The Cosmology of Modified Gauss-Bonnet Gravity (0705.3795v3)

Abstract: We consider the cosmology where some function f(G) of the Gauss-Bonnet term G is added to the gravitational action to account for the late-time accelerating expansion of the universe. The covariant and gauge invariant perturbation equations are derived with a method which could also be applied to general f(R,R^abR_ab,R^abcdR_abcd) gravitational theories. It is pointed out that, despite their fourth-order character, such f(G) gravity models generally cannot reproduce arbitrary background cosmic evolutions; for example, the standard LCDM paradigm with Omega_DE = 0.76 cannot be realized in f(G) gravity theories unless f is a true cosmological constant because it imposes exclusionary constraints on the form of f(G). We analyze the perturbation equations and find that, as in f(R) model, the stability of early-time perturbation growth puts some constraints on the functional form of f(G), in this case d^2 f/d G^2 < 0. Furthermore, the stability of small-scale perturbations also requires that f not deviate significantly from a constant. These analyses are illustrated by numerically propagating the perturbation equations with a specific model reproducing a representative LCDM cosmic history. Our results show how the f(G) models are highly constrained by cosmological data.

• The paper demonstrates that f(G) gravity can drive cosmic acceleration but is limited in reproducing arbitrary cosmological histories.
• The paper derives covariant, gauge-invariant perturbation equations, revealing that stability requires a negative second derivative of f(G) with respect to G.
• The paper’s numerical simulations show that even slight deviations from ΛCDM can trigger rapid small-scale perturbation growth against observational data.

An Analysis of Cosmology in Modified Gauss-Bonnet Gravity

The paper "The Cosmology of Modified Gauss-Bonnet Gravity" by Baojiu Li, John D. Barrow, and David F. Mota investigates a notable approach in theoretical physics: modifying Einstein's General Relativity by introducing additional terms in the gravitational action. In particular, the authors focus on the implications of incorporating a function of the Gauss-Bonnet invariant, denoted as $f(G)$, to explain the acceleration observed in the universe's expansion without invoking exotic dark energy components.

Key Findings and Analysis

The core hypothesis of the paper is the potential of the modified Gauss-Bonnet gravity (f(G) gravity) to account for cosmological observations that suggest a late-time accelerated expansion of the universe. The authors derive the covariant and gauge-invariant perturbation equations using a method applicable to general gravitational theories that involve higher-order curvature invariants.

Cosmology and Background Evolution

A significant section of the paper is dedicated to understanding the background evolution of the universe within the framework of $f(G)$ models. A central finding is the limitation of these models in reproducing arbitrary cosmological histories. Notably, the standard ΛCDM model is unreproducible unless the function $f(G)$ reduces to a constant, effectively becoming a cosmological constant. This arises due to the constraint that any $f(G)$ model, if fixed to resemble a ΛCDM scenario initially, loses the freedom to replicate such evolution throughout the entirety of cosmic history once the Gauss-Bonnet term $G$ changes its sign—a feature inherent in many plausible background evolutions.

Perturbation Dynamics and Stability

The treatment of perturbation dynamics unveils further constraints on $f(G)$ models. Parallel to previous findings in $f(R)$ gravity, the stability of perturbation growth imposes a necessary condition, $\partial^2 f/\partial G^2 < 0$, for the viability of these models. The research highlights that early-time stability requires this condition, while additional constraints must be satisfied for perturbations on small scales at later times. This results in limitations on the degree of deviation allowed from a cosmological constant to maintain consistency with observations, especially regarding the growth of small-scale perturbations, which is crucial for structure formation theories.

Numerical Simulations and Implications

The authors offer numerical simulations to examine the effects of $f(G)$ modifications on linear perturbation growth. These simulations demonstrate that for models closely resembling ΛCDM, even slight deviations in $f(G)$ can lead to significant discrepancies in perturbation behaviors, potentially generating rapid growth of small-scale perturbations. Such growth results in a strong scale dependence that is not empirically supported by current cosmic spectra data.

Conclusion and Future Outlook

The paper sheds light on the significant limitations and challenges faced by modified Gauss-Bonnet gravity models in explaining present cosmic acceleration without deviating considerably from observed cosmological parameters, such as those described by ΛCDM. By detailing these constraints, the paper emphasizes the intricate interplay between background evolution and perturbation stability in higher-order gravity theories.

Future research would benefit from exploring extensions and alterations to the f(G) models that could bypass these constraints or from considering alternative approaches to cosmic acceleration that align more naturally with observations. Furthermore, the report suggests additional investigations into local gravitational tests and their implications for the viability of such modified theories, potentially influencing how we understand gravitation on both large and small scales.