Primordial black holes and their implications for Inflation

Abstract

The standard cosmological model, ΛCDM, with the addition of an early inflationary phase, provides an accurate description of a nearly flat and homogeneous Universe, at large scales, which expands at an accelerated rate. Despite its vindication, our knowledge of the components that trigger the early formation of structures and drive the accelerated expansion of the Universe, that is, dark matter (DM) and dark energy respectively, is severely limited, given their feeble interactions with the other components of the Universe. A number of candidates from particle physics, e.g weakly interacting massive particles (WIMPs) or axions, have been proposed to constitute DM, but so far there has been no evidence to support their existence. However, the detection of a signal from the merger of a binary of black holes of stellar masses, reinvigorated the interest in an old candidate for DM, namely primordial black holes (PBHs). These black holes behave as the ones sitting at the end of stellar evolution, with the distinctive differences that they may form in significant fractions even well before the appearance of the first stars, with masses that may range from the Planck mass, to the order of MBH ∼ 1012 M. One possible formation mechanism involves perturbations originating from the fluctuations of a scalar field during inflation, that collapse after they re-enter the causal horizon in a radiation or matter domination era. The PBHs could easily form binaries in the early Universe and merge within our Hubble time, rendering them observable by the current detectors LIGO/VIRGO. The work presented in this thesis focuses on how such a population of PBHs could be utilised in order to elucidate certain spectral features of curvature perturbations characterizing the initial state of the Universe. Firstly, the effect of matter and radiation perturbations on the orbital parameter distributions of PBH binaries is studied. These perturbations are shown to provide a source of torque to the binary, particularly when their power spectrum is enhanced at the comoving scale of the binaries, leading to the suppression of the merger rate and subsequent relaxation of constraints on the PBH abundance. Secondly, the effect of primordial clustering on the distribution of orbital parameters of PBH binaries is investigated with the use of a phenomenological model of local non-Gaussianity. It is shown that due to the modal coupling of the perturbations, the merger rate and the stochastic background of gravitational waves (SBGW) sourced by merging PBH binaries, are altered. An immediate result of clustering is that the observational constraint on the abundance of PBHs in DM is relaxed considerably, allowing for significant fractions, even close to totality. Thirdly, the possibility that the SBGW from the mergers of massive PBHs could provide an explanation for the recently detected isotropic signal by the NANOGrav collaboration is considered. The presence of non-Gaussianity, sourced from a phase of constant roll, is essential in order for such massive PBHs to evade the CMB µ-distortions constraints, in which case they may have formed in small abundances, of order 0.1% with respect to DM. The present work aims to provide a more robust modelling of the observational consequences of a population of PBHs in order to gain more insight into the spectrum of primordial perturbations at small scales and therefore into the initial conditions of the early Universe.

El modelo cosmológico estándar, ΛCDM, con una temprana fase de inflación, nos proporciona una descripción precisa de un Universo casi plano y homogéneo a gran escala, que se expande a un ritmo acelerado. A pesar de las evidencias observacionales, nuestro conocimiento del 95% de la energía del Universo, es decir, la materia oscura (DM) y la energía oscura, está limitado por la falta de una detección directa, debido en parte a la poca interacción, aparte de la gravitacional, que tienen con el resto de la materia. La detección de la primera señal de un sistema binario de agujeros negros, revitalizó el interés por un viejo candidato a materia oscura, los agujeros negros primordiales (PBHs). Los PBHs han recibido atención dado que se pueden formar con abundancias importantes durante el Universo temprano y con una amplia gama de posibles masas. Esta tesis se centra en su empleo para explorar el espectro de potencias de las perturbaciones de curvatura a escala pequeña. Primero, se estudia el efecto de las perturbaciones cosmológicas sobre los parámetros orbitales de los sistemas binarios de PBHs. Cuando hay una meseta de amplitud considerable en el espectro de potencia en las escalas de los sistemas binarios, la tasa de fusión se ve afectada, relajando los limites de la abundancia de PBHs. Segundo, se muestra que debido al acoplamiento modal de las perturbaciones, introducido por la presencia de no-Gaussianidad, se alteran la tasa de fusión y el resultante fondo estocástico de las ondas gravitacionales (SBGW) y que esto tambien resulta en la relajación de las restricciones de la abundancia de PBH. Tercero, se considera la posibilidad de que el SBGW proveniente de los sistemas binarios de PBHs super masivos pueda proporcionar una explicación para la señal detectada por NANOGrav. La presencia de no-Gaussianidad es esencial para que estos PBHs masivos eviten las µ-distorsiones de la CMB y se puedan haberse formado en abundancias del orden ∼ 0, 1%. Los PBHs constituyen una sonda única para explorar las condiciones iniciales del Universo y este trabajo pretende aportar un modelaje más robusto de las consecuencias observacionales de una población de PBHs.