Non-local $R^2$-like inflation, Gravitational Waves and
  Non-Gaussianities
  The emergence of $R^2$ (Starobinsky) inflation from the semi-classical
modification of gravity due to matter quantum fields (trace anomaly) clearly
points out the importance of fundamental physics and the first principles in
the construction of successful cosmological models. Along with the
observational success, $R^2$ gravity is also an important step beyond general
relativity (GR) towards quantum gravity. Furthermore, several approaches of
quantum gravity to date are strongly indicating the presence of non-locality at
small time and length scales. In this regard, ultraviolet (UV) completion of
$R^2$ inflation has been recently studied in a string theory-inspired
ghost-free analytic non-local gravity. We discuss the promising theoretical
predictions of non-local $R^2$-like inflation with respect to the key
observables such as tensor-to-scalar ratio, tensor tilt which tell us about the
spectrum of primordial gravitational waves, and scalar Non-Gaussianities which
tell us about the three-point correlations in the CMB fluctuations. Any
signature of non-local physics in the early Universe will significantly improve
our understanding of fundamental physics at UV energy scales and quantum
gravity.
