Can the big rip ever be ruled out?

[Trollfaz]

In order for the big rip to happen, the dark energy equation of state w must be more negative than -1, allowing dark energy density to grow.
https://en.m.wikipedia.org/wiki/Big_Rip
According to Wikipedia, the current observed w value is very close to -1 but it acknowledges that there is insufficient evidence to strictly disprove the big rip
I read Katie Macks book called The End of Everything and inside it, she mentioned that all experiments have an error therefore we cannot force the value of w to be exactly -1. So we can push the big rips earliest date further into the future but not indefinitely far. So far the latest data assures that there will be no rips for the next 200 billion years according to the book.
But doesn't increasing dark energy density violate the law of energy conservation. There is no mechanism we know of that allows this.

 

[Ibix]

The actual value of $w$ might be greater than -1, in which case we might eventually exclude all $w\leq-1$ models. If the actual value of $w$ is exactly -1 then you are correct that we could not rule out the Big Rip from measurement of $w$ alone. Other discoveries could rule it out, of course. For example a working theory of quantum gravity might allow us to derive $w$ from more fundamental considerations.

But doesn't increasing dark energy density violate the law of energy conservation. There is no mechanism we know of that allows this.

Conservation of energy is a complicated topic in general relativity. In the global sense that you are using it here, there's no way to state it - and since we can't state it no scenario violates it. And in the local sense where a conservation law can be stated quintessence doesn't violate it.

It's worth noting that there are ways of "kind of" stating a global energy conservation law in GR. Some physicists are convinced by these and some aren't - I don't know where your book stands on the topic. I don't understand the subject well enough to comment on whether the Big Rip violates any of these kinda-sorta-laws, but there are enough serious physicists who don't accept them at all that I'd say worrying about possible violations of global energy conservation is putting the cart before the horse. We need to agree (a) that there is such a law, and (b) what it is before we worry about whether a scenario violates it.

 

[Orodruin]

As @Ibix has mentioned, if w is exactly -1 then experimental error will never allow you to rule out $w < -1$ (except by statistical errors - either systematic or random). This is true for any measured quantity with a particular value. Take the photon mass for example. It is zero in our models because that works very very well. However, experiments cannot rule out a teeny tiny mass $< 10^{-18}$ eV (pdg.lbl.gov).