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Astron. Astrophys. 345, 22-28 (1999)

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A dynamical approach to a self-similar universe

E. Abdalla 1, N. Afshordi 2, K. Khodjasteh 2 and R. Mohayaee 1,3

1 Instituto de Física, USP, C.P.66.318, Sao Paulo, Brazil (eabdalla@fma.if.usp.bf)
2 Physics Department, Sharif University, P.O. Box 8639, Tehran, Iran (niayesh@rose.ipm.ac.ir; kaveh@physics.ipm.ac.ir)
3 IPM, P.O. Box 19395-5531, Tehran, Iran (mohayaee@theory.ipm.ac.ir)

Received 28 August 1998 / Accepted 21 January 1999


We write a non-relativistic Lagrangian for a hierarchical universe. The equations of motion are solved numerically and the evolution of the fractal dimension is obtained for different initial conditions. We show that our model is homogeneous at the time of the last scattering, but evolves into a self-similar universe with a remarkably constant fractal dimension. We also show that the Hubble law is implied by this model and make an estimate for the age of the universe.

Key words: cosmology: large-scale structure of Universe – cosmology: theory

© European Southern Observatory (ESO) 1999

Online publication: April 12, 1999