Effective gravitational couplings for cosmological perturbations in the most general scalar-tensor theories with second-order field equations (1108.4242v2)

Abstract: In the Horndeski's most general scalar-tensor theories the equations of scalar density perturbations are derived in the presence of non-relativistic matter minimally coupled to gravity. Under a quasi-static approximation on sub-horizon scales we obtain the effective gravitational coupling $G_{eff}$ associated with the growth rate of matter perturbations as well as the effective gravitational potential $\Phi_{eff}$ relevant to the deviation of light rays. We then apply our formulas to a number of modified gravitational models of dark energy--such as those based on f(R) theories, Brans-Dicke theories, kinetic gravity braidings, covariant Galileons, and field derivative couplings with the Einstein tensor. Our results are useful to test the large-distance modification of gravity from the future high-precision observations of large-scale structure, weak lensing, and cosmic microwave background.

• The paper derives effective gravitational coupling terms for linear density perturbations in scalar-tensor theories, expanding our understanding beyond General Relativity.
• It formulates coupling modifications under the quasi-static approximation, clarifying deviations from Newton's constant in cosmic structures.
• The analysis across models like f(R), Brans-Dicke, and Galileons quantifies distinct signatures observable in large-scale structures and weak lensing.

Effective Gravitational Couplings in Scalar-Tensor Theories

The research paper "Effective gravitational couplings for cosmological perturbations in the most general scalar-tensor theories with second-order field equations" by Antonio De Felice, Tsutomu Kobayashi, and Shinji Tsujikawa presents a significant exploration into the field of scalar-tensor theories. These theories, including f(R) theories, Brans-Dicke theories, kinetic gravity braiding, covariant Galileons, and field-derivative couplings involve modifications to General Relativity which can offer explanations for the cosmic acceleration observed in our universe without invoking a cosmological constant.

Horndeski's theories, the most comprehensive within this context, provide scalar-tensor models characterized by second-order field equations, thereby avoiding Ostrogradski's instability. The paper is pivotal as it extends the analysis to cosmological perturbations within these theories, introducing effective gravitational couplings and potentials which modify the linear density perturbation equations. This research is crucial for understanding the implications of scalar-tensor theories on cosmological observations such as weak gravitational lensing and large-scale structure.

Major Contributions

1. Linear Perturbation Equations: The authors derive the equations for linear density perturbations within the framework of scalar-tensor theories, explicitly considering the background equations on the flat Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime.
2. Effective Gravitational Couplings: The remarkable aspect of this research is the derivation of effective gravitational coupling terms applicable under the quasi-static approximation on sub-horizon scales. These terms ascertain the deviations from Newton's gravitational constant G and are pivotal for exploring deviations in the growth rate of matter perturbations.
3. Analysis Across Different Models: The authors apply their formulations to several gravitational models including f(R) theories, Brans-Dicke theories, and covariant Galileons. Each model’s distinctive effective gravitational coupling and implications on anisotropic parameters reveal the models' varied potential impacts on large-scale cosmic observations.
4. Numerical Results: The paper meticulously quantifies the effective gravitational couplings and potentials for each gravitational model, showcasing disparate behaviors attributed to model-specific parameters. These results illuminate distinctive signatures which could be used to contrast competing theories using high-precision cosmological data.

Implications and Future Work

The implications of this research are profound. The paper provides a thorough framework to discriminate between modified gravity models using observational data from cosmic microwave background (CMB), large-scale structure, and weak lensing. This is particularly crucial as discrepancies from General Relativity could substantially inform about the fabric of cosmic acceleration and potential new physics.

Looking forward, the expansion of these analyses to include further detailed observational comparisons is necessary. The theoretical groundwork laid by such perturbation analyses enables future efforts to implement these models in comprehensive simulations and data analysis, potentially unveiling alternative gravitational interactions or components crucial for dark energy phenomenology.

In conclusion, this paper establishes a detailed pathway to exploring the cosmological ramifications of scalar-tensor theories with second-order field equations. By elaborating on effective gravitational couplings, it provides strong numerical and theoretical tools for testing the fundamental nature of gravity and the dynamics of our universe against observable cosmological phenomena.