https://doi.org/10.1140/epjc/s10052-023-11628-2
Regular Article - Theoretical Physics
Legendre scalarization in gravity and cosmology
1
Institute of Gravitation and Cosmology, RUDN University, ul. Miklukho-Maklaya 6, 117198, Moscow, Russia
2
Research Laboratory of Geometry, Dynamical Systems and Cosmology, University of the Aegean, 83200, Karlovassi, Samos, Greece
3
Departamento de Física and Instituto de Astrofísica e Ciências do Espaço Faculdade de Ciências, Universidade de Lisboa, Ed. C8, Campo Grande, 1769-016, Lisbon, Portugal
4
Department of Marine Sciences, University of the Aegean, University Hill, 81100, Mytilene, Greece
Received:
6
May
2023
Accepted:
14
May
2023
Published online:
24
May
2023
We propose a new formulation of f(R) gravity, dubbed scalarized f(R) gravity, in which the Legendre transform is included as a dynamical term. This leads to a theory with second-order field equations that describes general relativity with a self-interacting scalar field, without requiring the introduction of conformal frames. We demonstrate that the quadratic version of scalarized f(R) gravity reduces to general relativity with a massive scalar field, and we explore its implications for Friedmann cosmology. Our findings suggest that scalarized f(R) gravity may lead to simplified descriptions of cosmological applications, while the proposed formulation could offer a new perspective on the relationship between f(R) gravity and scalar–tensor theories.
© The Author(s) 2023
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