  In this study, we provide an alternatively reformulated interpretation of
Gibbons-Hawking radiation as well as inflation. By using a spacetime
quantization procedure, proposed recently by L.C. C\'eleri et al., in anti-de
Sitter space we show that Gibbons-Hawking radiation is an intrinsic property of
the concerned space, that arises due to the existence of a scalar field whose
quanta "carry" a length $l$ (i.e. the radius of the hyperboloid curvature).
Furthermore, within the context of Tsallis q-framework, we propose an
inflationary model that depends on the non-extensive parameter $q$. The main
source of such an inflation is the same scalar field mentioned before. Being
constrained by the observational data, the q-parameter along with the rest of
the model's parameters has been used to estimate the time at which inflation
ends as well as the reheating temperature. The latter is found to be related to
Gibbons-Hawking temperature. Thus, the present model offers an alternative
perspective regarding the nature of the cosmic background radiation (CMB).
