Solar System tests in Brans–Dicke and Palatini f(R)-theories

• Published in: European physical journal plus Vol. 135; no. 12; p. 951
• Main Authors: Bonino, A., Camera, S., Fatibene, L., Orizzonte, A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-12-2020; Springer Nature B.V
• Subjects: Applied and Technical Physics; Atomic; Complex Systems; Condensed Matter Physics; Cosmology; Decomposition; Equivalence; Focus Point on Modified Gravity Theories and Cosmology; Mathematical and Computational Physics; Mercury; Mercury (planet); Molecular; Optical and Plasma Physics; Physics; Physics and Astronomy; Precession; Regular Article; Relativity; Spacetime; Theoretical
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-020-00982-9

We compare Mercury’s precession test in standard general relativity, Brans–Dicke theories (BD), and Palatini
f
(
R
)
-theories. We avoid post-Newtonian approximation and compute exact precession in these theories. We show that the well-known mathematical equivalence between Palatini
f
(
R
)
-theories and a specific subset of BD theories does not extend to a really physical equivalence among theories since equivalent models still allow a different incompatible precession for Mercury depending on the solution one chooses. As a result one cannot use BD equivalence to rule out Palatini
f
(
R
)
-theories. On the contrary, we directly discuss that Palatini
f
(
R
)
-theories can (and specific models do) easily pass Solar System tests as Mercury’s precession.