  We argue that the presence of an inflationary epoch is a natural, almost
unavoidable, consequence of the existence of a sensible effective action
involving an infinite tower of higher-curvature corrections to the
Einstein-Hilbert action. No additional fields besides the metric are required.
We show that a family of such corrections giving rise to a well-posed
cosmological evolution exists and automatically replaces the
radiation-dominated early-universe Big Bang by a singularity-free period of
exponential growth of the scale factor, which is gracefully connected with
standard late-time $\Lambda$CDM cosmology. The class of higher-curvature
theories giving rise to sensible cosmological evolution share additional
remarkable properties such as the existence of Schwarzschild-like non-hairy
black holes, or the fact that, just like for Einstein gravity, the only degrees
of freedom propagated on the vacuum are those of the standard graviton.
