The cosmic microwave background (CMB). The "no edge" proposal was speculated as a result of the cosmic microwave background being mapped in 1964 because of how isotropic the data was, which spawned the flatness problem, which states that this isotropic nature geometrically implies a flat universe. This is an issue because it implies that information must have traveled faster than light, resulting in a fine-tuning explanation, which we [i]do not[/i] want. Just as Flat Earth theories and geocentricism require many unnatural "work arounds" to resolve contradictory observations.
There are several other issues surrounding the isotropic nature of the CMB, one of which deals with the supposed abundance of theoretical particles that we've never found evidence of, and would contradict the process by which our fundamental forces would form. Studying this in 1980, Alan Guth proposed an inflation era by which the universe expanded exponentially fast from initial conditions, which resolved all of these issues. What this implied is that the initial conditions of the universe had to be infinite, uniform vacuum energy in correspondence to the laws of thermodynamics. What this implies is that said energy is still infinite, therefor the universe is infinite.
This was fine and dandy, but the land-based telescope that mapped the CMB in 1964 had to have alot of noise in order to work around our atmosphere, and so while all the data supported this, we couldn't be conclusive. Well, with the power of space observatories, COBE (1989), WMAP (2003), Planck (2013), we have conclusive evidence. Each of these allowed for progressively more accurate data, the WMAP being accurate enough showed us that changes in the temperature were small enough to be caused by quantum fluctuations, of which Planck affirmed with extreme accuracy. The evidence provided is clean cut and conclusive.
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