Correspondence of cosmology from non-extensive thermodynamics with
  fluids of generalized equation of state
  We show that there is a correspondence between cosmology from non-extensive
thermodynamics and cosmology with fluids of redefined and generalized equation
of state. We first establish the correspondence in the case of basic
non-extensive thermodynamics, and then we proceed by investigating the more
consistent case, from the quantum field theoretical point of view, of varying
exponent, namely depending on the scale. The obtained duality provides a way of
explaining the complicated phenomenological forms of the effective fluid
equation-of-state parameters that are being broadly used in the literature,
since their microphysical origin may indeed lie in the non-extensive
thermodynamics of spacetime. Finally, concerning the cosmological behavior, we
show that at late times the effective fluid may drive the universe acceleration
even in the absence of an explicit cosmological constant, and even if the
initial fluid is the standard dust matter one. Similarly, at early times we
obtain an effective cosmological constant which is enhanced through screening,
and hence it can drive a a successful inflation without spoiling the correct
late-time acceleration.
