Abstract
An attractive and simple hypothesis for the formation of large-scale structure is that it developed by gravitational instability from primordial fluctuations with an initially Gaussian probability distribution. Non-linear gravitational evolution drives the distribution away from the Gaussian form, generating measurable skewness and kurtosis even when the variance of the fluctuations is much smaller than unity. We use perturbation theory to compute the kurtosis of the mass density field and the velocity divergence field that arises during the weakly non-linear evolution of initially Gaussian fluctuations. We adopt an Einstein--de~Sitter universe for the perturbative calculations, and we discuss the generalization to a universe of arbitrary $\Omega$. We obtain semi-analytic results for the case of scale-free, power-law spectra of the initial fluctuations and final smoothing of cosmic fields with a Gaussian filter. We also give an exact analytical formula for the dependence of the skewness of these fields on the power spectrum index. We show that the kurtosis decreases with the power spectrum index, and we compare our more accurate results for the kurtosis to previous estimates from Monte Carlo integrations. We also compare our results to values obtained from cosmological N-body simulations with power-law initial spectra. Measurements of the skewness and kurtosis parameters can be used to test the hypothesis that structure in the universe formed by gravitational instability from Gaussian initial conditions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.