How could we know if we are within 10 years of a Big Rip? The expansion of the universe might cause the Big Rip. The mathematical physics of the possible Big Rip has been worked out beyond my mathematical abilities. I want to know if we can calculate if we are within 10 or 100 years of the Big Rip. I understand that we could do nothing about it if we knew, but I still want to know if we can we possibly estimate an imminent Big Rip. I understand that nobody has predicted an imminent Big Rip while I wonder if that is even possible.
 A: Nice question. A useful paper on this topic is Caldwell et al., "Phantom Energy and Cosmic Doomsday," https://arxiv.org/abs/astro-ph/0302506 (great title). The paper discusses the theoretical and empirical motivation for models that give a big rip. The motivation is not particularly compelling yet, but it seems to make such models worth considering.
These models are parametrized by a quantity $w$, which equals $-1$ in ΛCDM. For $w<-1$, you get a big rip. Observations allow us to estimate $w$ with error bars. A 2008 paper by Allen, http://arxiv.org/abs/0706.0033 , gives $w=-1.14\pm 0.31$. (There are probably tighter estimates available since then.) So let's say that with pretty decent confidence we know that $w\gtrsim -1.5$. The value $-3/2$ is one that Caldwell uses as an example. For this value of $w$, there is a delay of about $10^9$ years between the time when galaxy clusters are disrupted and the time when the big rip arrives. Since we see that galaxy clusters still exist, we can say that a big rip, if it's going to happen, must still be at least about a billion years off.

How could we know if we are within 10 years of a Big Rip?

If you look at Caldwell's Table I, he says that 6 months before a big rip (again with $w=-3/2$), the solar system would become unbound. So if you want to imagine our distant descendants living 10 years before a big rip, the galaxy would have long since been dissipated, but at least part of the solar system would still exist. However, I would imagine that if a big rip was only 10 years away, it would already have had significant effects on our solar system -- effects that would have easily been observed, even by relatively crude measurements of the motion of the planets. For example, the earth's year would have gotten longer, and maybe the outer planets would already have been stripped off.
A: The current standard model of cosmology, the Lambda-Cold-Dark-Matter model, predicts no Big Rip. Ever. Not in 10 years. Not in 100 years. Not in 10 billion years. Not in 100 trillion years.
You should forget that you ever heard about the possibility of a Big Rip because there is zero evidence that it will happen. As Wikipedia explains, “The possibility of a sudden rip singularity occurs only for hypothetical matter (phantom energy) with implausible physical properties.”
