The Big Rip : an end to the Universe without recollapse

I have to admit, this has been one of the more startling revelations recently. It too sort of troubles me that the universe is accelerating, that we're not seeing some kind of "natural" inverse square velocity falloff. The deeper our understanding of the universe, the more more bizarre it seems to be. I'm starting more and more to lean towards the idea of Fecund Universes, but then again I'm no scientist, so what do I know?

When discussing the ultraviolet catastrophe, I believe you meant that it diverged at short wavelengths.

I agree that a beginning and an end is a more aesthetically pleasing universe, especially for us finite beings to understand.

"there still is a way we can allow for the most aesthetically appealing feature of the recollapsing Universe."

"Forever, like infinity, is a very troubling concept."

Dear Rob,
As a geologist, I hear these sorts of cosmological statements, and I don't see how they differ from the "blind watchmaker" arguements for intelligent design. e.g.:
"We have no data to suggest a guiding hand in evolution, but the idea of design is more philosophically comfortable than 4 billion years of blind chance, and the fossil record has gaps that give us wiggle room."

Admittedly I don't know much about cosmology- scales larger than our Galaxy don't impact on rocks that much- but the "we don't know if heat death is our fate" arguments seem to be made out of cofmort and hubris, instead of being derived from observational data.

Can you explain the difference?

Aesthetics are such a fickle guide. In some sense, I think you can't avoid real infinities.

If the universe truely extends into the infinite past, the question is moot. There is no 'before' to worry about (turtles all the way down?).

If the universe 'begins' - you have to answer the question 'why'? What transforms the true singularity of absolutely literal 'nothing' into 'something? If you don't have *at least* a pre-existing framework of time and space (of however many dimensions and whatever properties), the question appears completely ill-formed to me.

I suppose you could escape into a closed finite universe ala Hawkings 'no boundaries' proposal. But that feels like the universe, from some perspective, is actually a static object. A view that seems contrary to our experience that _time elapses_.

Lab Lemming -
No offense, but if there's any hubris, it's assuming that we must have a heat death. As Rob noted, a Big Rip (or a second Horrendous Space Kablooie, as I like to call it) is perfectly consistent with observation. So "we don't know if heat death is our fate" is simply a statement of fact -- we really don't know.

As for aesthetic judgements, they are indeed a fickle guide, seeing as it was exactly that which led Einstein to add the cosmological constant in order to preserve an eternal universe. Ah, irony. If history is any indication, aesthetics tend to be a rather poor guide to reasoning about the universe. Of course, I won't complain if the universe adheres to my aesthetic preferences and something like the Gott and Li CTC cosmology is true.

As I asked my students to prove on their GR final, this leads to a Universe whose density and expansion rate goes to infinity in finite time.

I have my final tomorrow. Wish me luck!

A.M.

qubit,
What are the observations?

Yick. The Big Rip, though exciting, sounds so much worse than the Big Chill, aesthetically. Death through freezing sounds so much more appealing than being ripped apart from the inside. Though, in the nearer future, w≠-1 would make lots of people very happy.

Oh, and:
The inevitable loneliness of the Milky Way should be a great incentive for TACs to offer more time to extragalactic sources, as soon extragalactic astronomy will be impossible. For certain values of "soon."

"What are the observations?"
The observations are the ones that established that there is expansion going on.
We don't have a handle on the rate. It is increasing with time, it seems, but by how much? We don't know. It could just as easily increase faster and faster and kablooie, or not. There is no preferred view, that is we can't say "current theories would lead us to conclude heat death" because they wouldn't without a good parameter on this expansion. That is the NEW thing we now know that we don't know - that we thought we did know 10 years ago. Cool to still be living in a time when things like this are popping up all the time!

Can you explain the difference?

The difference is I'm talking about what I think is cool and satisfying, not what I think is right. The intelligent designers use aesthetics to say what they think is right. If you reread my post, you can find out what I suspect is right, and the honest admission that really nobody knows.

-Rob

When discussing the ultraviolet catastrophe, I believe you meant that it diverged at short wavelengths.

Oops. I'll go back and fix that.

Wavelength, frequency, whatever. There is a student who took an oral final recently who would be very amused to see me make this mistake, given the context of this student's final... :)

Yick. The Big Rip, though exciting, sounds so much worse than the Big Chill, aesthetically. Death through freezing sounds so much more appealing than being ripped apart from the inside.

Commie! Ending in a big massive firely explosion ripping you apart is part of the True American Aesthetic! :)

-Rob

As for what are the observations....

This paper is not the latest on the topic, but it is the closest one to my heart:

Knop 2003

-Rob

There are a couple of different meanings of aesthetics. One has to do with the mathematical structure of the theory. The other with our preoccupation with the future. We'd like to think that we are part of the progress of life making progress. But if the universe ends in cold slow death, -or heat death or a giant kablooie -then long term everything we have done is for naught. We'd like to think that at least we could send an information time-capsule to the next instantiation of the universe (if there is such a thing), but that appears really-really unlikely.

I remember being taken in by Fred Hoyle's steady state universe when I was growing up. A case of the desire for an aesthetically appealing theory overcoming logic and observation!

...and who think I'm being naive when I say that the number of even integers (infinity) is clearly only half the number of integers (also infinity), even though I'm convinced I'm right.

