We demonstrate the occurrence of permanent spikes using the Lemaitre-Tolman-Bondi models, chosen because the solutions are exact and can be analyzed by qualitative dynamical systems methods. Three examples are given and illustrated numerically. The t
hird example demonstrates that spikes can form directly in the matter density, as opposed to indirectly in previous studies of spikes in the Kasner regime. Spikes provide an alternative general relativistic mechanism for generating exceptionally large structures observed in the Universe.
We investigate a general relativistic mechanism in which spikes generate matter overdensities in the early universe. When the cosmological fluid is tilted, the tilt provides another mechanism in generating matter inhomogeneities. We numerically inves
tigate the effect of a sign change in the tilt, when there is a spike but the tilt does not change sign, and when the spike and the sign change in the tilt coincide. We find that the tilt plays the primary role in generating matter inhomogeneities, and it does so by creating both local overdensities and underdensities. We discuss of the physical implications of the work.
We use a dynamical systems analysis to investigate the future behaviour of Einstein-Aether cosmological models with a scalar field coupling to the expansion of the aether and a non-interacting perfect fluid. The stability of the equilibrium solutions
are analysed and the results are compared with the standard inflationary cosmological solutions and previously studied cosmological Einstein-Aether models.
The cosmological backreaction from perturbations is clearly gauge-dependent, and obviously depends on the choice of averaged Hubble rate. We consider two common choices of Hubble rate and advocate the use of comoving volume-preserving gauges. We high
light two examples valid to an appropriate order in perturbation theory, uniform curvature gauge, which is as close to volume-preserving as possible, and a spatially-traceless uniform cold dark matter gauge which preserves the volume to linear order. We demonstrate the strong gauge- and frame-dependences in averaging. In traceless uniform CDM gauge the backreaction exhibits a strong ultra-violet divergence and can be tuned to an arbitrary magnitude with an appropriate choice of smoothing scale. In uniform curvature gauge we find that for a choice of Hubble rate locked to the spatial surface the backreaction vanishes identically, while for a Hubble rate defined from a fluids expansion scalar the effective energy density at the current epoch in an Einstein-de Sitter universe is Omega_eff~5e-4, slightly bigger than but in broad agreement with previous results in conformal Newtonian gauge.
In this Letter we discuss a natural general relativistic mechanism that causes inhomogeneities and hence generates matter perturbations in the early universe. We concentrate on spikes, both incomplete spikes and recurring spikes, that naturally occur
in the initial oscillatory regime of general cosmological models. In particular, we explicitly show that spikes occurring in a class of G_2 models lead to inhomogeneities that, due to gravitational instability, leave small residual imprints on matter in the form of matter perturbations. The residual matter overdensities from recurring spikes are not local but form on surfaces. We discuss the potential physical consequences of the residual matter imprints and their possible effect on the subsequent formation of large scale structure.
