https://doi.org/10.1140/epjc/s10052-024-12487-1
Regular Article - Theoretical Physics
The Brans–Dicke field in non-metricity gravity: cosmological solutions and conformal transformations
1
Institute of Systems Science, Durban University of Technology, 4000, Durban, South Africa
2
Departamento de Matemáticas, Universidad Católica del Norte, Avda. Angamos 0610, Casilla, 1280, Antofagasta, Chile
Received:
22
October
2023
Accepted:
28
January
2024
Published online:
6
February
2024
We consider the Brans–Dicke theory in non-metricity gravity, which belongs to the family of symmetric teleparallel scalar–tensor theories. Our focus lies in exploring the implications of the conformal transformation, as we derive the conformal equivalent theory in the Einstein frame, distinct from the minimally coupled scalar field theory. The fundamental principle of the conformal transformation suggests the mathematical equivalence of the related theories. However, to thoroughly analyze the impact on physical variables, we investigate the spatially flat Friedmann–Lemaître–Robertson–Walker geometry, defining the connection in the non-coincidence gauge. We construct exact solutions for the cosmological model in one frame and compare the physical properties in the conformal related frame. Surprisingly, we find that the general physical properties of the exact solutions remain invariant under the conformal transformation. Finally, we construct, for the first time, an analytic solution for the symmetric teleparallel scalar–tensor cosmology.
© The Author(s) 2024
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