Brazilian Journal of Physics
On-line version ISSN 1678-4448
ABDALLA, Elcio and MOHAYAEE, Roya. Gravitational clustering to all perturbative orders. Braz. J. Phys. [online]. 2001, vol.31, n.1, pp.42-44. ISSN 1678-4448. http://dx.doi.org/10.1590/S0103-97332001000100007.
We derive the time evolution of the density contrast to all orders of perturbation theory, by solving the Einstein equation for scale-invariant fluctuations. These fluctuations are represented by an infinite series in inverse powers of the radial parameter. In addition to the standard growing modes, we find infinitely many more new growing modes for open and closed universes.