We examine a framework with light new physics, which couples to the Standard Model only via neutrino mixing. Taking the hints from the short-baseline anomalies seriously and combining them with modern cosmological data and recent IceCube measurements, we obtain surprisingly effective constraints on the hidden force: keV $lesssim M lesssim0.3$ GeV for the mediator mass and $g_{h}>10^{-6}-10^{-3}$ for the coupling constant. Flavor equilibration between the hidden and active neutrinos can be delayed until temperatures of $sim 1$ MeV, but not below $sim 100$ keV. This scenario can be tested with next-generation Cosmic Microwave Background, IceCube, and oscillation experiments.
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