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Quantum mechanics is necessary to compute galaxy structures at kpc scales and below. This is so because near the galaxy center, at scales below 10 - 100 pc, warm dark matter (WDM) quantum effects are important: observations show that the interparticle distance is of the order of, or smaller than the de Broglie wavelength for WDM. This explains why all classical (non-quantum) WDM N-body simulations fail to explain galactic cores and their sizes. We describe fermionic WDM galaxies in an analytic semiclassical framework based on the Thomas-Fermi approach, we resolve it numerically and find the main physical galaxy magnitudes: mass, halo radius, phase-space density, velocity dispersion, fully consistent with observations, including compact dwarf galaxies. Namely, fermionic WDM treated quantum mechanically, as it must be, reproduces the observed galaxy DM cores and their sizes. [In addition, as is known, WDM simulations produce the right DM structures in agreement with observations for scales > kpc]. We show that compact dwarf galaxies are natural quantum macroscopic objects supported against gravity by the fermionic WDM quantum pressure (quantum degenerate fermions) with a minimal galaxy mass and minimal velocity dispersion. Interestingly enough, the minimal galaxy mass implies a minimal mass m_{min} for the WDM particle. The lightest known dwarf galaxy (Willman I) implies m > m_{min} = 1.91 keV. These results and the observed halo radius and mass of the compact galaxies provide further indication that the WDM particle mass m is approximately around 2 keV.
We present a detailed derivation of the observed galaxy number over-density on cosmological scales up to second order in perturbation theory. We include all relativistic effects that arise from observing on the past lightcone. The derivation is in a
We study up to second order the galaxy number over-density that depends on magnification in redshift space on cosmological scales for a concordance model. The result contains all general relativistic effects up to second order which arise from observ
High-precision constraints on primordial non-Gaussianity (PNG) will significantly improve our understanding of the physics of the early universe. Among all the subtleties in using large scale structure observables to constrain PNG, accounting for rel
Local non-Gaussianity, parametrized by $f_{rm NL}$, introduces a scale-dependent bias that is strongest at large scales, precisely where General Relativistic (GR) effects also become significant. With future data, it should be possible to constrain $
This is the third of a series of papers in which we derive simultaneous constraints on cosmological parameters and X-ray scaling relations using observations of the growth of massive, X-ray flux-selected galaxy clusters. Our data set consists of 238