Geometric Perfect Fluids from Extended Gravity
Salvatore Capozziello, Carlo Alberto Mantica, and Luca Guido Molinari

TL;DR
This paper explores how extended theories of gravity can naturally produce perfect fluid terms, offering a geometric approach to dark energy and dark matter in cosmology.
Contribution
It demonstrates that extended gravity theories inherently include perfect fluid components, providing a new geometric perspective on dark sector phenomena.
Findings
Field equations contain perfect fluid terms
Examples developed for FLRW metric
Supports geometric approach to dark energy/matter
Abstract
A main issue in cosmology and astrophysics is whether the dark sector phenomenology originates from particle physics, then requiring the detection of new fundamental components, or it can be addressed by modifying General Relativity. Extended Theories of Gravity are possible candidates aimed in framing dark energy and dark matter in a comprehensive geometric view. Considering the concept of perfect scalars, we show that the field equations of such theories naturally contain perfect fluid terms. Specific examples are developed for the Friedman-Lema\^itre-Roberson-Walker metric.
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