Cosmological Standard Timers: Framework and Perspectives

Cosmological standard timers (CSTs) are novel cosmological probes that aim to measure the cosmic time-redshift relation, which quantifies the size of the Universe with respect to cosmic time and further constrains cosmic evolution. With an initial statistical distribution of the dynamical systems as a standard reference, we can independently measure cosmic time from the time evolution of this statistical distribution. By combining the measured cosmic time with redshift extracted from observables, we can construct the cosmic time-redshift relation. Following this idea, we develop the framework of CSTs and discuss their perspectives in potential dynamical systems such as dark matter halo mass function, primordial black hole (PBH) mass function and PBH binaries as illustrative examples to demonstrate their feasibility in constructing the cosmic time-redshift relation.