Beyond Zeldovich-Type Approximations in Gravitational Instability Theory: Padé Prescription in Spheroidal Collapse

Among several analytic approximations for the growth of density fluctuations in the expanding universe, Zeldovich-type approximations in Lagrangian coordinate schemes are known to be effective, even in mildly nonlinear regimes. These approximations are very similar in appearance to Padé approximations. We first establish, however, that these two are actually different and independent approximations by using a model of spheroidal mass collapse. Based on this fact, we propose Padé-prescribed Zeldovich-type approximations and demonstrate, within this model, their quantitative and qualitative advantages.

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