re: Do you accept the notion of the Big Bang as the origin of our universe?

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Maybe there were more than 4 forces of nature in the early universe. Maybe this unknown force of nature prevented the formation of black holes during the time you're describing.

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Maybe, but if there weren't then it means that one or all of the forces, combined, were exerting a repulsive effect. In his research, Einstein identified a "repulsive gravity" but threw it out of his equations because he thought it was spurious. He later said this was the biggest blunder of his life. It's what we now call Dark Energy.

Wow! He could have saved us a hundred years of effort if he hadn't doubted his own genius. We might know what Dark Energy is, and maybe Dark Matter, too, if he had devoted more time to understanding it.

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I've long wondered if the birth of the universe wasn't brought about by a white hole.

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White holes have fallen out of favor since Stephen Hawking discovered that black holes emit what has logically been named "Hawking Radiation." This means that black holes evaporate over immense periods of time. Previously, white holes had been theorized as the "outlets" of black holes, and opened into a different spacetime.

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Perhaps this force of "anti-gravity" works on a very small scale, as well as, a very large scale.

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That's my idea, too. I think that gravity may work differently in different situations. It may periodically switch from an attractive to a repulsive force and then back again, if only, hopefully, on a cosmic scale and not locally.

Since we think that it's the spacetime field interacting with mass that generates gravity, this might make sense. Too much mass moving through space at great speeds might make gravity oscillate in this manner.