158 research outputs found

### 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

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