The astronomers think that the universe start with the big bang theory, so how we can say that the big bang theory happened?. there are a lot of evidence, but the main are: the red-shift, the background radiation and that the universe is expanding.
redshift is an increase in the wavelength of electromagnetic radiation received by one compared to the wavelength emitted by the source detector. This increase in the wavelength corresponds to a decrease in the frequency of electromagnetic radiation
Background radiation is a form of radiation electromagnetic. it is also the echo that comes from the beginning of the universe , it is feasible , the Echo Remains of the Big Bang giving rise to the Universe.
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The metric expansion of space is the increase of the distance between two distant parts of the universe with time.