Quantum Hubble horizon

The article addresses a possibility of obtaining cosmologically relevant effects from the quantum nature of the Hubble horizon. Following the observation made by E.~Bianchi and C.~Rovelli in Phys.\ Rev.\ D {\bf 84} (2011) 027502 we explore relationship between the Planck scale discreteness of the Hubble horizon and deformations of the symmetry of rotations. We show that the so-called $q$-deformations in a natural way lead to a mechanism of condensation in the very early Universe. We argue that this provides a possible resolution of the problem of initial homogeneity at the onset of inflation. Furthermore, we perform entropic analysis of the quantum Hubble horizon and show that the $\Lambda$CDM model may arise from linearly (in area of the horizon) corrected Bekenstein-Hawking entropy. Based on this, we have shown that the current accelerating expansion can be associated with the entropy decrease in the Hubble volume. The presented results open new ways to explore relation between the Planck scale effects and observationally relevant features of our Universe.