Gradienttiekspansion sovelluksia : primordiaalisten mustien aukkojen synty primordiaalisista perturbaatioista - Vastamaa, Jesse (2024)
There have been a few observations in cosmology in recent decades that do not fit our theories well. We detect the existence of dark matter for example by gravitational lensing, but we do not know what it consists of in microscopic scale and there is a chance that we have discovered more black holes in the universe than theories are predicting. The uncertainty rises from the imperfection of simulations. We usually think of a black hole as being born from the collapse of a star, but if they could arise from a strong energy density fluctuations in the radiation dominated universe (= primordial black hole), they could explain part of both problems. However, we do not know about their existence yet. \par In my thesis, I calculate Einstein's equations for a spherically symmetric metric and make use of the long wavelength approximation to describe an overdensity in an arbitrary point in space which can give birth to a primordial black hole. In addition, I familiarize myself with perturbations created from inflation and derive the theory of how to get the magnitude of overdensity from them for the formation of a primordial black hole. Finally, I calculate an example mass of the primordial black hole and the corresponding abundance at the time of birth, based on a chosen model. By comparing the result with dark matter abundance, we get an estimate for the amount of Primordial black holes in the universe in the chosen model.