We consider the potential density of rational points on an algebraic variety defined over a number field K, i.e., the property that the set of rational points of X becomes Zariski dense after a finite field extension of K. For a non-uniruled projective variety with an int-amplified endomorphism, we show that it always satisfies potential density. When a rationally connected variety admits an int-amplified endomorphism, we prove that there exists some rational curve with a Zariski dense forward orbit, assuming the Zariski dense orbit conjecture in lower dimensions. As an application, we prove the potential density for projective varieties with int-amplified endomorphisms in dimension less than or equal to 3. We also study the existence of densely many rational points with the maximal arithmetic degree over a sufficiently large number field.

The authors would like to thank the referee for very careful reading and the suggestions to improve the paper. The first, second and third authors are supported, from NUS, by the President's scholarship, a Research Fellowship and an ARF, respectively.