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Emergence of $R^2$ inflation which is the best fit framework for CMBobservations till date comes from the attempts to attack the problem ofquantization of gravity which in turn have resulted in the trace anomalydiscovery. Further developments in trace anomaly and different frameworksaiming to construct quantum gravity indicate an inevitability of non-localityin fundamental physics at small time and length scales. A natural questionwould be to employ the $R^2$ inflation as a probe for signatures ofnon-locality in the early Universe physics. Recent advances of embedding $R^2$inflation in a string theory inspired non-local gravity modification providesvery promising theoretical predictions connecting the non-local physics in theearly Universe and the forthcoming CMB observations.

Analytic infinite derivative gravity, $R^2$-like inflation, quantum gravity and CMB