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It is stated in V. Mukhanov's book "Physical foundations of Cosmology" the following (page 44, after equation 2.25): "

*In contrast, for the dust dominated universe, where η*" could someone please explain why is this true? the equation for the event horizon in a closed, dust dominated universe is (again from Mukhanov): d

_{max}=2π, the event horizon exists only during the contraction phase when η>π._{e}(t)=a

_{m}(1-cosη)(η

_{max}-η),(a

_{m}is a constant) which clearly has non-vanishing values for η≤π

Thanks!