  The Continuous Spontaneous Localisation (CSL) theory in the cosmological
context is subject to uncertainties related to the choice of the collapse
operator. In this paper, we constrain its form based on generic arguments. We
show that, if the collapse operator is even in the field variables, it is
unable to induce the collapse of the wavefunction. Instead, if it is odd, we
find that only linear operators are such that the outcomes are distributed
according to Gaussian statistics, as required by measurements of the cosmic
microwave background. We discuss implications of these results for previously
proposed collapse operators. We conclude that the cosmological CSL collapse
operator should be linear in the field variables.
