Currently, the rate of expansion is measured by the shift towards the red end of the spectrum of light from distant objects. On current calculations, the rate of recession is between 65 and 73 Km/s per megaparsec. Or in round figures, 20 Km/s per million light years.

Before the Big Bang, all matter and energy was concentrated in a point singularity. Under these conditions, time stands still and gravity is infinite. After the Big Bang, gravity decreases and time progresses, increasing its rate of change, probably exponentially towards a steady rate. This is exemplified by the fact that the oldest galaxies appear to be receding fastest.

When we look back in time to distant galaxies and measure their red shift, we are measuring it using our present standard of time rather than the rate of change of time that existed then. This will distort our calculations of the rate of recession of the galaxies.

Let me explain the cumbersome expression 'the rate of change of time'. It is intended to be a measure of the warping of time and could be defined as ∂t_here/∂t_there both measured by our present standard of time.

The proportion of red shift is recession speed/ speed of light, 20,000/300,000,000 = 0.0000664

Should we attribute all of this shift to dilation of time in the past, then the rate of progress of time 1 million years ago compared to now is 1/1.0000664 = 0.9999336

If the rate of progress of time rising from the Big Bang at 15 billion years ago as an exponential, it is possible to work out the time constant of the curve, i.e. its shape:

e ^{-(time now - 1,000,000)/T} = 0.0000664

T = (time now - 1,000,000) / log_e ( 1/0.0000664)

T = 1,559,177,836 years

This is calculated with the assumption that all of the red shift is attributable to the warping of time. However, without the expansion of the universe, there would be no warping of time. This leads one to speculate how much of the red shift is because of the expansion of the universe and how much is because of the warping of time?