Models of f(R) Cosmic Acceleration that Evade Solar-System Tests (0705.1158v1)

Abstract: We study a class of metric-variation f(R) models that accelerates the expansion without a cosmological constant and satisfies both cosmological and solar-system tests in the small-field limit of the parameter space. Solar-system tests alone place only weak bounds on these models, since the additional scalar degree of freedom is locked to the high-curvature general-relativistic prediction across more than 25 orders of magnitude in density, out through the solar corona. This agreement requires that the galactic halo be of sufficient extent to maintain the galaxy at high curvature in the presence of the low-curvature cosmological background. If the galactic halo and local environment in f(R) models do not have substantially deeper potentials than expected in LCDM, then cosmological field amplitudes |f_R| > 10^{-6} will cause the galactic interior to evolve to low curvature during the acceleration epoch. Viability of large-deviation models therefore rests on the structure and evolution of the galactic halo, requiring cosmological simulations of f(R) models, and not directly on solar-system tests. Even small deviations that conservatively satisfy both galactic and solar-system constraints can still be tested by future, percent-level measurements of the linear power spectrum, while they remain undetectable to cosmological-distance measures. Although we illustrate these effects in a specific class of models, the requirements on f(R) are phrased in a nearly model-independent manner.

• The paper presents f(R) models that induce cosmic acceleration without a cosmological constant while converging to ΛCDM in high-curvature regimes.
• The authors employ scalar field dynamics and numerical simulations to demonstrate that deviations from general relativity remain consistent with both large-scale and solar-system observations.
• The study identifies critical thresholds for the field value |f_R0| and galactic halo effects, laying groundwork for future modified gravity research.

Insights into $f(R)$ Cosmic Acceleration Models and Solar-System Tests

The paper by Wayne Hu and Ignacy Sawicki explores a specific class of metric-variation $f(R)$ models intended to explain cosmic acceleration without invoking a cosmological constant and, crucially, that also satisfy both cosmological and solar-system tests. The authors focus on models where deviations from general relativity (GR) can align with observational requirements across varying scales.

Key Aspects of $f(R)$ Models

The research investigates an $f(R)$ model class characterized by a modified Einstein-Hilbert action, aiming to induce acceleration in the universe's expansion. The functional form of $f(R)$ is designed to converge towards $\Lambda$CDM at high curvatures while deviating at cosmological scales. A significant feature is its dependence on a scalar field, $f_R \equiv df(R)/dR$, which governs both the background expansion and the growth of structures.

Numerical Findings

• Cosmological Implications: In these models, the effective equation of state can evolve across the phantom divide ($w_{\rm eff} = -1$), providing a distinct observational signature. For small deviations, the maximum allowed cosmological field value, denoted $|f_{R0}|$, is crucial. The authors simulate various scenarios, showing that $n>1$ allows for notable deviations compatible with GR predictions, especially in structure formation dynamics.
• Solar-System Tests: The paper confirms that high-curvature solutions can evade local GR deviations. solar-system tests primarily constrain the galactic field value, $|f_{Rg}|$, suggesting that models with $|f_{R0}| \sim 10^{-1}$ can satisfy current observational limits when the galactic $f_R$ field is at a potential minimum.

Implications and Speculations

The results suggest that models which deviate significantly from GR can still be viable under solar-system constraints, provided certain conditions on galactic halo structure and evolution are met. The authors propose that for $|f_{R0}| \gtrsim 10^{-6}$, deviations in the galaxy’s gravitational potential will penetrate to cosmological scales, propulsion further research into cosmological simulations to capture this evolution during the acceleration epoch.

Future Directions

Looking ahead, the research signals potential restrictions on $f(R)$ theories driven by percent-level linear power spectrum measurements. Such precision could constrain cosmological amplitudes below current solar-system limits. The authors point out necessary future work involving numerical simulations to ascertain detailed dynamics of $f(R)$ models, especially as they transition from the high-curvature galactic scale to low-curvature cosmic backgrounds.

In summary, Hu and Sawicki's study offers an insightful exposition into $f(R)$ cosmic acceleration, marrying large-scale cosmological effects with minute local solar-system checks, providing a plausible groundwork for future investigations in modified gravity theories.