The same type of evidence that supports the idea that our Earth goes around our Sun -- if our solar system is geocentric, we'd observe one thing; if heliocentric, we'd observe something different. Since what we DO observe is what we WOULD observe if our Earth goes around our Sun, then we conclude it DOES -- even if 25% of Americans do not believe that to be the case.
The evidence that the space within our Universe was almost infinitely dense about 13.7 billion years ago, and has been expanding at a (pretty much) steady rate ever since, is overwhelmingly persuasive.
Amongst the evidence in favor:
1) The distance between us and all distant galaxies is increasing, and the rate at which the distance is increasing is directly proportional to the distance between us and these galaxies.
2) There exists an isotropic (to one part in 10,000) and continuous radiation, with a spectrum of a blackbody at 2.7K. This is exactly as predicted by BBC, and allows to see light from our early Universe -- less than 400,000 years after the Big Bang.
3) The ratio of hydrogen to helium in all parts of our Universe are exactly as predicted by BBC.
4) The ratio of long-lived isotopes to their decay products shows decays began about 10 billion years ago.
5) Quasars are seen far from us, but not close to us.
6) The absence of white dwarf stars older than about ten billion years.
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The Big Bang theory is accepted by the majority of the scientific community and is supported by evidence like the cosmic microwave background radiation. It is estimated that a significant majority of scientists and researchers in relevant fields accept the theory as the most plausible explanation for the origins of the universe. It is difficult to provide an exact number of people who believe in the Big Bang theory outside of the scientific community.
Scientists do not sit in the coffeeshop and dream up a theory and thengo looking for evidence to support it. Scientists make observations andmeasurements of what IS ... the "evidence" you might say ... and then tryto put together a theory to explain what they see.The "Big Bang" theory is the best explanation so far for the observation that allgalaxies in every direction are receding from us at speeds that are proportionalto their distance from us, and for the observation that all of space is filled withan almost uniform level of electromagnetic radiation with a distribution of wavelengthsthat is characteristic of a blackbody at the temperature of 2.7 K, and for theobservation that on the largest scale, the universe consists of roughly 75%hydrogen and 24% helium.
Two tools astronomers use to gather evidence in support of the Big Bang Theory are telescopes and cosmic microwave background radiation observations. Telescopes allow astronomers to observe the expansion of the universe and the cosmic microwave background radiation provides a snapshot of the universe shortly after the Big Bang.
Dalton used his atomic theory to explain and predict the behavior of gases, particularly in his work on combining volumes of gases in chemical reactions. This provided experimental evidence that supported the atomic theory and ultimately led to its acceptance by scientists.
Many scientists dismissed the theory because it flew in the face of conventional wisdom.