https://doi.org/10.1140/epjc/s10052-021-09004-z
Regular Article – Theoretical Physics
CDM suitably embedded in f(R) with a non-minimal coupling to matter
1
Department of Physics, University of the Basque Country UPV/EHU, P.O. Box 644, 48080, Bilbao, Spain
2
IKERBASQUE, Basque Foundation for Science, 48011, Bilbao, Spain
3
Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451, Szczecin, Poland
Received:
29
January
2021
Accepted:
23
February
2021
Published online:
17
March
2021
In this work, we further study a metric modified theory of gravity which contains a non-minimal coupling to matter, more precisely, we assume two functions of the scalar curvature, 
and 
, where the first one generalises the Hilbert–Einstein action, while the second couples to the matter Lagrangian. On the one hand, assuming a CDM background, we calculate analytical solutions for the functions and . We consider two setups: on the first one, we fix and compute and on the second one, we fix and compute . Moreover, we do the analysis for two different energy density contents, a matter dominated universe and a general perfect fluid with a constant equation of state fuelling the universe expansion. On the other hand, we complete our study by performing a cosmographic analysis for and . We conclude that the gravitational coupling to matter can drive the accelerated expansion of the universe.
© The Author(s) 2021
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