The pattern of growth in viable f(R) cosmologies

Abstract: We study the evolution of linear perturbations in metric f(R) models of gravity and identify a potentially observable characteristic scale-dependent pattern in the behavior of cosmological structures. While at the background level viable f(R) models must closely mimic LCDM, the differences in their prediction for the growth of large scale structures can be sufficiently large to be seen with future weak lensing surveys. While working in the Jordan frame, we perform an analytical study of the growth of structures in the Einstein frame, demonstrating the equivalence of the dynamics in the two frames. We also provide a physical interpretation of the results in terms of the dynamics of an effective dark energy fluid with a non-zero shear. We find that the growth of structure in f(R) is enhanced, but that there are no small scale instabilities associated with the additional attractive "fifth force". We then briefly consider some recently proposed observational tests of modified gravity and their utility for detecting the f(R) pattern of structure growth.

• The paper presents a designer approach that reproduces the ΛCDM background while revealing scale-dependent deviations in cosmic structure growth due to the scalaron.
• It leverages both analytical modeling and numerical simulations to detail how sub-horizon modifications affect the gravitational potentials Φ and Ψ.
• The results highlight the potential of upcoming weak lensing surveys to empirically test f(R) modifications against standard gravitational theories.

Analytical Insights into $f(R)$ Cosmological Growth Patterns

The paper, authored by Levon Pogosian and Alessandra Silvestri, offers a thorough examination of the linear perturbation evolution in viable $f(R)$ models of gravity, shedding light on the scale-dependent growth patterns of cosmological structures. These models, while mimicking $\Lambda$CDM at the background level, present a distinguishable growth pattern that may become observable with forthcoming weak lensing surveys. The study elaborates on the dynamics in both the Jordan and Einstein frames, while the latter formulations further interpret the results through the lens of an effective dark energy fluid dynamics exhibiting notable shear phenomena.

Key Contributions

The investigation begins by framing the context of modified gravity theories, specifically $f(R)$ gravity models, which serve as alternatives to General Relativity by eschewing additional exotic energy components. The viability of these models hinges on satisfying stringent cosmological and local constraints. The authors highlight a consistent set of constraints ensuring solar system and cosmological viability, focusing on conditions like $f_{RR}>0$ and negligible $f_R$ to allow for compatibility with local gravity tests.

Results and Analytical Discussion

Notably, the authors utilize a "designer" approach to $f(R)$ models, allowing them to derive functions with specified expansion histories, such as adhering to a $\Lambda$CDM framework, yet permitting observable deviations in structure growth dynamics. The researchers present compelling numerical simulations alongside analytical models, emphasizing the modifications introduced by an additional scalar degree of freedom—termed the scalaron—characterized by a scale called the Compton wavelength. This scale denotes the boundary where deviations from standard gravitational interactions manifest significantly, especially under conditions where matter perturbations are enhanced.

Sub-Horizon Behavior

In the sub-horizon regime, detailed in both Jordan and Einstein frames, the dynamics reveal that as modes transition into the Compton scale, traditional metric potentials such as $\Phi$ and $\Psi$ exhibit an induced gravitational slip—quantitatively articulated through parameters like $\omega$ and $\eta$. The scalaron’s influence, essentially serving as a manifest "fifth force," reshapes the relation between these potentials, impacting growth rates of structures in a scale-dependent manner. Although gravitational enhancements due to this "fifth force" are scale selective, large-scale observational data might potentially capture it, particularly through ISW effects or weak lensing methodologies.

Implications and Future Prospects

The theoretical implications arising from this work suggest distinctive observational signatures in the growth pattern of cosmic structures when compared to the standard $\Lambda$CDM model. Although deeply compatible with current cosmological models at the background level, $f(R)$ theories enable scientists to explore the full parameter space of cosmic growth and gravitational interactions, which can be critically tested through next-generation cosmological probes. While challenges remain, particularly in achieving observational accuracies necessary to capture these subtle deviations, continued advancements in survey techniques hold promise for empirically distinguishing among competing cosmological paradigms. The paper thus lays groundwork for future empirical investigations, propelling further inquiry into the field of modified gravity and its role in cosmic evolution.