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I have been investigating inflation and the big difference in the theoretically predicted value of the cosmological constant and the actually measured value of it. There would be 120 orders of magnitude in difference for the latter, which became known as 'the largest discrepancy between theory and experiment in all of science'. What we measure today is a very slightly accelerating expansion of the universe, which is ascribed to the negative pressure of dark energy. According to the theoretical prediction, dark energy density would be so great and the expansion of the universe would accelerate so fast that everything would be torn apart almost immediately (known as the Big Rip). So here comes my idea (which is, if I am right, a form of quintessence): what if there was a phenomenon (a field with negative potential?) that counterbalances the theoretically predicted negative pressure of dark energy with positive pressure? The main way in which I can imagine this is that the universe is like a rubber membrane with a certain elasticity (or plasticity). During inflation the membrane would be in the linear range of the stress-strain curve and expand fast. During the post-inflationary phase the expansion would be much slower because the membrane is partially plastic due to strain hardening. But if the universe keeps expanding, there will be a point in the stress-strain curve where the membrane breaks, followed by an immediate Big Rip (much faster than the classical Big Rip scenario). This would be the analogue of a balloon that pops. So is this a scenario that has been proposed in the literature, next to the Big Rip, the Big Crunch, and the Big Freeze scenarios for the future of the universe: the Big Break? And if not, are there good reasons to reject this possibility?

I know that inflation is classically explained by an inflaton field. But that proposal does not seem to solve the infamous discrepancy with respect to dark energy. I also found there is a theory called the Big Pop, but that appears to be about the beginning of the universe, not the end of it.

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According to the theoretical prediction, dark energy density would be so great and the expansion of the universe would accelerate so fast that everything would be torn apart almost immediately (known as the Big Rip).

Incorrect. Even a very large $\Lambda$ would just lead the Universe to grow exponentially. A Big Rip means the expansion is infinite in a finite time. A parameter called $w$ needs to satisfy $w<-1$ for this to happen, whereas $\Lambda$ dominance defaults to $w=-1$.

what if there was a phenomenon... that counterbalances the theoretically predicted negative pressure of dark energy

Something must make the true $\Lambda$ surprisingly small. There are two main ways this could happen:

  • What you describe, which requires very nearly but not perfectly matched contributions (you try finding a person exactly $1-10^{-120}$ times as strong as another person; this is called a fine-tuning problem.)
  • That the formula for $\Lambda$ is wrong. Basically, it's an integral from $0$ to $\infty$ whose integrand we probably only understand well for small values.

the universe is like a rubber membrane with a certain elasticity

I think there are some finite-elasticity spacetime models, although none are currently very popular, but surprisingly it doesn't look like any existing Physics SE questions concern them.

During inflation the membrane would be in the linear range of the stress-strain curve

In the consensus model the time-dependence of the universe's expansion depends only on density and a curvature parameter. I can't speak to how finite-elasticity models adjust this, but I doubt they modify inflation's explanation.

is this a scenario that has been proposed in the literature, next to the Big Rip, the Big Crunch, and the Big Freeze scenarios for the future of the universe: the Big Break? And if not, are there good reasons to reject this possibility?

Again, I'm no expert, but my experience with field theory suggests that what would instead happen in the equations is processes that would otherwise cause infinite expansion would only cause finite expansion. If I can pick an analogy, it's like how arbitrary kinetic energy still doesn't get you beyond the speed of light in special relativity.

an inflaton field... does not seem to solve the infamous discrepancy with respect to dark energy

These problems might not warrant the same solution.

I also found there is a theory called the Big Pop

Judging by the Figure 2. caption here, that idea is something different, whereby a combination of expansion and contraction is applicable, and not to something as simple as the usual scale factor.

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