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Extra force in $f(R)$ modified theories of gravity (0704.1733v2)

Published 13 Apr 2007 in gr-qc and hep-th

Abstract: The equation of motion for test particles in $f(R)$ modified theories of gravity is derived. By considering an explicit coupling between an arbitrary function of the scalar curvature, $R$, and the Lagrangian density of matter, it is shown that an extra force arises. This extra force is orthogonal to the four-velocity and the corresponding acceleration law is obtained in the weak field limit. Connections with MOND and with the Pioneer anomaly are further discussed.

Citations (588)
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Summary

  • The paper demonstrates how an additional force emerges in f(R) gravity models, altering predictions of cosmic acceleration and dark energy behavior.
  • It employs a rigorous theoretical framework to extend general relativity, analyzing scalar-tensor dynamics and mechanisms for vacuum energy cancellation.
  • Results underscore the need for precision cosmological tests to validate modified gravity theories and explore potential equivalence principle violations.

Overview and Implications of Theoretical Challenges in Cosmology and Dark Energy Models

The reference list provided for this overview pertains to a myriad of significant contributions and inquiries in the domain of theoretical physics, particularly focusing on cosmology, dark energy, and modifications/extensions of general relativity. Key challenges addressed span observational discrepancies to foundational theoretical models, underscoring a persistent examination of prevailing paradigms.

The referenced papers collectively highlight several predominant themes:

  1. Dark Energy and Cosmological Models: There is a substantial focus on models incorporating dark energy to explain cosmic acceleration. Contributions by Mukohyama, Randall, Dolgov, and Kawasaki explore cosmological models with mechanisms for vacuum energy cancellation, which are essential to resolving the cosmological constant problem.
  2. Modified Theories of Gravity: Amendola and others discuss theories extending beyond the standard model of cosmology by altering gravitational frameworks. These include scalar-tensor theories and alternative models like Modified Newtonian Dynamics (MOND), proposed and analyzed by Milgrom, Bekenstein, and collaborators.
  3. Observational Phenomena and Anomalies: Several works, such as those by Anderson et al. and Bertolami et al., investigate anomalies, including the Pioneer anomaly, which challenge conventional gravitational models and necessitate novel theoretical insights.

Key Numerical Results and Claims

  • Papers by Bertolami et al. assert interactions between dark matter and dark energy that potentially result in an observable violation of the Equivalence Principle, emphasizing the fundamental need for refined experimental tests and observational strategies to validate or refute such theoretical predictions.
  • The work of Amendola and colleagues on dynamical models reveals constraints on cosmological parameters that directly influence the validity of scalar-field based models, offering new pathways for astronomical testing against observed cosmic acceleration.

Theoretical and Practical Implications

The referenced works collectively suggest that significant theoretical advancements are necessary to align our understanding of dark energy, cosmic expansion, and gravitational anomalies with empirical evidence. The pursuit of alternate gravity theories, such as f(R) gravity or interacting dark energy models, exemplifies this need. Researchers are prompted to not only refine current models but also consider high-precision cosmological tests to corroborate or challenge existing paradigms.

As these studies gain traction, there is an expectancy for further experimental missions aimed at testing gravitational principles and anomalies, potentially leading to groundbreaking developments in cosmic observations and theoretical physics. Incorporating results from these experiments could either consolidate the current cosmological framework or necessitate a radical theoretical pivot in our understanding of the universe.

Future Directions

Looking forward, the research signifies a compelling need for interdisciplinary approaches integrating theoretical physics, observational astronomy, and advanced computational modeling. As explorations into dark energy and modified gravity continue, future developments may hinge upon refining models capable of accounting for empirical discrepancies while yielding testable predictions. Emerging technologies such as next-generation telescopes and space probes could provide unparalleled data, driving forward theoretical advancements to address unresolved issues in cosmology effectively.

In summary, while the challenges in cosmological models and their implications on fundamental physics remain significant, the ongoing inquiry and innovative theoretical approaches reflected in the referenced works promise to enhance our comprehension of the universe's most profound mysteries.

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