We revisit the question of whether fluctuations in hydrodynamical , adiabatical matter could explain the observed structures in our Universe .
We consider matter with variable equation of state w = p _ { 0 } / \varepsilon _ { 0 } and a concomitant ( under the adiabatic assumption ) density dependent speed of sound , c _ { s } .
We find a limited range of possibilities for a set up when modes start inside the Hubble radius , then leaving it and freezing out .
For expanding Universes , power-law w ( \varepsilon _ { 0 } ) models are ruled out ( except when c _ { s } ^ { 2 } \propto w \ll 1 , requiring post-stretching the seeded fluctuations ) ; but sharper profiles in c _ { s } do solve the horizon problem .
Among these , a phase transition in c _ { s } is notable for leading to scale-invariant fluctuations if the initial conditions are thermal .
For contracting Universes all power-law w ( \varepsilon _ { 0 } ) solve the horizon problem , but only one leads to scale-invariance : w \propto \varepsilon _ { 0 } ^ { 2 } and c _ { s } \propto \varepsilon _ { 0 } .
This model bypasses a number of problems with single scalar field cyclic models ( for which w is large but constant ) .