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Abstract Dark radiation (DR) appears as a new physics candidate in various scenarios beyond the Standard Model. While it is often assumed that perturbations in DR are adiabatic, they can easily have an isocurvature component if more than one field was present during inflation, and whose decay products did not all thermalize with each other.By implementing the appropriate isocurvature initial conditions (IC), we derive the constraints on both uncorrelated and correlated DR density isocurvature perturbations from the full Planck 2018 data alone, and also in combination with other cosmological data sets.Our study on free-streaming DR (FDR) updates and generalizes the existing bound on neutrino density isocurvature perturbations by including a varying number of relativistic degrees of freedom, and for coupled DR (CDR) isocurvature, we derive the first bound. We also show that for CDRqualitatively new physical effects arise compared to FDR. One such effect is that for isocurvature IC, FDR gives rise to larger CMB anisotropies compared to CDR — contrary to the adiabatic case.More generally, we find that a blue-tilt of DR isocurvature spectrum is preferred. This gives rise to a larger value of the Hubble constant H 0 compared to the standard ΛCDM+Δ N eff cosmology with adiabatic spectra and relaxes the H 0 tension.
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Local Existence, lower mass bounds, and a new continuation criterion for the Landau equation
We consider the spatially inhomogeneous Landau equation with soft potentials. First, we establish the short-time existence of solutions, assuming the initial data has sufficient decay in the velocity variable and regularity (no decay assumptions are made in the spatial variable). Next, we show that the evolution instantaneously spreads mass throughout the domain. The resulting lower bounds are sub-Gaussian, which we show is optimal. The proof of mass-spreading is based on a stochastic process, and makes essential use of nonlocality. By combining this theorem with prior results, we derive two important applications: $$C^\infty$$-smoothing, even for initial data with vacuum regions, and a continuation criterion (the solution can be extended as long as the mass and energy densities stay bounded from above). This is the weakest condition known to prevent blow-up. In particular, it does not require a lower bound on the mass density or an upper bound on the entropy density.
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- Award ID(s):
- 1816643
- PAR ID:
- 10089553
- Date Published:
- Journal Name:
- Journal of differential equations
- Volume:
- 266
- Issue:
- 2-3
- ISSN:
- 0022-0396
- Page Range / eLocation ID:
- 1536–1577
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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