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You are literally arguing with Alexander Vilenkin. It was his statement that I posted.There is no such thing as "proof" in physics. It is a mathematical term and depends on premises. Premises in math are fine. Premises in physics are often transient and change with new observations or experiments.
But I suspect the proof he is talking about is the mathematical proof that the universe began being created from nothing.
An interesting idea is that the universe could be spontaneously created from nothing, but no rigorous proof has been given. In this paper, we present such a proof based on the analytic solutions of the Wheeler-DeWitt equation (WDWE). Explicit solutions of the WDWE for the special operator ordering factor p = −2 (or 4) show that, once a small true vacuum bubble is created by quantum fluctuations of the metastable false vacuum, it can expand exponentially no matter whether the bubble is closed, flat or open. The exponential expansion will end when the bubble becomes large and thus the early universe appears. With the de Broglie-Bohm quantum trajectory theory, we show explicitly that it is the quantum potential that plays the role of the cosmological constant and provides the power for the exponential expansion of the true vacuum bubble. So it is clear that the birth of the early universe completely depends on the quantum nature of the theory.
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