In this thesis I test the modified Newtonian dynamics as an alternative to the cold dark matter hypothesis. In the Milky Way, I show that the dynamics of the dwarf galaxies are well described by the paradigm and I confirm its distant low surface brightness globular clusters provide a strong test, for which I make predictions. Through analysis of a sample of 26 X-ray bright galaxy groups and clusters I demonstrate that the three active neutrinos and their anti-particles are insufficient to reconcile modified Newtonian dynamics with the observed temperatures of the X-ray emitting gas, nor with weak-lensing measurements, in particular for the bullet cluster. To this end, I propose an 11eV sterile neutrino to serendipitously resolve the residual mass problem in X-ray bright groups and clusters, as well as matching the angular power spectrum of the Cosmic Microwave Background. With this in mind, I show that the large collision velocity of the bullet cluster and the high number of colliding clusters is more naturally reproduced in MOND than in standard dynamics.

The cosmic neutrino background (CNB) can be composed of both active and hypothetical sterileneutrinos. At approximately one second after big bang, neutrinos decoupled from radiationand matter at a temperature of approximately one MeV. Neutrinos played an important role inthe origin and evolution of our universe and have been indirectly verified by cosmological dataon the BBN (Big Bang nucleosynthesis) of the Big Bang.It was Steven Weinberg in 1962 that first theorized on the direct detection of relic neutrinos.The signal of the relic neutrino capture on a tritium target can be observed by studying theendpoint of the electrons kinetic energy that are above the endpoint energy of the beta decayspectrum. The PTOLEMY project aims to archive direct detection of the relic neutrinobackground with a large tritium target of 100 gram, MAC-E-Filter, RF-tracking, Time of flighttracking and a cryogenic calorimetry.In this thesis the MAC-E-Filter have been simulated in two filter configurations. In the firstconfiguration, the electron were simulated five times in the filter. Two in the opposite sideof the detector, one in the middle, and two at the detector. In the second configuration theelectrons was simulated in the entrance solenoid at a fixed position of y = -0.19634954 m fromthe center of the filter and in random positions. Both multiple electrons and single electronswere simulated in the second configuration.In the single electron configuration the electron had a starting position of y = -0.19634954 mfrom the center of the filter, and an initial kinetic energy of 18.6 KeV. The first filter configurationsuccessfully accomplished to simulate the electron track, as the electron was reflectedback and forth between the entry and detector solenoid. The electric and magnetic field profilediered at the entry and detector solenoid. The second filter configuration successfully showedthat the electron will reach the end solenoid, when the filter length was 0.5 m. When the filterlength was increased to 0.7 m, then the electron was reflected in the middle of the filter. Thesimulation showed that the electron energy dropped below 1 eV from 18.6 KeV as the electronpropagated through the filter. The magnetic and electric fields decreased exponentially in thedirection of the detector solenoid. The Simulation of multiple electrons showed mixed resultsand would need more modifications in order to come to a final conclusion.