Constraining Inverse-Curvature Gravity with Supernovae

We show that models of generalized modified gravity, with inverse powers of the curvature, can explain the current accelerated expansion of the Universe without resorting to dark energy and without conflicting with solar system experiments. We have solved the Friedmann equations for the full dynamical range of the evolution of the Universe and performed a detailed analysis of supernovae data in the context of such models that results in an excellent fit. If we further include constraints on the current expansion of the Universe and on its age, we obtain that the matter content of the Universe is $0.07\le {\omega }_m\le 0.21$ (95% C.L.). Hence the inverse-curvature gravity models considered cannot explain the dynamics of the Universe just with a baryonic matter component.

Figure 1

The $1\sigma$ and $2\sigma$ joint likelihoods on ${\overline{\omega }}_m$ and $\alpha$. In the low region $\sigma =-1$, whereas in the high region $\sigma =+1$. The shaded area in the bottom right-hand corner determines the region that is excluded because of a singularity being hit in the past. The diamonds denote the maximum likelihood points.

Figure 2

The $1\sigma$ and $2\sigma$ joint likelihoods in the ${\omega }_m\mathrm{\text{−}}\widehat{\mu }$ plane, when additional priors on $H_0$ and the age of the Universe are imposed. On the left for the low region and on the right for the high region. Diamonds are the maximum likelihoods. Further, the dashed contours are the joint likelihoods if we impose only the $H_0$ prior.