Non-standard primordial clocks from induced mass in alternative to inflation scenarios

In the primordial universe, oscillations of heavy fields can be considered as standard clocks to measure the expansion or contraction history of the universe. Those standard clocks provide a model-independent way of distinguishing inflation and alternative scenarios. However, the mass of the heavy fields may not be a constant mass, but rather mass induced by non-minimal coupling to the Ricci scalar, or self-interactions. In the case of induced mass, the mass of the heavy field is generically of order Hubble, and thus is time-dependent in alternative to inflation scenarios. We show that such generated mass terms can be considered as non-standard primordial clocks for alternative to inflation, providing similar oscillatory frequencies as standard clocks of inflation. Additional information on scale dependence can distinguish such non-standard clocks from standard clocks.