Multigrid Preconditioning for a Space-Time Spectral-Element Discontinuous-Galerkin Solver

In this work we examine a multigrid preconditioning approach in the context of a high- order tensor-product discontinuous-Galerkin spectral-element solver. We couple multigrid ideas together with memory lean and efficient tensor-product preconditioned matrix-free smoothers. Block ILU(0)-preconditioned GMRES smoothers are employed on the coarsest spaces. The performance is evaluated on nonlinear problems arising from unsteady scale- resolving solutions of the Navier-Stokes equations: separated low-Mach unsteady ow over an airfoil from laminar to turbulent ow. A reduction in the number of ne space iterations is observed, which proves the efficiency of the approach in terms of preconditioning the linear systems, however this gain was not reflected in the CPU time. Finally, the preconditioner is successfully applied to problems characterized by stiff source terms such as the set of RANS equations, where the simple tensor product preconditioner fails. Theoretical justification about the findings is reported and future work is outlined

Imprints of Spinning Particles on Primordial Cosmological Perturbations

If there exist higher-spin particles during inflation which are light compared to the Hubble rate, they may leave distinct statistical anisotropic imprints on the correlators involving scalar and graviton fluctuations. We characterise such signatures using the dS/CFT$_3$ correspondence and the operator product expansion techniques. In particular, we obtain generic results for the case of partially massless higher-spin states.Comment: 21 pages, 2 figures, v2: matching published versio

Primordial Black Holes from Inflation and non-Gaussianity

Primordial black holes may owe their origin to the small-scale enhancement of the comoving curvature perturbation generated during inflation. Their mass fraction at formation is markedly sensitive to possible non-Gaussianities in such large, but rare fluctuations. We discuss a path-integral formulation which provides the exact mass fraction of primordial black holes at formation in the presence of non-Gaussianity. Through a couple of classes of models, one based on single-field inflation and the other on spectator fields, we show that restricting to a Gaussian statistics may lead to severe inaccuracies in the estimate of the mass fraction as well as on the clustering properties of the primordial black holes.Comment: 21 pages, 2 figures, v2: matching published versio

A chloride channel in rat and human axons

Current recordings from single chloride channels were obtained from excised and cell-attached patches of rat and human axons. In rat axons the channels showed an outwardly rectifying current-voltage relationship with a slope conductance of 33 pS at negative membrane potentials and 65 pS at positive potentials (symmetrical 150 mM CsCl). They were measurably for cations (PNa/PCs/PCl=0.1/0.2/1). Channel currents were independent of cytoplasmatic calcium concentration. Inactivation was not observed and gating was weakly voltage dependent. Cl− channels in human axons showed similar gating behavior but had a lower conductance

Stochastic gravitational-wave background at 3G detectors as a smoking gun for microscopic dark matter relics

Microscopic horizonless relics could form in the early universe either directly through gravitational collapse or as stable remnants of the Hawking evaporation of primordial black holes. In both cases they completely or partially evade cosmological constraints arising from Hawking evaporation and in certain mass ranges can explain the entirety of the dark matter. We systematically explore the stochastic gravitational-wave background associated with the formation of microscopic dark-matter relics in various scenarios, adopting an agnostic approach and discussing the limitations introduced by existing constraints, possible ways to circumvent the latter, and expected astrophysical foregrounds. Interestingly, this signal is at most marginally detectable with current interferometers but could be detectable by third-generations instruments such as the Einstein Telescope, strengthening their potential as discovery machines.Comment: 11 pages, 4 figure

The Ineludible non-Gaussianity of the Primordial Black Hole Abundance

We study the formation of primordial black holes when they are generated by the collapse of large overdensities in the early universe. Since the density contrast is related to the comoving curvature perturbation by a nonlinear relation, the overdensity statistics is unavoidably non-Gaussian. We show that the abundance of primordial black holes at formation may not be captured by a perturbative approach which retains the first few cumulants of the non-Gaussian probability distribution. We provide two techniques to calculate the non-Gaussian abundance of primordial black holes at formation, one based on peak theory and the other on threshold statistics. Our results show that the unavoidable non-Gaussian nature of the inhomogeneities in the energy density makes it harder to generate PBHs. We provide simple (semi-)analytical expressions to calculate the non-Gaussian abundances of the primordial black holes and show that for both narrow and broad power spectra the gaussian case from threshold statistics is reproduced by increasing the amplitude of the power spectrum by a factor ${\cal O}(2\div 3)$.Comment: 26 pages, 10 figures, matching published versio

Testing Primordial Black Holes as Dark Matter through LISA

The idea that primordial black holes (PBHs) can comprise most of the dark matter of the universe has recently reacquired a lot of momentum. Observational constraints, however, rule out this possibility for most of the PBH masses, with a notable exception around $10^{-12} M_\odot$. These light PBHs may be originated when a sizeable comoving curvature perturbation generated during inflation re-enters the horizon during the radiation phase. During such a stage, it is unavoidable that gravitational waves (GWs) are generated. Since their source is quadratic in the curvature perturbations, these GWs are generated fully non-Gaussian. Their frequency today is about the mHz, which is exactly the range where the LISA mission has the maximum of its sensitivity. This is certainly an impressive coincidence. We show that this scenario of PBHs as dark matter can be tested by LISA by measuring the GW two-point correlator. On the other hand, we show that the short observation time (as compared to the age of the universe) and propagation effects of the GWs across the perturbed universe from the production point to the LISA detector suppress the bispectrum to an unobservable level. This suppression is completely general and not specific to our model.Comment: 22 pages, 12 figures. v3: matching published versio

Lensing constraints on ultradense dark matter halos

Cosmological observations precisely measure primordial variations in the density of the Universe at megaparsec and larger scales, but much smaller scales remain poorly constrained. However, sufficiently large initial perturbations at small scales can lead to an abundance of ultradense dark matter minihalos that form during the radiation epoch and survive into the late-time Universe. Because of their early formation, these objects can be compact enough to produce detectable microlensing signatures. We investigate whether the EROS, OGLE, and HSC surveys can probe these halos by fully accounting for finite source size and extended lens effects. We find that current data may already constrain the amplitudes of primordial curvature perturbations in a new region of parameter space, but this conclusion is strongly sensitive to yet undetermined details about the internal structures of these ultradense halos. Under optimistic assumptions, current and future HSC data would constrain a power spectrum that features an enhancement at scales $k \sim 10^7/{\rm Mpc}$, and an amplitude as low as $\mathcal{P}_\zeta\simeq 10^{-4}$ may be accessible. This is a particularly interesting regime because it connects to primordial black hole formation in a portion of the LIGO/Virgo/Kagra mass range and the production of scalar-induced gravitational waves in the nanohertz frequency range reachable by pulsar timing arrays. These prospects motivate further study of the ultradense halo formation scenario to clarify their internal structures.Comment: 17 pages, 10 figures. v2: matching published versio