In the gravitational instability theory, the present structure in the Universe is envisaged to have evolved from small initial inhomogeneities which are of two generic types: isothermal and adiabatic. It has been shown that in the grand unified theory (GUT) for baryosynthesis primordial isothermal perturbations are incompatible with the standard Friedman-Robertson-Walker (FRW) universe. Here we discuss four non-standard models in which the two are compatible. Of these models two prove to be viable: (1) a universe which is initially dominated by large-scale inhomogeneous shear and (2) a universe which undergoes a de Sitter phase during the GUT phase transition. We also show how to deduce new constraints on chaotic behaviour near the cosmological singularity.