Large-scale structure formation with global topological defects

Abstract

We investigate cosmological structure formation seeded by topological defects which may form during a phase transition in the early universe. First we derive a partially new, local and gauge invariant system of perturbation equations to treat microwave background and dark matter uctuations induced by topological defects or any other type of seeds. We then show that this system is well suited for numerical analysis of structure formation by applying it to seeds induced by uctuations of a global scalar eld. Our numerical results cover a larger dynamical range than previous investigations and are complementary to them since we use substantially di erent methods. The resulting microwave background uctuations are compatible with older simulations. We also obtain a scale invariant spectrum of uctuations although with somewhat higher amplitude. On the other hand, our dark matter results yield a smaller bias parameter compatible with b 2 on scales of 20h ?1 Mpc in contrast to previous work which yielded to large bias factors. Our conclusions are thus more positive. According to the aspects analyzed in this work, global topological defect induced uctuations yield viable scenarios of structure formation and do better than standard CDM on large scales.

Cosmic structure formation with topological defects

“…. [115,50]) are probably strongly affected by finite size effects and not very reliable. On the other hand, with the more successful method to compute power spectra just by determining the unequal-time two point distribution of the defects, one loses all information about higher order correlations and thus about non-Gaussianity.…”

“…The functions f ρ and f π are then determined by energy momentum conservation, Eqs. (49,50). The function E is chosen such that the power spectrum of f π is white noise on super horizon scales, a condition which is required for purely scalar causal seeds as we have seen in the previous section.…”

“…[1] for a seed energy momentum tensor modeled by a few random parameters and in Ref. [50] where the CMB anisotropies on large scales have been determined in x-space by direct line of sight integration and averaging over several observer positions.…”

Erratum: Cosmological perturbations seeded by topological defects: Setting the initial conditions [Phys. Rev. D 56, 7608 (1997)]

“…Having defined gauge invariant scalar perturbations for the metric (eq (7)), for the radiation fluid (eq (10)(11)(12)) and for the sources (eq (13)), we now write their evolution equations. We shall write them in Fourier space, the Fourier transform of any function f (x i , η) being defined aŝ…”

“…[9][10][11]). However some of its statistical properties can be inferred from general arguments (see below Section 5).…”