Cosmological constraints on $\gamma$-gravity models

In this paper we place observational constraints on the well-known $\gamma$-gravity $f(R)$ model using the latest cosmological data, namely we use the latest growth rate, Cosmic Microwave Background, Baryon Acoustic Oscillations, Supernovae type Ia and Hubble parameter data. Performing a joint likelihood analysis we find that the $\gamma$-gravity model is in very good agreement with observations. Utilizing the AIC statistical test we statistically compare the current $f(R)$ model with $\mathrm{\Lambda }\mathrm{CDM}$ cosmology and find that they are statistically equivalent. Therefore, $\gamma$-gravity can be seen as a useful scenario toward testing deviations from General Relativity. Finally, we note that we find somewhat higher values for the $f(R)$ best-fit values compared to those mentioned in the past in the literature and we argue that this could potential alleviate the halo-mass function problem.

Figure 1

The effective equation of state $w_{\mathrm{DE}}(z)$ of the $\gamma$-gravity model for $n=2$, ${\mathrm{\Omega }}_{m0}=0.28$ and $\alpha =(1,1.1,1.2,1.4,1.6,1.8)$. As can be seen, for realistic values of the parameter $\alpha$ the deviation of the background expansion from the $\mathrm{\Lambda }\mathrm{CDM}$ model can be significant, for example it can reach approximately $\sim 5\%$ at intermediate redshifts.

Figure 2

The 68.3%, 95.4% and 99.7% of the $\gamma$-gravity model for various parameter combinations. The black dots correspond to the mean values of the parameters in the MCMC chain.

Figure 3

The 68.3%, 95.4% and 99.7% of the $\mathrm{\Lambda }\mathrm{CDM}$ model for various parameter combinations. The black dots correspond to the mean values of the parameters in the MCMC chain.

Figure 4

The 1D marginalized PDFs of the $\gamma$-gravity model for various parameter combinations.

Figure 5

The 1D marginalized PDFs of the $\mathrm{\Lambda }\mathrm{CDM}$ model for ${\mathrm{\Omega }}_m$ (left), ${\mathrm{\Omega }}_b{h}^2$ (center) and ${\sigma }_8$ (right).

Figure 6

Plots of the growth parameter $f{\sigma }_8(z)$ (left) and the Hubble parameter $H(z)$ (right) with their $1\sigma$ errors for the $\gamma$-gravity (dotted black line) and the $\mathrm{\Lambda }\mathrm{CDM}$ (dashed black line) models respectively for the best-fit parameters show in Table 3. As can be seen, in this case the best-fit curves are practically indistinguishable from each other.