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

TL;DR

This work analyzes a class of metric-only $f(R)$ gravity models that can drive late-time cosmic acceleration without a cosmological constant and remain consistent with cosmological observations and solar-system tests in the small-field limit. The authors frame the theory via a scalar degree of freedom $f_R$, derive background and linear perturbation dynamics, and identify the Compton wavelength as a key scale controlling deviations from GR. They show solar-system tests alone provide weak constraints, because the Sun can reside in a high-curvature, GR-like regime, with the galactic halo playing a crucial role in shielding interiors; stronger constraints emerge from the galaxy-to-cosmology transition and from future percent-level measurements of the linear matter power spectrum, potentially probing $|f_{R0}| o 10^{-7}$ in the linear regime. The results stress that viability depends on galactic halo structure and evolution, motivating cosmological simulations of $f(R)$ models to complement local tests and to interpret potential observational signals.

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.

Figures (10)

• Figure 1: Functional form of $f(R)$ for $n=1,4$, with normalization parameters $c_1,c_2$ given by $|f_{R0}|=0.01$ and a matching to $\Lambda$CDM densities (see § \ref{['sec:expansion']}). These functions transition from zero to a constant as $R$ exceeds $m^{2}$. The sharpness of the transition increases with $n$ and its position increases with $|f_{R0}|$. During cosmological expansion, the background only reaches $R/m^2 \sim 40$ for $|f_{R0}| \ll 1$ and so the functional dependence for smaller $R/m^2$ has no impact on the phenomenology.
• Figure 2: Cosmological evolution of the scalar field $f_R$ and the Compton wavelength parameter $B$ for models with $n=1,4$. Both parameters control observable deviations from general relativity and deviations decline rapidly with redshift as $n$ increases.
• Figure 3: Evolution of the effective equation of state for $n=1, 4$ for several values of the cosmological field amplitude today, $f_{R0}$. The effective equation of state crosses the phantom divide $w_{\rm eff}=-1$ at a redshift that decreases with increasing $n$ leading potentially to a relatively unique observational signature of these models.
• Figure 4: Fractional change in the matter power spectrum $P(k)$ relative to $\Lambda$CDM for a series of the cosmological field amplitude today, $f_{R0}$, for $n=1,4$ models. For scales that are below the cosmological Compton wavelength during the acceleration epoch $k \gtrsim (aH) B^{1/2}$ perturbation dynamics transition to the low-curvature regime where $\gamma=1/2$ and density growth is enhanced. This transition occurs in the linear regime out to field amplitudes of $|f_{R0}| \sim 10^{-6}-10^{-7}$.
• Figure 5: Density profile in the solar interior and vicinity (solid curve). Under general relativity (GR), the curvature $R$ would track the density profile. For the $f(R)$ model with $n=4$, cosmological field amplitude $|f_{R0}|=0.1$ and a galactic field amplitude that minimizes the scalar potential, the curvature tracks the GR or high-curvature limit out to the edge of the solar corona at about 1AU (dashed line).