Numerical simulations of primordial black holes­­­­­­­­­­

Abstract

This thesis has been devoted to the study of the gravitational collapse of spherically symmetric perturbations on a Friedman-Robertson-Walker (FRW) universe filled by a perfect fluid. Large cosmological perturbations generated by inflation, are known to be statistically almost spherical. For this reason, this thesis aims to provide the conditions for Primordial Black Hole (PBH) formation due to the collapse of inflationary density fluctuations. PBHs are considered one of the best candidate for the missing dark matter (DM). To simulate the collapse of large spherical overdensities, it has been used a pseudo-spectral method which maps differential equations into an algebraic system. The numerical code developed, allows to outline the conditions for black hole formation with a greater than ever precision in some extreme cases. By using a combination of an excision technique and analytical estimations of accretion rates, it was found that the estimation of the black hole’s masses via a self-similar scaling law, gets worse and worse for larger and larger values. In addition, it was also found that the accretion of the BH masses relevant for the DM abundance, follows the law MBH,f roughly equal to 3MBH,i where, MBH,I is the initial mass of the BH at the time of apparent horizon formation and MBH,f is the final mass of the BH after the accretion process. In the case in which the fluid permeating the universe is of the form p equal to wρ, where p is the pressure, ρ is the density of the fluid and w is a constant, it is here shown that for w greater or equal to 1/3 the conditions for black hole formation, to a very good approximation, only depend upon the curvature of the local excess-mass (compaction function) around its peak value (δc), δc (the ”threshold” for PBH formation) and the equation of state of the collapsing fluid. This fact, has been used to build an analytical formula for δc in the case of w greater or equal to 1/3, which is accurate enough to be used for cosmological applications, conversely to previous attempts. For smaller w’s instead, the knowledge of the full shape of the compaction function is necessary, in contradiction to previous claims. Moreover, while the threshold for w greater or equal to 1/3 does not strongly depend from the full shape of the compaction function, in this thesis it is also shown that the BH mass does. While inflationary fluctuations are predominantly Gaussianly distributed at the cosmic microwave back-ground scales, those leading to PBH formation at smaller scales can have larger non-Gaussianities (NG). In the final part of this thesis, it was considered the effect (numerically and analytically) of those NG to the threshold for primordial black hole formation. By monitoring the non-gaussian parameter fNL, it was found that; i) for fNL roughly greater than 3.5, the population of PBH coming from false vacuum regions dominates over that coming from the collapse of large adiabatic overdensities; ii) the effect of the statistical dispersion of profiles is small in determining δc of the mean profile.

Esta tesis pretende proporcionar las condiciones necesarias para la formación de Agujeros Negros Primordiales (PBHs) producidos por el colapso de perturbaciones cosmológicas. Los PBHs se consideran uno de los mejores candidatos para la materia oscura, cuya composición es todavía un misterio. Para simular el colapso de grandes sobredensidades esféricas y obtener las condiciones para la formación de un PBH, se ha utilizado un método pseudoespectral que mapea ecuaciones diferenciales en un sistema algebraico. En el caso en el que el fluido que impregna el universo se comporte como un fluido perfecto (p igual a wρ, donde p es la presión, ρ es la densidad del fluido y w es una constante), hemos comprobado que para w mayor o igual a 1/3 las condiciones para la formación de un agujero negro, en una muy buena aproximación, solo dependen de la curvatura del exceso de masa local (también llamado función de compactación) alrededor de su valor máximo (δc) , δc (el ” umbral ” para la formación de PBH) y la ecuación de estado del fluido que colapsa. Este remarcable resultado se ha utilizado para construir una fórmula analítica para δc en el caso de w mayor o igual a 1/3, que es lo suficientemente precisa como para usarse en aplicaciones cosmológicas. En cambio, para w más pequeños, es necesario conocer la forma completa de la función de compactación. Por otro lado, si bien es cierto que las fluctuaciones inflacionarias se distribuyen predominantemente de manera gaussiana en las escalas del fondo de microondas cósmicas, las que conducen a la formación de PBH a menores escalas pueden distribuirse de forma altamente no gaussiana (NG). En la parte final de esta tesis, se ha considerado el efecto de esas NGs en el umbral de formación de agujeros negros primordiales, tanto numérica como analíticamente.