  Massive fields can imprint unique oscillatory features on primordial
correlation functions or inflationary correlators, which is dubbed the
cosmological collider signal. In this work, we analytically investigate the
effects of a time-dependent mass of a scalar field on inflationary correlators,
extending previous numerical studies and implementing techniques developed in
the cosmological bootstrap program. The time-dependent mass is in general
induced by couplings to the slow-roll inflaton background, with particularly
significant effects in the case of non-derivative couplings. By linearly
approximating the time dependence, the mode function of the massive scalar is
computed analytically, on which we derive analytic formulae for two-, three-,
and four-point correlators with the tree-level exchange of the massive scalar.
The obtained formulae are utilized to discuss the phenomenological impacts on
the power spectrum and bispectrum, and it is found that the scaling behavior of
the bispectrum in the squeezed configuration, i.e., the cosmological collider
signal, is modified from a time-dependent Boltzmann suppression. By
investigating the scaling behavior in detail, we are in principle able to
determine the non-derivative couplings between the inflaton and the massive
particle.
