Modified Gravity and Cosmology (1106.2476v3)

Abstract: In this review we present a thoroughly comprehensive survey of recent work on modified theories of gravity and their cosmological consequences. Amongst other things, we cover General Relativity, Scalar-Tensor, Einstein-Aether, and Bimetric theories, as well as TeVeS, f(R), general higher-order theories, Horava-Lifschitz gravity, Galileons, Ghost Condensates, and models of extra dimensions including Kaluza-Klein, Randall-Sundrum, DGP, and higher co-dimension braneworlds. We also review attempts to construct a Parameterised Post-Friedmannian formalism, that can be used to constrain deviations from General Relativity in cosmology, and that is suitable for comparison with data on the largest scales. These subjects have been intensively studied over the past decade, largely motivated by rapid progress in the field of observational cosmology that now allows, for the first time, precision tests of fundamental physics on the scale of the observable Universe. The purpose of this review is to provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a self-contained, comprehensive and up-to-date introduction to the subject as a whole.

• The paper presents a comprehensive review of modified gravity theories offering scalar-tensor, vector-tensor, and bimetric frameworks as alternatives to General Relativity.
• It employs both theoretical and observational analyses, highlighting constraints from Solar System tests and cosmic surveys to evaluate these models.
• The study discusses mechanisms like quintessence and chameleon effects that potentially explain cosmic acceleration without relying solely on dark matter or dark energy.

An Academic Overview: Modified Gravity and Cosmology

The paper of modified theories of gravity is an active arena of scientific inquiry driven by both theoretical motivations and experimental anomalies that cannot be trivially explained by General Relativity (GR). The paper, "Modified Gravity and Cosmology," compiles comprehensive insights into various theoretical frameworks and their cosmological consequences, addressing numerous attempts to extend GR, through both fundamental field-theoretical considerations and phenomenological models.

Theoretical Landscapes

The foundational structure of General Relativity is challenged by a multitude of alternative theories, each bringing its own scalar, vector, or tensor modifications. The scalar-tensor theories of gravity, first formalized through the Brans-Dicke framework, generalize the gravitational interaction by introducing a scalar field that modulates the effective gravitational coupling. This approach is deeply analyzed in the context of cosmology, with the coupling parameter $\omega$ impacting the weak-field limit, which is pertinent for Solar System tests. Observational constraints, particularly from the Cassini mission, necessitate that $\omega$ must be exceedingly large, suggesting that any scalar-tensor deviation from GR is minimal in the local universe.

The exposition extends to vector-tensor and bimetric theories, which introduce Lorentz-violating elements, as seen in Einstein-Æther theories. This framework epitomizes the breaking of Lorentz invariance while maintaining diffeomorphism symmetry, posited as a testbed for understanding possible vector field contributions within cosmological models.

Additionally, the review articulates the complexities of massive gravity, exploring its historical challenges such as the vDVZ discontinuity and the elusive Boulware-Deser ghost. Innovative attempts like the de Rham-Gabadadze-Tolley (dRGT) models showcase how tuning coupling constants potentially circumvents traditional inconsistencies.

Cosmological Implications

The paper conspicuously traverses the potential of modified gravity theories to resolve the enduring dark energy quandary, which currently invokes a cosmological constant, $\Lambda$, within the standard model ($\Lambda$CDM). A prominent feature of these alternatives is their endeavor to reconcile accelerated cosmic expansion without invoking exotic dark matter or energy, contingent upon a blend of quintessence and chameleon mechanisms, thus providing a concordant expansion history with observational footprints of the cosmic microwave background (CMB) and large-scale structure (LSS).

Galileon fields and ghost condensates represent higher-order derivative theories, effectively capturing late-time acceleration phenomena. These models aim to provide a self-accelerating universe free from fine-tuning issues inherent in $\Lambda$CDM, employing non-standard kinetic terms and higher curvature invariants as potential sources of cosmic inflation or late-time acceleration.

Bimetric theories further illustrate how the interplay of two metric fields might simulate what is perceived as dark matter and energy. These frameworks thrive on constructing phenomenological potentials that interpolate between different regimes of gravitational interaction, potentially offering solutions to galaxy rotation curve anomalies, traditionally attributed to unseen dark halos.

Experimental and Observational Prospects

While theory dictates the playground of modified gravity, empirical validation remains paramount. Proposals like the Parameterised Post-Friedmannian approach serve as a parallel to the PPN formalism but are tailored for cosmological scales, scrutinizing modifications in gravitational potentials on a cosmic stage. Surveys detailing weak lensing, galactic clustering, and the ISW effect provide fertile empirical ground for these theories, capable of differentiating between modified gravity models and $\Lambda$CDM scenarios.

In conclusion, the paper meticulously delineates the nuances of various modified theories of gravity, juxtaposing their theoretical elegance against demanding empirical scrutiny. These theories strive to extend our comprehension of gravity beyond GR, each offering a potential path to unravel the mysteries of cosmic acceleration and galaxy dynamics without solely relying on dark matter and energy. Yet, they face the unyielding constraints and opportunities impressed by observational cosmology, suggesting a compelling symbiosis of theoretical exploration and observational investigation for future advancements in our understanding of the universe.