Statistics – Computation
Scientific paper
May 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993apj...408..403l&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 408, no. 2, p. 403-408.
Statistics
Computation
22
Approximation, Computational Astrophysics, Cosmology, Euler-Lagrange Equation, Fluctuation Theory, Gravitational Fields, Dynamic Models, Tensor Analysis
Scientific paper
The Lagrangian theory of self-gravitating fluctuations in an expanding dust (no pressure) universe, with no cosmological constant, is considered. A tensorial notation which makes it possible to put the dynamical equations under a simple and physically meaningful form is introduced. A formal solution is presented of these dynamical equations under a peculiar form which generalizes the Zel'dovich approximation; the deformation tensor remains proportional to its initial value, at each Lagrangian position. A development with respect to initial perturbations assumed to be small is introduced. Ways in which the third-order solution can be found by quadrature is shown, and its explicit expression in the case of a flat universe is given. It is also shown that the growth rate at order n is proportional to the linear growth rate at the nth power.
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