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Relativity, Black Hole and some doubts

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In the model of the big bang I would like to pose the following question. My understanding is that

1. The expansion of the universe is accelerating and

2. The radiation or shock wave to keep the analogy going is something we can measure.

My question is this. While we can rewind the clock to a single moment when the universe was infinity dense how do we know that this was a moment at all. Let me elaborate. As the universe expands could time or space time not also expand and if so than when the big bang occurred is something we cannot measure merely by rewinding the clock. If we are experiencing time at a given rate when the universe is at its current size would time not be being effected by the expansion also and if so would that mean the there was simply no start and no end to the universe? Perhaps the big bang is not as accurate as we may wish and perhaps it is our ability to comprehend that is limited. I propose there is no start or end to the universe it has always and will always be as it, and we, cannot exist without time and as such these two objects or things form a symbiotic relationship with each other. While the universe expands so does time and its effects are reduced in line with its expansion. Does this sound plausible and if not why?

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