Dynamics of a dark matter field with a quartic self-interaction potential - art. no. 023502

It may prove useful in cosmology to understand the behavior of the energy d istribution in a scalar field that interacts only with gravity and with its elf by a pure quartic potential, because if such a field existed, it would be gravitationally produced, as a squeezed state, during inflation. It is k nown that the mean energy density in such a field after inflation varies wi th the expansion of the universe in the same way as radiation. I show that if the field initially is close to homogeneous, with energy density contras t \delta rho/rho \much less than 1 and coherence length L, the energy densi ty fluctuations behave like acoustic oscillations in an ideal relativistic fluid Tor a time on the order of L/\delta rho/rho \. This ends with the app earance of features that resemble shock waves but interact in a close to el astic way that reversibly disturbs the energy distribution.