The Little Rip cosmology with the time-dependent equation of state

Abstract

The discovery of accelerated expansion of the Universe resulted in the development of new theoretical models in cosmology [1, 2]. In this work, we discuss the cosmological models, where the parameter w in the equation of state is smaller than 1 − ( ) 1 w < − , however, 1 w →− asymptotically in such a way that there arises no singularity at finite time t . This nonsingular cosmology is referred to as Little Rip [3]. The LR models describe an intermediate evolution of the Universe between the model with the de Sitter asymptotic expansion and those with a Big Rip (BR) singularity. In so doing, two cases are possible. In the first case, the dark-energy density is increased with time without occurrence of the BR singularity. In the second one, the dark-energy density tends to a cosmological constant value with time (de Sitter asymptotic space). This case corresponds to the Pseudo Rip (PR) model discussed in [4]. An interesting scenario is connected with the LR cosmology where the Hubble parameter tends to infinity in the infinite future [5–10]. The LR cosmology can be described in terms of an ordinary liquid with a complicated equation of state [11, 12]. The nonsingular LR cosmology results in the decay of the objects bound by gravity force (galaxies, solar system, etc.) in the future similar to the BR cosmology. This work is concerned with the study of the effect of time-dependent parameters w and Λ on the LR occurrence in different cosmological models of the effect.