Modified gravity models of dark energy (1101.0191v1)

Abstract: We review recent progress of modified gravity models of dark energy--based on f(R) gravity, scalar-tensor theories, braneworld gravity, Galileon gravity, and other theories. In f(R) gravity and Brans-Dicke theory it is possible to design viable models consistent with local gravity constraints under a chameleon mechanism, while satisfying conditions for the cosmological viability. The Dvali-Gabadazde-Porrati braneworld model can be compatible with local gravity constraints through a nonlinear field self-interaction arising from a brane-bending mode, but the self-accelerating solution contains a ghost mode in addition to the tension with observational data about the cosmic expansion history. The extension of the field self-interaction to more general forms satisfying a Galilean symmetry in the flat space-time allows a possibility to avoid the appearance of ghosts and Laplacian instabilities, while the late-time cosmic acceleration can be realized by the field kinetic energy. We study the evolution of cosmological perturbations in those models to place constraints on model parameters from the observations of large-scale structure, cosmic microwave background, and weak lensing. We also briefly review other modified gravitational models of dark energy-- such as those based on Gauss-Bonnet gravity and Lorentz-violating theories.

• The paper systematically assesses modified gravity models—particularly f(R) and scalar-tensor theories—demonstrating compatibility with both cosmic and local gravitational tests.
• It details the use of mechanisms like the chameleon effect in f(R) models and outlines crucial conditions to avoid ghost instabilities.
• The review highlights observational diagnostics such as matter perturbations and ISW effects as key tests for validating these dark energy alternatives.

Insights into "Modified gravity models of dark energy"

This paper provides a comprehensive exploration of modified gravity models as potential explanations for dark energy, addressing different theoretical frameworks and observational implications. The author, Shinji Tsujikawa, systematically reviews five categories of theories: $f(R)$ gravity, scalar-tensor theories, the Dvali-Gabadadze-Porrati (DGP) model, Galileon gravity, and other models including Gauss-Bonnet variants and Lorentz-violating theories.

$f(R)$ Gravity Models

The $f(R)$ gravity models propose extensions to the Einstein-Hilbert action by introducing a general function of the Ricci scalar, which can lead to self-consistent models in line with local gravity constraints. The use of a chameleon mechanism, where the scalar degree of freedom (or "scalaron") dynamically changes mass depending on the environment's density, allows these theories to adhere to both cosmological and local tests of gravity. Notably, conditions for avoiding ghosts (instabilities in the quantum field) such as ensuring $f_{,RR} > 0$ are critical for the viability of these models. The discussion presents specific forms of $f(R)$ that adhere to these stability and observational criteria, providing potential alternatives to the standard $\Lambda$CDM by allowing a dynamically-varying dark energy equation of state.

Scalar-Tensor Theories

These theories extend the paradigm by permitting the coupling of a scalar field with gravity. The paper elaborates on Brans-Dicke theory, emphasizing that a significant coupling with matter (termed as $Q$) is permissible when local gravity constraints are mediated through a chameleon mechanism, akin to $f(R)$ models. Tsujikawa highlights the potential of scalar-tensor theories to not only address the coincidence problem but also remain aligned with solar system tests by modulating the scalar field's mass and coupling strength.

Braneworld Models (DGP)

The DGP model provides a distinct perspective by embedding our 4D universe in a 5D bulk, naturally invoking accelerated expansion without a cosmological constant. Despite its appeal, the model faces challenges, notably the presence of ghost modes in scalar perturbations and tension with combined datasets from Supernovae Ia and Baryon Acoustic Oscillations. The ghost issue arises due to the propagation of an unphysical degree of freedom. While modifications such as the inclusion of additional terms or higher-dimensional proposals are outlined, traditional DGP models are critiqued for inherent instabilities.

Galileon Gravity

Galileon gravity, extending from the idea of a brane-bending mode in the DGP framework, introduces a set of derivative self-interactions that remain invariant under Galilean shift transformations. The paper meticulously walks through the cosmological implications of these models, underscoring their success in converging diverse initial conditions towards common late-time behaviors (tracker solutions) while avoiding ghosts and instabilities. Additionally, Tsujikawa addresses extensions potential for these theories, exploring broader forms that offer further stabilization and accommodate observations.

Other Models

The review briefly ventures into other realms, such as Gauss-Bonnet gravity with a scalar coupling and $f(\mathcal{G})$ theories, both built on exploiting higher-order curvature invariants. However, they face stringent constraints from local gravity tests and are less favored as primary dark energy contenders. Lorentz-violating models shine light on another angle, presenting frameworks where phantom-like equations of state emerge without breaking ultraviolet stability, though practical observational persistency remains a challenge.

Observational Signatures and Future Directions

Tsujikawa emphasizes the importance of observational metrics, detailing how deviations in growth rates of matter perturbations, Integrated-Sachs-Wolfe effects in CMB anisotropies, and responses in weak lensing regimes could all serve as diagnostic tools for these modified gravity models. The observational pursuits—especially with future survey datasets—are posited as vital efforts to scrutinize the validity of these theories beyond the $\Lambda$CDM construct.

In summary, the paper not only assesses the theoretical robustness of each model but ambitiously ties them to a spectrum of observational measures, offering a roadmap for reconciling theoretical advancements with empirical queries, thereby advancing the understanding of our universe's accelerated expansion.