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The aether is composed of molecules moving in all directions. Be sure it sinks very well in your head that 'space' here is NOT the aether. Rather, think of the word 'space' here to mean a rigid object imerced in the ocean of aether. During big bang, the aeither molecules were jiggling around in all directions at an average speed of light. The aether also perfectly percolates through 'space' (er the rigid object). This scenario can be seen as the space itself moving at c relative to the aether molecules. Then special relativity states that such as 'space' will be contracted to zero in the direction of travel. But since the aether moleculs are moving in all directions, the space behaves as it were moving in all directions relative to aether. Therefore the 'space' will be shrunk to zero in all directions. This is what it mean to say that during big bang, the universe was in a singularity.
So the expansion of space is simply caused by the 'cooling down' of the ocean of aether! You should be able to see that should the aether molecules cools down to an average velocity of v, the radius, r, of the universe will be now given by some like r=r'{1-(v/c)^2}, where r' is its radius at 'absolute zero' temperature of aether.
The latter is just the relativistic LENGTH CONTRACTION and hence possible length 'dilation' seen as to occur in all directions (in a generalised relativity). Think for instance of an aether converging at speed v to a point in space so that the 'space' can be thought of as moving at v in all directions relative to aether. Then the lengths will contract in all directions as seen from the aether frame of riferance as demanded by special relativity. Likewise, there will be a time dilation, but be careful to note that this time dilation is caused by motion relative to aether and not due to the perceived motion due to the contraction of space. In otherwords, time dilation in GR is part of what DEFINES spacetime expansion and not a phenomenon created by the expansion. Time itself is seen as to be part of the expanding space.