Cosmological constraints on f(R) gravity theories within the Palatini approach

TL;DR

The paper tests Palatini $f(R)$ gravity as an alternative to dark energy by deriving the expansion history $H(a)$ for a general $f(R)$ and confronting it with multiple cosmological probes. Adopting a leading correction form $f(R)=R\left[1+\alpha\left(-\frac{R}{H_0^2}\right)^{\beta-1}\right]$, the authors translate observational constraints from background probes—SNIa, the CMBR shift parameter ${\cal R}$, and BAO—into bounds on $(\alpha,\beta)$ and identify a best-fit near $(\alpha,\beta)=(-3.6,0.09)$, while ruling out the simple $1/R$ case. They also analyze linear perturbations within a Palatini framework using a spherical-collapse approach to derive the growth equation and compare the predicted growth rate to 2dFGRS data, yielding best-fit $(\alpha,\beta)=(-4.25,0.05)$ with persistent degeneracies. Overall, current background data provide strong discrimination among viable $f(R)$ Palatini models, and although the data do not require non-standard gravity, the methodology demonstrates how combined probes test the gravitational theory beyond GR.

Abstract

We investigate f(R) theories of gravity within the Palatini approach and show how one can determine the expansion history, H(a), for an arbitrary choice of f(R). As an example, we consider cosmological constraints on such theories arising from the supernova type Ia, large scale structure formation and cosmic microwave background observations. We find that best fit to the data is a non-null leading order correction to the Einstein gravity, but the current data exhibits no significant preference over the concordance LCDM model. Our results show that the often considered 1/R models are not compatible with the data. The results demonstrate that the background expansion alone can act as a good discriminator between modified gravity models when multiple data sets are used.

Figures (7)

• Figure 1: The $68,\, 95$ and $99\%$ confidence contours arising from fitting the CMBR shift parameter. The parameter values corresponding to the concordance $\Lambda$CDM model ($\Omega_m=0.27, \Omega_{\Lambda}=0.73$ or $\alpha=-4.38,\ \beta=0$) are marked with a cross. The gray area represents a section of the parameter space that is not allowed.
• Figure 2: The $68,\, 95$ and $99\%$ confidence contours arising from fitting the SN Ia data. The parameter values corresponding to the concordance $\Lambda$CDM model ($\Omega_m=0.27, \Omega_{\Lambda}=0.73$ or $\alpha=-4.38,\ \beta=0$) are marked with a cross. The gray area represents a section of the parameter space that is not allowed.
• Figure 3: The combined $68,\, 95$ and $99\%$ confidence contours arising from fitting the SN Ia and the CMBR shift parameter data. The parameter values corresponding to the concordance $\Lambda$CDM model ($\Omega_m=0.27, \Omega_{\Lambda}=0.73$ or $\alpha=-4.38,\ \beta=0$) are marked with a cross. The gray area represents a section of the parameter space that is not allowed.
• Figure 4: The $68,\, 95$ and $99\%$ confidence contours arising from fitting the length scale associated with the baryon oscillations. The parameter values corresponding to the concordance $\Lambda$CDM model ($\Omega_m=0.27, \Omega_{\Lambda}=0.73$ or $\alpha=-4.38,\ \beta=0$) are marked with a cross. The gray area represents a section of the parameter space that is not allowed.
• Figure 5: The $68,\, 95$ and $99\%$ confidence contours arising from fitting the combined data from the SNIa, CMBR shift parameter and the length scale associated to the baryon oscillations. The parameter values corresponding to the concordance $\Lambda$CDM model ($\Omega_m=0.27,\ \Omega_{\Lambda}=0.73$ or $\alpha=-4.38,\ \beta=0$) are marked with a cross. The gray area represents a section of the parameter space that is not allowed.