Finite-time Singularities in Swampland-related Dark Energy Models
  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 $H(t)=f_1(t)+f_2(t)(t-t_s)^{\alpha}$, 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
$\alpha<-1$ and $\alpha>2$ 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.
