Acoustic modes and gravitational instabilities in the early universe

Two acoustic modes are possible in the Universe before cosmological hydrogen decoupling occurs: they involve fluctuations which can be roughly described as either adiabatic or isothermal. In this article the two modes are studied in detail, together with the different kinds of gravitational instabilities connected with them. A particular study is devoted to the time when the decoupling itself occurs, as this is the only time during which it is reasonable to expect a transfer of energy from one mode to the other. As this transfer can be relevant only over large scales, a lower limit can be imposed on the mass of a matter fluctuation after decoupling arising from an adiabatic fluctuation prior to decoupling. (orig./BJ)