https://doi.org/10.1140/epjp/s13360-023-03676-0
Regular Article
The effective equation of state in Palatini 
cosmology
1
Department of Physics, University of Torino, via P.Giuria 1, 10125, Torino, Italy
2
Sez. Torino, Istituto Nazionale di Fisica Nucleare (INFN), via P.Giuria 1, 10125, Torino, Italy
3
Dipartimento di Fisica “E. Pancini”, Università di Napoli “Federico II”, Via Cinthia 21, 80126, Napoli, Italy
4
Scuola Superiore Meridionale, Largo S. Marcellino 4, 80138, Napoli, Italy
5
Sez. Napoli, Istituto Nazional di Fisica Nucleare (INFN), via Cinthia 21, 80126, Napoli, Italy
6
Department of Mathematics, University of Torino, via C.Alberto 10, 10123, Torino, Italy
Received:
30
December
2022
Accepted:
9
January
2023
Published online:
27
February
2023
We investigate how the cosmological equation of state can be used for scrutinizing extended theories of gravity, in particular, the Palatini gravity. Specifically, the approach consists, at first, in investigating the effective equation of state produced by a given model. Then, the inverse problem can also be considered in view of determining which models are compatible with a given effective equation of state. We consider and solve some cases and show that, for example, power-law models are (the only models) capable of transforming barotropic Equations of State into effective barotropic ones. Moreover, the form of equation of state is preserved (only) for 
, as expected. In this perspective, modified Equations of State are a feature capable of distinguishing extended gravity with respect to general relativity. We investigate also quadratic and non-homogeneous effective Equations of State showing, in particular, that they contain the Starobinsky model and other ones.
© The Author(s) 2023
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