On the viability of Planck scale cosmology with quartessence

In this paper, using a qualitative theory of dynamical systems, we study the stability of a unified dark matter-dark energy framework known as quartessence Chaplygin model (QCM) with three different equation-of-states within ultraviolet (UV) deformed Friedmann-Robertson-Walker (FRW) cosmologies without Big-Bang singularity. The UV deformation is inspired by the non-commutative (NC) Snyder spacetime approach in which by keeping the transformation groups and rotational symmetry there is a dimensionless, Planck scale characteristic parameter $\mu_0$ with dual implications dependent on its sign that addresses the required invariant cutoffs for length and momentum in nature, in a separate manner. Our stability analysis is done in the $(H,\rho)$ phase space at a finite domain concerning the hyperbolic critical points. According to our analysis, due to constraints imposed on the signs of $\mu_0$ from the phenomenological parameters involved in quartessence models $(\Omega_m^*, c_s^2, \rho_*)$, for an expanding and accelerating late universe, all three QCMs can be stable in the vicinity of the critical points. The requirement of stability for these quartessence models in case of admission of a minimum invariant length, can yield a flat as well as non-flat expanding and accelerating universe in which Big-Bang singularity is absent. This feedback also phenomenologically credits to braneworld-like framework versus loop quantum cosmology-like one as two possible scenarios which can be NC Snyder spacetime generators (correspond to $\mu_0<0$ and $\mu_0>0$, respectively). As a result, our analysis show that between quartessence models with Chaplygin gas equation-of-states and accelerating FRW backgrounds occupied by a minimum invariant length, there is a possibility of viability.