Red-shift is the concept that the wavelengths of light from distant galaxies are higher than expected. The further away the galaxy, the more significant the increase in wavelength.

Red-shift occurs because the light emitted by an object moving away from us will be stretched. The stretching causes the light's wavelength to increase. The faster an object moves away from us, the larger the red-shift will be.

Red-shift shows that the universe is expanding, which supports the big-bang theory.

The Universe expanded from a single tiny point of high density and pressure.

Space and the universe itself is expanding and this makes galaxies further apart.

CMBR is electromagnetic radiation from the Big Bang, now observed in all directions as the universe has expanded and cooled.

Red shift suggests that galaxies are moving away from us, indicating that the universe is expanding.

Where:

Δλ= change in wavelength (m)

λ0​= original reference wavelength (m)

v = recessional velocity of the galaxy (m/s)

c = speed of light in a vacuum (300,000,000 m/s) 

It suggested that the universe has always existed much as we see it today, with a constant density over time.

The theory proposed that new galaxies form in the spaces where older ones have moved apart, keeping the universe's density constant.

It struggled to compete with evidence supporting the Big Bang theory, which eventually became the more accepted model.