Equivalence Principle Implications of Modified Gravity Models (0905.2966v2)

Abstract: Theories that attempt to explain the observed cosmic acceleration by modifying general relativity all introduce a new scalar degree of freedom that is active on large scales, but is screened on small scales to match experiments. We show that if such screening occurrs via the chameleon mechanism such as in f(R), it is possible to have order one violation of the equivalence principle, despite the absence of explicit violation in the microscopic action. Namely, extended objects such as galaxies or constituents thereof do not all fall at the same rate. The chameleon mechanism can screen the scalar charge for large objects but not for small ones (large/small is defined by the gravitational potential and controlled by the scalar coupling). This leads to order one fluctuations in the inertial to gravitational mass ratio. In Jordan frame, it is no longer true that all objects move on geodesics. In contrast, if the scalar screening occurrs via strong coupling, such as in the DGP braneworld model, equivalence principle violation occurrs at a much reduced level. We propose several observational tests of the chameleon mechanism: 1. small galaxies should fall faster than large galaxies, even when dynamical friction is negligible; 2. voids defined by small galaxies would be larger compared to standard expectations; 3. stars and diffuse gas in small galaxies should have different velocities, even on the same orbits; 4. lensing and dynamical mass estimates should agree for large galaxies but disagree for small ones. We discuss possible pitfalls in some of these tests. The cleanest is the third one where mass estimate from HI rotational velocity could exceed that from stars by 30 % or more. To avoid blanket screening of all objects, the most promising place to look is in voids.

• The paper demonstrates that modified gravity models with a chameleon mechanism can induce substantial equivalence principle violations in large-scale structures.
• It categorizes theories into f(R) and DGP models, highlighting differences in screening mechanisms and gravitational dynamics.
• The authors propose observational tests using galaxy dynamics, void sizes, and internal star motions to verify deviations from general relativity.

Equivalence Principle Implications of Modified Gravity Models

In the paper titled "Equivalence Principle Implications of Modified Gravity Models," the authors Lam Hui, Alberto Nicolis, and Christopher W. Stubbs investigate the implications of modified gravity models concerning the equivalence principle. They scrutinize theories that aim to elucidate cosmic acceleration by modifying general relativity (GR), particularly focusing on the introduction of new scalar degrees of freedom that are active on large scales but screened on smaller scales to align with experimental observations.

Key Findings and Methodology

The paper broadly categorizes these modified gravity models into those that involve adding curvature invariants to the Einstein-Hilbert action, notably $f(R)$ theories, and those that incorporate graviton mass modifications, exemplified by the Dvali-Gabadadze-Porrati (DGP) braneworld model. In both cases, a light scalar field emerges, necessitating suppression or screening mechanisms due to the stringent constraints from solar system and terrestrial experiments.

The authors focus primarily on the chameleon screening mechanism, where the scalar field acquires a mass dependent on local density, leading to violations of the equivalence principle. They demonstrate that under the chameleon mechanism, extended objects such as galaxies can exhibit significant fluctuations in the ratios of inertial to gravitational mass. As a result, different objects do not uniformly fall at the same rate—hence equivalence principle violations—even though the microscopic action explicitly adheres to universality. This is in contrast to theories employing the Vainshtein screening mechanism, which show reduced equivalence principle violations.

Major Analytical Contributions

The paper delivers calculations showing how large and small objects differentiate under these modified gravity theories and proposes derivations in both Einstein and Jordan frames, revealing the distinction between screened and unscreened objects. The chameleon mechanism predicts sizable equivalence principle violations for galaxies and their constituents when the scalar field is not universally suppressed. On the other hand, the Vainshtein mechanism, typical of DGP models, results only in relativistic or post-Newtonian order $1/c^2$ equivalence principle violations.

Observational Tests and Implications

To verify the chameleon mechanism, the authors suggest several observational approaches:

1. Galaxy dynamics test: Examine if smaller galaxies accelerate faster than larger ones due to their unscreened nature in environments where dynamical friction is negligible.
2. Void Size Test: Investigate whether voids defined by small galaxies are larger than expected, given their rapid expansion.
3. Internal Motions Test: Compare the velocities of stars and diffuse gas in small galaxies; discrepancies indicate deviations from the equivalence principle.
4. Lensing and Dynamical Mass Estimation: Assess the agreement between lensing-based mass assertions and dynamical calculations in galaxies.

The authors recommend further scrutinizing environments where blanket screening may not apply, such as voids, to observe pronounced violations of the equivalence principle. This approach allows indeed to pinpoint discrepancies indicating departures from GR.

Conclusion

Through this extensive analysis, the paper raises insightful questions about the nature of gravity and the behavior of celestial bodies under modified gravity models with scalar fields. The findings reveal potentially observable effects in cosmological structures and contribute to the fundamental understanding of gravity beyond the conventional parameters of general relativity. The proposed tests serve as critical assessments that could differentiate between various modified theories and traditional GR, thus advancing research in cosmology and astrophysics.

These contributions are framed within a rigorous analytical methodology and hold significant implications for theoretical physics and observational astronomy, particularly in testing and refining our understanding of gravity's behavior across different scales in the universe.