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The emergence of $R^2$ (Starobinsky) inflation from the semi-classicalmodification of gravity due to matter quantum fields (trace anomaly) clearlypoints out the importance of fundamental physics and the first principles inthe construction of successful cosmological models. Along with theobservational success, $R^2$ gravity is also an important step beyond generalrelativity (GR) towards quantum gravity. Furthermore, several approaches ofquantum gravity to date are strongly indicating the presence of non-locality atsmall time and length scales. In this regard, ultraviolet (UV) completion of$R^2$ inflation has been recently studied in a string theory-inspiredghost-free analytic non-local gravity. We discuss the promising theoreticalpredictions of non-local $R^2$-like inflation with respect to the keyobservables such as tensor-to-scalar ratio, tensor tilt which tell us about thespectrum of primordial gravitational waves, and scalar Non-Gaussianities whichtell us about the three-point correlations in the CMB fluctuations. Anysignature of non-local physics in the early Universe will significantly improveour understanding of fundamental physics at UV energy scales and quantumgravity.

Non-local $R^2$-like inflation, Gravitational Waves and Non-Gaussianities