Cosmic inflation without inflaton

We propose a novel explanation for universe's inflationary period. We argue that when the Einstein-Hilbert action is supplemented by an infinite tower of higher-curvature terms - selected order by order by the criterium that they give rise to a well-posed cosmological evolution - the usual Big Bang characteristic of Einstein gravity is replaced by a singularity-free period of exponential growth of the scale factor, which is gracefully connected with standard late-time ACDM cosmology. No inflaton or any additional fields besides the metric are required.