Two main pieces of evidence support the big bang theory and the idea that our universe is continually expanding: doppler shift and cosmic background radiation. explain how these phenomena provide evidence of the expansion of the universe. explain how both are used to understand the history of the development of earth.

The cosmic microwave background (CMB) is the thermal radiation left over from the time of recombination in Big Bang cosmology.
The CMB is a snapshot of the oldest light in our Universe, imprinted on the sky when the Universe was just 380,000 years old. It shows tiny temperature fluctuations that correspond to regions of slightly different densities, representing the seeds of all future structure: the stars and galaxies of today.
As the universe expanded, both the plasma and the radiation filling it grew cooler. When the universe cooled enough, protons and electrons combined to form neutral hydrogen atoms. These atoms could no longer absorb the thermal radiation, and so the universe became transparent instead of being an opaque fog.
Throughout our universe, light is bursting from stars, bouncing off planets, diving into black holes, wandering into nebulae, and generally going every which way. Meanwhile, a little bit of it actually shows up here on earth.
The light that does arrive here all seems to bear the same message: the universe is expanding.
How can light from the night sky tell us that the universe is growing in size? The main clue comes from something called redshift.
Redshift is light's version of a phenomenon we experience all the time with sound. Have you ever noticed how the pitch of a police siren seems to drop suddenly as the car zooms by you? As the siren approaches you, the waves of sound are squeezed together, and you hear them as being higher-pitched. After the car passes by, sound waves from the receding siren are stretched apart. You hear these stretched waves as being lower-pitched.
This apparent change in the pitch (or frequency) of sound is called Doppler shift. Light from distant stars and galaxies can be shifted in much the same way.
Like sound, light is a wave that can be described in terms of its frequency, the number of wave peaks that pass by each second. Just like a cosmic police car, a star zooming toward you has its light waves squeezed together. You see these light waves as having a higher frequency than normal. Since blue is at the high-frequency end of the visible spectrum, we say the light from an approaching star is shifted toward blue, or blueshifted.
Likewise, if a star is zooming away from you, any light it emits gets stretched. You see these stretched-out light waves as having a lower frequency. Since red is at the low-frequency end of the visible spectrum, we say that light from a receding star is shifted toward red, or red-shifted.
The amount of the shift depends on the speed of the star, relative to you. For a moving object to create an appreciable redshift or blueshift requires some pretty serious speeds. To get just a 1% change in the frequency of light, a star has to be moving 1,864 miles per second. For a blue lightbulb to look red, it would have to be flying away from you at 3/4 of the speed of light.