Finite-time singularities in swampland-related dark-energy models

¹ ICREA - Passeig Luis Companys, 23, 08010 Barcelona, Spain
² Institute of Space Sciences (ICE, CSIC) - C. Can Magrans s/n, 08193 Barcelona, Spain
³ Institute of Space Sciences of Catalonia (IEEC) - Barcelona, Spain
⁴ Institute of Physics, Kazan Federal University - Kazan 420008, Russia
⁵ Department of Physics, Aristotle University of Thessaloniki - Thessaloniki 54124, Greece
⁶ Laboratory for Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR) 634050 Tomsk, Russia
⁷ Tomsk State Pedagogical University - 634061 Tomsk, Russia

Received: 16 January 2019
Accepted: 23 April 2019

Abstract

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 , 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 and , 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.