Cosmological Constraints on f(R) Acceleration Models

TL;DR

This work tests whether $f(R)$ gravity can mimic the $\Lambda$CDM expansion while leaving distinctive imprints on cosmic structure. It parameterizes the extra scalar by the present Compton-scale quantity $B_0$, computes observables with a modified CAMB, and constrains the model using a Markov Chain Monte Carlo analysis of WMAP, SDSS LRG, SNLS, and galaxy–ISW data. The results show the ISW-dominated CMB constraints bound $B_0$ to about $<1$ for horizon-scale Compton wavelengths, while the joint CMB+LRG+SN bound is $B_0<4.3$ (95% CL); nonlinear uncertainties weaken LRG constraints and galaxy–ISW data provide tighter limits. The study highlights the need for nonlinear simulations to break degeneracies with $Q_{nl}$ and suggests that future surveys could probe $B_0$ down to a few Mpc scales, offering a cosmological test of gravity beyond local tests.

Abstract

Models which accelerate the expansion of the universe through the addition of a function of the Ricci scalar f(R) leave a characteristic signature in the large-scale structure of the universe at the Compton wavelength scale of the extra scalar degree of freedom. We search for such a signature in current cosmological data sets: the WMAP cosmic microwave background (CMB) power spectrum, SNLS supernovae distance measures, the SDSS luminous red galaxy power spectrum, and galaxy-CMB angular correlations. Due to theoretical uncertainties in the nonlinear evolution of f(R) models, the galaxy power spectrum conservatively yields only weak constraints on the models despite the strong predicted signature in the linear matter power spectrum. Currently the tightest constraints involve the modification to the integrated Sachs-Wolfe effect from growth of gravitational potentials during the acceleration epoch. This effect is manifest for large Compton wavelengths in enhanced low multipole power in the CMB and anti-correlation between the CMB and tracers of the potential. They place a bound on the Compton wavelength of the field be less than of order the Hubble scale.

Figures (2)

• Figure 1: Time evolution of the effective gravitational potential $\Phi_- = (\Phi-\Psi)/2$ for $k=10^{-3}/$Mpc near the peak contribution to the ISW effect at low multipoles. As the Compton wavelength parameter $B_0$ increases, the decay of the gravitational potential in $\Lambda$CDM decreases and eventually turns to growth. This reversal changes the sign of the ISW effect in overdense regions traced by galaxies.
• Figure 2: CMB angular power spectrum $C_{\ell}$ for $f(R)$ models with the Compton wavelength parameter $B_{0}=0$ ($\Lambda$CDM), 0.5, 1.5, 3.0, 5.0. As $B_{0}$ increases, the ISW contributions to the low multipoles decrease, change sign, and then increase. WMAP3 data with noise error bars are overplotted and rule out $B_{0} \ge 4.3$ (95% CL).