Neutrinos are the only particles that confirm the existence of physics beyond the Standard Model. This makes neutrinos the perfect candidates for asking the question regarding the existence of new physics, in addition to the non-zero neutrino masses connected with those ghostly particles. The primary aim of this thesis is to investigate the impact of physics beyond the Standard Model on stellar evolution and observable at the Earth low energy astrophysical neutrino fluxes.
The first part of the thesis provides a general overview of the aspects of neutrino physics, core-collapse supernovae, nuclear reactions in the Sun, and non-standard physics studied in this work. The second part of the thesis focuses on improving theoretical calculations of well motivated new physics scenarios such as keV mass scale sterile neutrinos. The findings of the studies included in this thesis indicate that the new treatment of active-sterile neutrino mixing in supernova core challenges the previous sterile neutrino bounds. The previously reported constraints on the sterile neutrino mass-mixing angle parameter space in the region relevant for dark matter searches are relaxed. The following third part of the thesis examines the consequences of the existence of non-standard mediators coupling to neutrinos and quarks on the astrophysical neutrino fluxes observable at the Earth and physics inside these sources. We find that the detection of these astrophysical neutrinos in the proposed and planned detectors employing coherent elastic neutrino-nucleus scattering as the primary channel of detection might be able to set the most stringent limits on the masses and couplings of these non-standard particles. Additionally, in the case of non-standard mediators that couple to quarks, we identify the regions of the mass-coupling parameter space where the existence of these mediators would result in changes observable in the solar neutrino fluxes. Finally, in the fourth part of the thesis, we present the calculations demonstrating that the large-scale coherent elastic neutrino-nucleus scattering detectors might place the most stringent limits on the non-electron components of diffuse supernova neutrino background.