Model-independent reconstruction of f(T) and f(R) gravity

Yufen Han; En-Kun Li; Lixin Xu

doi:10.1140/epjc/s10052-024-13195-6

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 863
https://doi.org/10.1140/epjc/s10052-024-13195-6

Regular Article – Theoretical Physics

Model-independent reconstruction of f(T) and f(R) gravity

Yufen Han¹, En-Kun Li² and Lixin Xu¹^c

¹ Institute of Theoretical Physics, School of Physics, Dalian University of Technology, 116024, Dalian, China
² MOE Key Laboratory of TianQin Mission, TianQin Research Center for Gravitational Physics and School of Physics and Astronomy, Frontiers Science Center for TianQin, Gravitational Wave Research Center of CNSA, Sun Yat-sen University (Zhuhai Campus), 519082, Zhuhai, China

^c lxxu@dlut.edu.cn

Received: 21 February 2023
Accepted: 4 August 2024
Published online: 29 August 2024

Abstract

In this paper, we revisit the model-independent reconstruction of f(T) and f(R) gravity at the cosmological background and linear matter density perturbation levels respectively via Gaussian process by using the currently available cosmic observations, which consist Pantheon+ SNe Ia samples, observed Hubble parameter H(z) and the redshift space distortion $f σ_{8} (z)$ $f\sigma _8(z)$ data points. For the f(T) gravity, we find the reconstructed form of f(T) from the background and perturbation levels cannot match each other well in 1 $σ$ $\sigma$ regions, it might imply the tension between the background and perturbation evolutions. For the f(R) gravity, due to the existence of an extra degree for freedom $\dot{F}$ ${\dot{F}}$ , the form of f(R) can be reconstructed by the addition of the growth rate function. The results show that the reconstructed form of f(R) might be viable in the redshift range of $z < 0.75$ $$z<0.75$$ based on the currently available cosmic observations, for filling the requirement of $f_{, R} > 0$ $f_{,R}>0$ and $f_{, R R} > 0$ $f_{,RR}>0$ to avoid a tachyonic instability and be ghosts free in theory.

© The Author(s) 2024

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