Cosmological Standard Timers from Unstable Primordial Relics

In this article we study a hypothetical possibility of tracking the evolution of our Universe by introducing a series of the so-called standard timers. Any unstable primordial relics generated in the very early Universe may serve as the standard timers, as they can evolve through the whole cosmological background until their end while their certain time-varying properties could be a possible timer by recording the amount of physical time elapsed since the very early moments. Accordingly, if one could observe these quantities at different redshifts, then a redshift-time relation of the cosmic history can be attained. To illustrate such a hypothetical possibility, we consider the primordial black hole bubbles as a concrete example and analyze the mass function inside a redshifted bubble by investigating the inverse problem of Hawking radiation. To complete the analyses theoretically, the mass distribution can serve as a calibration of the standard timers.