresponding to the cosmological system is an autonomous polynomial dynamical system, and by using a mathematical theorem we shall investigate whether finite-time singularities can occur in the dynamical system variables. As we demonstrate, the solutions of the dynamical system are non-singular for all cosmic times and this result is general, meaning that the initial conditions corresponding to the regular solutions, belong to a general set of initial conditions and not to a limited set of initial conditions. As we explain, a dynamical system singularity is not directly related to a physical finite-time singularity. Then, by assuming that the Hubble rate with functional form H(t) = f1(t) + f2(t)(t - ts)α, is a solution of the dynamical system, we investigate the implications of the absence of finite-time singularities in the dynamical system variables. As we demonstrate, Big Rip and a Type-IV singularities can always occur if α ≥ -1 and α ≤ 2, respectively. However, Type-II and Type-III singularities cannot occur in the cosmological system, if the Hubble rate we quoted is considered a solution of the cosmological system.
