The stochastic gravitational background: detection methods in non-Gaussian regimes.

Summary Standard methods for detecting the stochastic gravitational background are based on the simplifying assumption that its distribution as well as that of the detector noise are Gaussian. In this thesis, we propose improved methods for detecting the stochastic gravitational background that explicitly take into account the non-Gaussian character of these distributions. Using an Edgeworth development, we first obtain an analytical expression for the likelihood ratio statistic in the presence of a non-Gaussian distribution of the stochastic gravity background. This expression generalizes the usual expression when the symmetry coefficient and the kurtosis coefficient of the stochastic background distribution are non-zero. On the basis of stochastic simulations for different symmetric distributions with thicker tails than the Gaussian distribution, we show that the 4th cumulant can be estimated with an acceptable accuracy when the signal-to-noise ratio is higher than 1%, which should allow to provide interesting additional constraints on the values of parameters from astrophysical and cosmological models. In a second step, we seek to analyze the impact of deviations from normality in the detector noise distribution on the stochastic gravitational background detection methods.