Emergence of cosmic space and horizon entropy maximization from Tsallis and Cirto entropy

In this note by use of the idea of the emergence of cosmic space suggested by Padmanabhan (Emergence and expansion of cosmic space as due to the quest for holographic equipartition; Res Astro Astrophys 12:891, 2012), we derive the modified Friedmann equation of a Friedmann-Robertson-Walker (FRW) Universe from Tsallis and Cirto entropy in $$(n+1)$$ dimension with any spatial curvature. We investigate further the consistency of the law of emergence with the maximization of horizon entropy in the context of Tsallis and Cirto horizon entropy. Our results reveal the deep connection between the law of emergence and horizon thermodynamics