Exact solution of the Lifshitz equations governing the growth of fluctuations in cosmology

Details Exact solution of the Lifshitz equations governing the growth of fluctuations in cosmology Exact solution of the Lifshitz equations governing the growth of fluctuations in cosmology

Dec 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975phrvd..12.3793a&link_type=abstract

Physical Review D - Particles and Fields, 3rd Series, vol. 12, Dec. 15, 1975, p. 3793-3799.

Astronomy and Astrophysics

Astrophysics

7

Cosmology, Equations Of State, Galactic Evolution, Jeans Theory, Particle Density (Concentration), Perturbation Theory, Astrophysics, Baryons, Fluctuation Theory, Gravitation Theory, Small Perturbation Flow, Space Density, Time Dependence

Scientific paper

The exact solution of the Lifshitz equations governing the cosmological evolution of an initial fluctuation is presented. Lifshitz results valid for squares of the sound velocity equal to zero and 1/3 are extended in closed form to any equation of state where the pressure equals the total energy density times the square of the sound velocity. The solutions embody all the results found previously for special cases of the square of the sound velocity. It is found that the growth of any initial fluctuation is only an exponential function of time with an exponent of not more than 4/3 and is insufficient to produce galaxies unless the initial fluctuation is very large. A possible way to produce very large initial fluctuations by modifying the equation of state by including gravitational interactions is also examined. It is found that a phase transition can occur at baryonic density of 1 nucleon per cubic Planck length or equivalently, at a time of about 10 to the -43rd power sec. At those early times, the masses allowed by causality requirements are too small to be of interest in galaxy formation.

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