Question

What it the current value of the Hubble constant and why is the value so important?

Answer 1

`H_0 = 67.80 \pm 0.77 \quad km.s^{-1}.Mpc^{-1}` (Planck Mission - 2013)
`H_0 = 69.32 \pm 0.80 \quad km.s^{-1}.Mpc^{-1}` (WMAP Mission - 2012)

Explanation:

The value of the Hubble Parameter varies with time and so should not be called a constant. It is not a constant. However its value does not change appreciably in human time scales.

Though this is a fundamental cosmological parameter, estimating its value was always fraught with problems. Confusion regarding this resulted in the great debate between van den Bergh and Gustav Tammann in 1996.

Note : The debate was titled "The Scale Of The Universe" and was held at the Smithsonian's national museum of natural history.

van den Bergh argued for a higher value for the Hubble parameter around `80\quad km.s^{-1}.Mpc^{-1}` while Tammann argued for a lower value near `55 \quad km.s^{-1}.Mpc^{-1}`.

Prior to 1958 there were no reliable way of determining its value. The first reasonable estimate of the Hubble Constant was made by Alan Sandage in 1958. (`H_0=75\quad km.s^{-1}Mpc^{-1}`).

Given below is a plot that shows the evolution of the Hubble Parameter estimate.

Image Source : https://www.cfa.harvard.edu/~dfabricant/huchra/hubble/