  Power-law corrections (having the exponent strictly between 2 and 3) to the
Einstein-Hilbert action yield an extended theory of gravity which is consistent
with Solar-System tests and properly reproduces the main phases of the Universe
thermal history. We find two distinct constraints for the characteristic length
scale of the model: a lower bound from the Solar-System test and an upper bound
by requiring the existence of the matter-dominated era. We also show how the
extended framework can accommodate the existence of an early de Sitter phase.
Within the allowed range of characteristic length scales, the relation between
the expansion rate and the energy scale of inflation is modified, yielding a
value of the rate several orders of magnitude smaller than in the standard
picture. The observational implication of this fact is that a tiny value of the
tensor-to-scalar ratio is expected in the extended framework. The suppression
of primordial tensor modes also implies that the inflationary scale can be made
arbitrarily close to the Planck one according to the current limits. Finally,
an analysis of the propagation of gravitational waves on a Robertson-Walker
background is addressed.
