| This thesis is divided in three parts. In the first part, finite temperature corrections to the expansion rate of the universe and the predictions of the big-bang nucleosyntheis have been considered. We find that the corrections are very sensitive to the temperature at which the helium synthesizes. Corrections to the helium fraction are found to be {dollar}Delta Ysb4simeq 3.6times10sp{lcub}-6{rcub}{dollar}, which are much smaller (in magnitude) than the previously reported estimates of {dollar}Delta Ysb4simeq {lcub}-{rcub}1.5times10sp{lcub}-4{rcub}{dollar}. At the present levels of theoretical uncertainties in {dollar}sp4{dollar}He calculations of about a few tenths of a percent and the observational uncertainties of about one percent, we find that the the finite temperature corrections are almost unimportant. But we have shown that one needs to do actual calculations to show that such corrections are not important.; In the second part, uncertainties in the fluxes of the atmospheric neutrinos due to the uncertainties in the interaction cross sections of various hadrons, have been calculated. Uncertainties in the total neutrino flux ({dollar}nusbmu+barnusbmu{dollar}) are found to range from {dollar}{lcub}sim{rcub}{lcub}pm{rcub}{dollar}5% at {dollar}Esbnusimeq2.5{dollar} GeV to about {dollar}pm{dollar}8% at {dollar}Esbnusimeq10sp4{dollar} GeV. Corresponding uncertainties: in {dollar}nusbmu/barnusbmu{dollar} ratio range from {dollar}{lcub}sim{rcub}{lcub}pm{rcub}{dollar}6% to {dollar}{lcub}sim{rcub}{lcub}pm{rcub}{dollar}13%; Finally, in the third part, we explore the possibility of using the anthropic principle to solve the gauge hierarchy problem. We concentrate on a scenario where 18 parameters of the standard model are held fixed, but {dollar}musp2{dollar}, the mass squared of the Higgs potential, is allowed to vary. Varying {dollar}musp2{dollar}, causes the vacuum expectation value for the Higgs field, {dollar}v = langlephisp2ranglesp{lcub}1/2{rcub}{dollar}, to vary-which in turn affects the masses of particles in the standard model. We have investigated small deviations in v from the actual value {dollar}vsb0simeq246{dollar} GeV. We find plausible arguments that the existence of life requires v to lie in the range {dollar}0.1vsb0 sbsp{lcub}sim{rcub}{lcub}<{rcub} v sbsp{lcub}sim{rcub}{lcub}<{rcub} 1.6vsb0{dollar}. |
