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