[0707.0121] Generation of primordial cosmological density inhomogeneities with scale invariant power spectrum during the standard radiation dominated expansion of the universe

Authors:  David H. Oaknin
Abstract:  The expansion/contraction of a bubble of gas of radius $R_0(t)$ immersed in an incompressible fluid that fills the infinite 3D space around it, $r \ge R_0(t)$, generates a radial flow, ${\vec v}(r,t) = \frac{R^2_0(t)}{r^2}\ \dot{R}_0(t) {\hat r}$, which is set by the velocity of the bubble surface, $\dot{R}_0(t)$. The kinetic energy that the expanding/contracting bubble pumps, at the expense of its own internal energy, into each unit volume of the flowing incompressible fluid is ${\it e}(r,t) = \frac{\rho_0}{2} |{\vec v}(r,t)|^2 = \frac{\rho_0}{2} \dot{R}^2_0(t) R^4_0(t) r^{-4}$, where $\rho_0$ is the mass density of the fluid. This incompressible flow generates equal time energy density (anti)correlations over infinitely long distances. They are imposed by global conservation laws and, therefore, do not violate causality. We notice that energy density inhomogeneities that are (anti)correlated as $f(r) \sim - r^{-4}$ as $r \to \infty$ have scale invariant power spectrum in the range of very small wavenumbers, ${\cal P}(k) = {\cal O}(k)$ as $k \to 0$. We discuss this mechanism as a toy model of physical processes that could operate in the cosmic plasma during the standard Friedmann-Robertson-Walker radiation dominated expansion of the universe to generate scale invariant primordial cosmological structures at the time of decoupling.
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Aseem Paranjape
Posts: 7
Joined: December 23 2005
Affiliation: IUCAA, Pune, India

[0707.0121] Generation of primordial cosmological density i

Post by Aseem Paranjape » July 10 2007

I found this paper quite interesting. The author has shown that energy density correlations which are weakly suppressed (with the two point correlation falling as [tex]r^{-4}[/tex] for [tex]r\to\infty[/tex]) at the last scattering epoch, can lead to a scale invariant power spectrum at large scales [tex]k\to0[/tex]. Further he constructs a toy mechanism using standard (non-inflationary) physics that can generate such correlations.

The paper is quite readable and uses very simple arguments. I have one observation though. Some work done by Tarun Souradeep and coworkers (astro-ph/0312174, astro-ph/0611352) has shown that the primordial power spectrum estimated directly from the CMB angular power spectrum, in fact has several features which include a sharp infrared cutoff at roughly the horizon scale. I wonder whether arguments such as those presented in Oaknin's paper will be sufficient to explain such features. (Of course it is not yet clear whether inflationary models can explain such features either.)

Any comments?

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