Relic gravitational waves in the expanding Universe

Abstract

Las ondas gravitatorias primordiales representan una ventana privilegiada para determinar la evolución del Universo, ya que a partir de su espectro seria posible reconstruir el factor de escala desde los instantes iniciales de expansión hasta el instante presente. En esta tesis, trabajando en aproximación de vacío adiabático, hemos revisado como la expansión del Universo amplifica las fluctuaciones del vacío cuántico. Hemos evaluado el espectro en un modelo de expansión del universo que considera una era inicial inflacionaria, una era dominada por agujeros negros primordiales y radiación, una era dominada por radiación y finalmente una era de la materia. Hemos demostrado como el espectro de este escenario es mucho menor que el del modelo habitual (inflación- era de radiación-era de materia), también hemos visto como las anisotropías observadas del CMB ponen limites a los parámetros libres del modelo de las cuatro eras. Hemos calculado el espectro en un modelo con un universo dominado por energía oscura en la era presente, concluyendo que pese a que este espectro coincide con el del escenario de las tres eras evoluciona de manera diferente. También hemos calculado el espectro en una hipotética segunda era de la materia, en el caso de que esta era de expansión acelerada sea sólo una etapa transitoria. Hemos estudiado como se cumple la segunda ley de la termodinámica durante la era de expansión acelerada, asignando una entropía a las ondas gravitatorias primordiales que debe cumplir una determinada condición. Finalmente, dejando de lado las ondas gravitatorias, hemos estudiado la segunda ley de la termodinámica en universos dominados por energía oscura fantasma, concluyendo que la entropía de estos fluidos es negativa y que la segunda ley es respetada.

Cosmology has for a long time been a rather speculative science. Hubble's discovery that the Universe is expanding, and -more recently- the realization that at present this expansion is accelerated, the measured abundance of light elements, the mass distribution of galaxies and clusters thereof, and the discovery and posterior measurements of the anisotropies of the CMB have changed this picture. Hopefully, measurements of GWs will soon be added to this short list. At any rate, now we can speak confidently of physical cosmology as a fully-fledged branch of Science. The relic GWs constitute a privileged window to determine the evolution of the Universe. Little is known from the early evolution of the Universe and the predictions for their spectrum depend on the model considered. According to these predictions, a spectrum of relic GWs is generated making feasible its detection with the technology currently being developed. In this thesis, using the adiabatic vacuum approximation, we have reviewed how the expansion of the Universe amplifies the quantum vacuum fluctuations, and how the relic GWs spectrum is related with the scale factor. We have later evaluated the spectrum in a four-stage model (which consist on a De Sitter stage, a stage dominated by a mixture of MBHs and radiation, a radiation dominated stage and finally a non-relativistic matter (dust) dominated stage). We have demonstrated that the spectrum in this scenario is much lower than the predicted by three-stage model (De Sitter-radiation era-dust era). We have also shown how the bound over the GWs spectrum from the measured CMB anisotropies places severe constraints over the free parameters of the four-stage model. We have also considered a scenario featuring an accelerated expanding era dominated by dark energy, right after the dust era of the three-stage model. We have found that the current power spectrum of this four-stage scenario exactly coincides with that of the three-stage, but it evolves in a different fashion. We have considered as well the possibility that the dark energy decays in non-relativistic matter leading to a second dust era in the far future and obtained the power spectrum of the GWs as well as the evolution of the density parameter. We have applied the generalized second law of thermodynamics to the four-stage model of above. Assuming the GWs entropy proportional to the number of GWs, we have found the GSL is fulfilled provided a certain proportionality constant does not exceed a given upper bound. Finally, we have extended the GSL study to a single stage universe model dominated by dark energy (either phantom or not), and found that the GSL is satisfied and that the entropy of the phantom fluid is negative. Likewise, we have found a transformation between phantom and non-phantom scenarios preserving the Einstein field equations that entails a "quasi" duality between the thermodynamics of both scenarios.