Oscillating scalar potential and its implications for cosmic neutrino background searches

We propose a novel mechanism in which an external oscillatory wave modulates the mass-squared term of a scalar potential, periodically switching its sign. As a result of this "potential oscillation," the vacuum transitions between symmetry-broken and symmetry-restored phases. This repeated toggling leads to a time-varying vacuum state with rich phenomenological consequences, driven by the scalar field's couplings to other sectors. As a concrete illustration, we demonstrate how these oscillations can open a new avenue for probing the cosmic neutrino background.