https://doi.org/10.1140/epjc/s10052-024-12842-2
Regular Article - Theoretical Physics
Signature of f(R) gravity via Lemaître–Tolman–Bondi inhomogeneous perturbations
1
Galileo Galilei Institute for Theoretical Physics, Largo Enrico Fermi 2, 50125, Florence, Italy
2
Instituto de Astrofisíca e Ciências do Espaço, Faculdade de Ciências da Universidade de Lisboa, Edificio C8, Campo Grande, 1740-016, Lisbon, Portugal
3
Fusion and Nuclear Safety Department C. R. Frascati, ENEA, Via E. Fermi 45, 00044, Frascati, RM, Italy
4
Physics Department, Sapienza University of Rome, Piazzale A. Moro 5, 00185, Rome, Italy
Received:
10
January
2024
Accepted:
14
April
2024
Published online:
14
May
2024
We analyze inhomogeneous cosmological models in the local Universe, described by the Lemaître–Tolman–Bondi (LTB) metric and developed using linear perturbation theory on a homogeneous and isotropic Universe background. Focusing on the different evolution of spherical symmetric inhomogeneities, we compare the 
LTB model, in which the cosmological constant is included in the LTB formalism, with inhomogeneous cosmological models based on 
modified gravity theories viewed in the Jordan frame. We solve the system of field equations for both inhomogeneous cosmological models adopting the method of separation of variables: we integrate analytically the radial profiles of local perturbations, while their time evolution requires a numerical approach. The main result of the analysis concerns the different radial profiles of local inhomogeneities due to the presence of a non-minimally coupled scalar field in the Jordan frame of gravity. While radial perturbations follow a power-law in the LTB model, Yukawa-like contributions appear in the theory. Interestingly, this latter peculiar behavior of radial profile is not affected by the choice of the functional form. The numerical solution of time-dependent perturbations exhibits a non-diverging profile. This work suggests that investigations about local inhomogeneities in the late Universe may allow us to discriminate if the present cosmic acceleration is caused by a cosmological constant term or a modified gravity effect.
© The Author(s) 2024
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Funded by SCOAP3.
