Steady State Theory was a theory proposed in twentieth-century cosmology to explain evidence that the universe was expanding, but still retain the core idea that the universe always looks the same, and is therefore unchanging in practice (and has no beginning and no end). This idea has largely been discredited due to astronomical evidence that suggests the universe is, in fact, changing over time.
When Einstein created his theory of general relativity, early analysis showed that it created a universe that was unstable—expanding or contracting—rather than the static universe that had always been assumed. Einstein also held this assumption about a static universe, so he introduced a term into his general relativity field equations called the cosmological constant, which served the purpose of holding the universe in a static state. However, when Edwin Hubble discovered evidence that distant galaxies were, in fact, expanding away from the Earth in all directions, scientists (including Einstein) realized that the universe didn't seem to be static and the term was removed.
The evidence against the steady state theory grew as new astronomical evidence was detected. For example, certain features of distant galaxies—such as quasars and radio galaxies—weren't seen in nearer galaxies. This makes sense in the big bang theory, where the distant galaxies actually represent "younger" galaxies and nearer galaxies are older, but the steady state theory has no real way to account for this difference. In fact, it's precisely the sort of difference that the theory was designed to avoid!
The final "nail in the coffin" of steady state cosmology, however, came from the discovery of the cosmological microwave background radiation, which had been predicted as part of the big bang theory but had absolutely no reason to exist within the steady state theory.
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