We study the cosmological and weak-field properties of theories of gravity derived by extending general relativity by means of a Lagrangian proportional to R ^ { 1 + \delta } .
This scale-free extension reduces to general relativity when \delta \rightarrow 0 .
In order to constrain generalisations of general relativity of this power class we analyse the behaviour of the perfect-fluid Friedmann universes and isolate the physically relevant models of zero curvature .
A stable matter-dominated period of evolution requires \delta > 0 or \delta < -1 / 4 .
The stable attractors of the evolution are found .
By considering the synthesis of light elements ( helium-4 , deuterium and lithium-7 ) we obtain the bound -0.017 < \delta < 0.0012. We evaluate the effect on the power spectrum of clustering via the shift in the epoch of matter-radiation equality .
The horizon size at matter–radiation equality will be shifted by \sim 1 \% for a value of \delta \sim 0.0005. We study the stable extensions of the Schwarzschild solution in these theories and calculate the timelike and null geodesics .
No significant bounds arise from null geodesic effects but the perihelion precession observations lead to the strong bound \delta = 2.7 \pm 4.5 \times 10 ^ { -19 } assuming that Mercury follows a timelike geodesic .
The combination of these observational constraints leads to the overall bound 0 \leq \delta < 7.2 \times 10 ^ { -19 } on theories of this type .