Super-horizon fluctuations and acoustic oscillations in relativistic heavy-ion collisions

We focus on the initial state spatial anisotropies, originating at the thermalization stage, for central collisions in relativistic heavy-ion collisions. We propose that a plot of the root mean square values of the flow coefficients $\sqrt\bar v_n^2 ≡ v_n^rms$, calculated in a lab fixed coordinate system, for a large range of $n$, from 1 to about 30, can give non-trivial information about the initial stages of the system and its evolution. We also argue that for all wavelengths $λ$ of the anisotropy (at the surface of the plasma region) much larger than the acoustic horizon size $H_s^fr$ at the freezeout stage, the resulting values of $v_n^rms$ should be suppressed by a factor of order $2H_s^fr/λ$. With initial flow being zero, we discuss the possibility that the resulting flow could show imprints of coherent oscillations in the plot of $v_n^rms$ for sub-horizon modes. For gold-gold collision at 200 GeV, these features are expected to occur for n $≥$ 5, with $n < 4$ modes showing supression. This has strong similarities with the physics of the anisotropies of the cosmic microwave background radiation (CMBR) resulting from inflationary density fluctuations in the universe. It seems possible that the statistical fluctuations due to finite multiplicity may not be able to mask such features in the flow data, or, at least a non-trivial overall shape of the plot of $v_n^rms$ may be inferred. In that case, the successes of analysis of CMBR anisotropy power spectrum to get cosmological parameters can be applied for relativistic heavy-ion collisions to learn about various relevant parameters at the early stages of the evolving system.