Solar system constraints on f(T) gravity

Abstract: We use recent observations from solar system orbital motions in order to constrain f(T) gravity. In particular, imposing a quadratic f(T) correction to the linear-in-T form, which is a good approximation for every realistic case, we extract the spherical solutions of the theory. Using these spherical solutions to describe the Sun's gravitational field, we use recently determined supplementary advances of planetary perihelia, to infer upper bounds on the allowed f(T) corrections. We find that the maximal allowed divergence of the gravitational potential in f(T) gravity from that in the teleparallel equivalent of General Relativity is of the order of 6.2 \times 10^{-10}, in the applicability region of our analysis. This is much smaller than the corresponding (significantly small too) divergence that is predicted from cosmological observations, as expected. Such a tiny allowed divergence from the linear form should be taken into account in f(T) model building.

• The paper derives spherical solutions and sets a stringent bound (~6.2×10⁻¹⁰) on deviations from General Relativity using solar system data.
• The study employs planetary perihelion advances to constrain the parameters of f(T) gravity and validate its minimal divergence from linearity.
• Findings underscore that any significant modification to teleparallel gravity requires rigorous testing against high-precision solar observations.

An Analytical Study on Solar System Constraints for f(T) Gravity

The paper "Solar System Constraints on f(T) Gravity" by Lorenzo Iorio and Emmanuel N. Saridakis represents a comprehensive analysis of f(T) gravity implemented using the observational data available from the solar system. Through an examination of the modifications proposed by f(T) gravity and their potential to deviate from General Relativity (GR), this study aims to constrain the parameters of f(T) gravity using solar system datasets.

The rationale for this investigation is rooted in the empirical evidence that suggests the universe's accelerated expansion. Theories proposed to explain this phenomenon include the introduction of dark energy and modifications to the general relativistic framework. The f(T) gravity theory, an extension of the teleparallel equivalent of General Relativity (TEGR), modifies the action integral by incorporating a function of the torsion scalar T instead of the curvature scalar R. The study at hand takes particular interest in examining the divergence of f(T) gravity from linearity.

Through their methodology, the authors derive the spherical solutions of the theory, using them to describe the Sun's gravitational field. Recent observations pertaining to the supplementary advances in planetary perihelion are utilized to establish upper bounds on permissible deviations within this theoretical framework. The investigation focuses on whether f(T) gravity is a valid alternative to GR in explaining gravitational phenomena at both cosmic and solar scales.

Several key numerical outcomes emerge from the analysis. The study finds that the permissible divergence from TEGR—or equivalently GR—is of the order ≈6.2 × 10^-10, signifying an extremely small divergence from linearity as concluded from solar system data. This bound is noteworthy because it is more stringent than those obtained from cosmological observations, often anticipated as such due to the accuracy of solar system data.

The paper's implications extend to both theoretical and practical realms. Theoretically, it corroborates the postulation that any significant divergence from GR within f(T) gravity models should be carefully scrutinized and minimal. Practically, this constraint provides a clear framework for refining theoretical models using f(T) gravity parameters, thereby influencing future efforts in both observational astrophysics and theoretical physics that deal with extended theories of gravity.

Future exploration into this domain might include finer examination at smaller scales by employing experiments that can test gravitational interaction at closer proximities given the scalar form α/r term becoming significant in scenarios beyond the solar system's context. Moreover, the implementation of a full Parametrized-Post-Newtonian (PPN) framework could offer further insights.

In conclusion, this essay has dissected the investigative prowess of Iorio and Saridakis, highlighting their contribution to constraining extensions of GR within solar system dynamics. Their findings underscore the necessity for minimal alterations to GR when applied to current solar system dynamics under the f(T) gravity framework. This work fundamentally serves as a benchmark for ongoing and future inquiries into modified theories of gravity and fosters a reevaluation of criteria that define these modifications across varying cosmic scales.