General Constraints on Isocurvature from the CMB and Ly-$\alpha$ Forest

Current cosmological data are well-described by the Lambda-Cold Dark Matter ($\Lambda$CDM) model, which assumes adiabatic initial conditions for the primordial density perturbations. This agreement between data and theory enables strong constraints on new physics that generates isocurvature perturbations. Existing constraints typically assume a simple power law form for the isocurvature power spectrum. However, many new physics scenarios -- such as cosmological phase transitions and gravitational particle production -- can deviate from this assumption. To derive general constraints which apply to a wide variety of new physics scenarios, we consider four types of isocurvature modes (dark matter, baryon, dark radiation and neutrino density isocurvature) and parametrize the isocurvature power spectrum using two general forms: a delta function and a broken power law. Using data from the cosmic microwave background (CMB), baryon acoustic oscillations, the Lyman-$\alpha$ forest, and CMB spectral distortions, we place constraints on the isocurvature power spectrum across a wide range of scales, from $10^{-4}\,\textrm{Mpc}^{-1}$ to $10^{4}\,\textrm{Mpc}^{-1}$.