COSMIC TURBULENCE REVISITED

Primordial cosmic turbulence has been suggested in the past as a mecha nism for the formation of large-scale structure in the universe, since it is more efficient than the growth of density perturbations. Howeve r, difficulties arose when it was pointed out that (1) the amplitude o f the turbulence required to explain the large-scale structure would b e in conflict with the observed high degree of isotropy of the microwa ve background radiation. (2) In addition, following recombination, the turbulence would have become supersonic and produced too large densit y contrasts on scales of galaxies and clusters of galaxies. (3) Finall y, a difficulty of fundamental rather than observational nature: the l ack of a specific physical process that could have generated the turbu lence in the first place. In this paper, we argue that inflation natur ally provides mechanisms for the direct generation of turbulence on th e same scales on which density perturbations are formed, thus solving problem 3 above. This calls for a reexamination of the issue of cosmic turbulence since the observational constraints on turbulence (problem s 1 and 2, above) could translate into constraints on inflation itself . We find that by the end of inflation, the amplitude of the generated turbulent velocity has been suppressed by a factor greater-than-or-si milar-to 10(100) (this result also applies to any turbulence assumed t o be part of the initial conditions). Thus, inflation guarantees the a bsence of turbulence on scales of galaxies and clusters of galaxies an d avoids difficulties 1 and 2 above. Alternatively, they constitute an additional support for inflationary cosmology. We show that the densi ty fluctuations generated by inflation can excite longitudinal turbule nce after they reenter the Hubble radius at later cosmic epochs (at z greater-than-or-similar-to 27z(eq)). The scales on which this happens are much smaller than those of galaxies. The largest scale corresponds to a present-epoch size of less-than-or-similar-to 6.3 kpc and contai ns a mass of less-than-or-similar-to 3.6 x 10(4) M.. The smallness of these scales renders the turbulence immune from the observational diff iculties 1 and 2 above. Since the generation of this ''secondary'' and ''small-scale'' turbulence seems unavoidable, it should be regarded a s yet another ingredient of cosmology. In spite of its small scale, th is turbulence can have an important impact on the formation of structu re on scales of galaxies and clusters of galaxies. This is so because any part of the turbulence that survived dissipation by the radiative viscosity will become supersonic following the decoupling time. Shocks collisions would lead to large density contrasts on the above small s cales. Such an early population of objects of mass less-than-or-equal- to 3.6 x 10(4) M. can serve as a seed that could help the growth of de nsity on the scales of galaxies and clusters of galaxies.