Solar System tests and chameleon effect in f(R) gravity

Abstract

Using a novel and self-consistent approach that avoids the scalar-tensor identification in the Einstein frame, we reanalyze the viability of f (R) gravity within the context of solar-system tests. In order to do so, we depart from a simple but fully relativistic system of differential equations that describe a compact object in a static and spherically symmetric spacetime, and then make suitable linearizations that apply to non-relativistic objects such as the Sun. We then show clearly under which conditions the emerging chameleon-like mechanism can lead to a Post-Newtonian Parameter γ compatible with the observational bounds. To illustrate this method, we use several specific f (R) models proposed to explain the current acceleration of the Universe, and we show which of them are able to satisfy those bounds. PACS numbers: 04.50.Kd, 95.36.+x, 04.40.Dg I. INTRODUCTIONf (R) gravity remains one of the most popular and viable mechanisms to explain the current accelerated expansion of the Universe (see Refs [1-6] for a review) while predicting an equation of state for the "dark energy" that changes in cosmic time and that might accommodate to future observations better than a simple cosmological constant Λ [7-9]. This proposal consists of taking for the action functional a (non linear) function f (R) of the Ricci scalar R different from the General Relativity (GR) f GR (R) = R − 2Λ. Thus, unless otherwise stated, and in order to avoid confusion, hereafter f (R) refers to those non-linear models. This alternative, while very attractive for it does not require additional fields, opens, however, a Pandora box that risks spoiling many of the GR predictions that have been verified with high accuracy during the past hundred years (e.g. solar-system tests, binary pulsar phenomenology), including the recent detection of gravitational waves by the LIGO-VIRGO collaboration [10]. Several specific f (R) models have been put forward to explain the cosmic acceleration, but many of them have failed other tests, including more refined cosmological scrutinies (e.g. the analysis of cosmological perturbations and the CMB), solar system (weak gravity tests) and strong gravity tests (e.g. neutron stars). One of the drawbacks of this kind of modifications of gravity is that there is a priori no fundamental principle

Post-Newtonian $γ$-like parameters and the gravitational slip in scalar-tensor and $f(R)$ theories

“…This misidentification between gammas and the slip is also found in a slightly distinct context of scalar-tensor theories using different frames [51], scalar-torsion formulations [52], and f (R) theories using an alternative method of linearization [53].…”

Constraining f(R) models with cosmic chronometers and the HII galaxy Hubble diagram

“…Moreover comparison with solar system data was performed in Ruggiero and Iorio (2007); Chiba et al (2007); Amendola and Tsujikawa (2008); Nojiri and Odintstov (2007); Capozziello and Tsujikawa (2008); Hu & Sawicki (2007). In a recent paper Negrelli et al (2020) the authors use a chameleon-like mechanism to obtain a Post-Newtonian Parameter γ for some f (R) models, and show that this is compatible with observational bounds. In addition, any f (R) cosmological model must satisfy a number of conditions related to its stability and the prediction of a matter-dominated era (see Hu & Sawicki (2007); Amendola et al (2007b) for details), namely (i) f (R) > 0 for R ≥ R0 > 0, where R0 is the Ricci scalar at the present time for the FLRW metric in Equation ( 6).…”

Classical and Quantum f(R) Cosmology: The Big Rip, the Little Rip and the Little Sibling of the Big Rip

“…It is a well-known fact that local tests pose rather tight constraints on the metric formulation of f (R) theories of gravity (see, for example, references [93][94][95][96][97][98][99]). Thus, any candidate for a reliable alternative to GR should pass or, somehow, evade these lowcurvature-regime tests (see also [100][101][102][103][104][105] for an interesting discussion). However, the metric f (R) models presented here were expressly built to reproduce a high curvature regime very different from that of (an effective) ΛCDM.…”