General Relativistic Self-Similar Solutions in Cosmology

We present general relativistic solutions for self-similar spherical perturbations in an expanding cosmological background of cold pressure-less gas. We focus on solutions having shock discontinuities propagating in the surrounding cold gas. The pressure, $p$, and energy-density, $\mu$, in the shock-heated matter are assumed to obey $p=w\mu$, where $w$ is a positive constant. Consistent solutions are found for shocks propagating from the symmetry center of a region of a positive density excess over the background. In these solutions, shocks exist outside the radius marking the event horizon of the black hole which would be present in a shock-less collapse. For large jumps in the energy-density at the shock, a black hole is avoided altogether and the solutions are regular at the center. The shock-heated gas does not contain any sonic points, provided the motion of the cold gas ahead of the shock deviates significantly from the Hubble flow. For shocks propagating in the uniform background, sonic points always appear for small jumps in the energy-density. We also discuss self-similar solutions without shocks in fluids with $w<-1/3$.Comment: 6 pages, 3 figures, mnras styl

Modified Newtonian Dynamics of Large Scale Structure

We examine the implications of Modified Newtonian Dynamics (MOND) on the large scale structure in a Friedmann-Robertson-Walker universe. We employ a ``Jeans swindle'' to write a MOND-type relationship between the fluctuations in the density and the gravitational force, \vg. In linear Newtonian theory, |\vg| decreases with time and eventually becomes $<g_0$, the threshold below which MOND is dominant. If the Newtonian initial density field has a power-law power-spectrum of index $n<-1$, then MOND domination proceeds from small to large scale. At early times MOND tends to drive the density power-spectrum towards $k^{-1}$, independent of its shape in the Newtonian regime. We use N-body simulations to solve the MOND equations of motion starting from initial conditions with a CDM power-spectrum. MOND with the standard value $g_0=10^{-8} cm s^{-2}$, yields a high clustering amplitude that can match the observed galaxy distribution only with strong (anti-) biasing. A value of $g_0 \approx 10^{-9}cm s^{-2}$, however, gives results similar to Newtonian dynamics and can be consistent with the observed large scale structure.Comment: Version accepted for publication in the MNRAS. Results of more simulations are include

Analytic solutions for coupled linear perturbations

Analytic solutions for the evolution of cosmological linear density perturbations in the baryonic gas and collisionless dark matter are derived. The solutions are expressed in a closed form in terms of elementary functions, for arbitrary baryonic mass fraction. They are obtained assuming $\Omega=1$ and a time independent comoving Jeans wavenumber, $k_J$. By working with a time variable $\tau\equiv \ln(t^{2/3})$, the evolution of the perturbations is described by linear differential equations with constant coefficients. The new equations are then solved by means of Laplace transformation assuming that the gas and dark matter trace the same density field before a sudden heating epoch. In a dark matter dominated Universe, the ratio of baryonic to dark matter density perturbation decays with time roughly like $\exp(-5\tau/4)\propto t^{-5/6}$ to the limiting value $1/[1+(k/k_J)^2]$. For wavenumbers $k>k_J/\sqrt{24}$, the decay is accompanied with oscillations of a period $8\pi/\sqrt{24 (k/k_J)^2 -1}$ in $\tau$. In comparison, as $\tau$ increases in a baryonic matter dominated Universe, the ratio approaches $1-(k/k_J)^2$ for $k\le k_J$, and zero otherwise.Comment: Correction in equation 2