The set of integers is just that, a set, not an ordered sequence. You're assuming that in a fundamental way for every even integer, there are two integers in the set of integers (the even number itself, and the number plus one). But I could just define some relationship between an odd number and four even numbers that are unique to the odd number (e.g. for every n that is odd, there are four even numbers 4n - 2, 4n, 4n + 2, 4n + 4). Now there are clearly 4 times as many even numbers as odd numbers.

"The set of integers is just that, a set, not an ordered sequence."

AFAIK, the integers form a complete ordered field, the requirements for which is that it be a field in which any nonempty subset has both a least upper and greatest lower bound (in the field). In that sense it is an infinite sequence.

"You're assuming that in a fundamental way for every even integer, there are two integers in the set of integers (the even number itself, and the number plus one)."

That is fundamental. What you're describing is closure, which is a requisite attribute of a field.

Magnum -- it's mathematical doubletalk like that that sometimes makes me suspect that some mathematicians are really pseudophilosophers in disguise who desire to have no other purpose than to prove to the rest of us that nothing is true via impeccable logic.

My answer: foo.

To me, infinity is a limit. The limit of 1/x is half the limit of 2/x, even though both of them limit to infinity. So there.

-Rob

I remember being taken in by Fred Hoyle's steady state universe when I was growing up. A case of the desire for an aesthetically appealing theory overcoming logic and observation!

This reminds me of a conversation I had at some point with somebody who's in some other department. (I forget the department, but it's one of those hoary places that came up with the whole post-modern notion that reality is nothing but a social construction, or something crazy like that.)

A mutual friend introduced me when this guy showed up to our table at lunch. This mutual friend mentioned that I'd worked on measuring the expansion of the Universe.

"Bah," this guy instantly says in a dismissive tone. "The only reason you astronomers believe in the Big Bang is the judeo-christian philosophy that pervades western culture, which includes the notion that there is a moment of beginning."

I sputter a bit. I mean, I'd heard that BS comes out of humanities departments in colleges, but I had no idea. This was before I spent some time poking about and learning that indeed there was (is?) this intellectual movement that says that all the results we claim to have found via science are just social constructions, and that indeed they exist primarily to prop up the patriarchy. Or something. Post-modernist crap. The Sokal affair should have deflated all of that, but I suppose it didn't.

In any event, here I am trying to sputter about evidence, about cosmic microwave backgrounds, about big bang nucleosynthesis calculations, but here's hearing none of it. Scientific evidence, I suppose, is not relevant to him. The fact that the cultural bias he perceives matches the answer we've come up with is all he needs to know.

I finally point out that his sociological conclusion isn't even true. Indeed, the notion of the hot big bang is relatively new, and that for a part of the 20th century a substantial number of astronomers believed in the steady state Universe, the idea that the Universe is now as it always has been, expanding, and staying at a constant density because matter is constantly being created, at a rate that just matches the volume dilution that comes from the expansion.

"Ah," this distinguished professor says. "I like that one better!"

That was about the end of lunch, and the conversation didn't go any further.

It did, for a while, shake my confidence that academics in non-science fields should be taken seriously at all. The fact that they clearly don't take us seriously didn't help. Fortunately, I've come to realize that while lots of humanities types are deeply ignorant about how science works, similarly lots of science types are deeply ignorant about humanities works... and *more* of the scientists are deluded into think that they do know what they don't. There are humanities and social science types who persist with this social construction nonsense, and who think that what they know leads them to know all kinds of things about science that us scientists can't see for being to close to our subject. Fortunately, those sort of ignorant blowhards are very much in the minority.

-Rob

"To me, infinity is a limit. The limit of 1/x is half the limit of 2/x, even though both of them limit to infinity. So there."

It all depends on definition. When mathematicians talk about the limit of the function f(x) are x approaches infinity they are talking about something quantitatively different from whether a mathematical object (like a field, i.e., your example of the integers) is countably or uncountably infinite. In this example, the limit is the same value for both functions, while the ordinates of the respective functions has unequal decimal expansions that are infinite in the latter sense.

Hopefully you won't pick on mathematicians too much, only a few aspire to be contrarians. Most are satisfied with simply being pedantic. ;)

I hear that there are other possible ends for the observable universe, like tunneling to other vacuum states. But it seems to me this first order consequence of todays observations should be answered first.

As aesthetics goes, I think the eternal picture is appealing. It would also work together with parsimony, the Big Rip is a phenomena (in any case as it is elevated to here) we could as well live without. Alternatively it is boundary conditions that we presumably don't need, and would have difficulty explain.

The same goes for Big Bang - if it is merely a local phenomena for pocket universes, it could increase parsimony by removing initial conditions. But all of this is rumination which will not be used to pick theories.

Btw, on aesthetics; there are infinities and infinities. Besides the mathematical idealizations in ordinals, cardinals, limits, and like stuff, it can be used to describe unboundedness and singularities. I could be off here, but I rather think of the latter as more primary physical descriptions. Especially since unboundedness is weaker, I believe.

Hmm. Re weaker concepts, the epsilon-delta definition of limits would make them close companions with unboundedness of course.

Lab Lemming -
In addition to Rob's reply, I'd add that your burden of proof is in exactly the wrong direction. Until observations rule out a Big Rip, it's a viable possibility. I never said, and I don't think Rob said, that observations require a Big Rip, simply that a) cosmic acceleration makes it a possibility, and b) observations don't rule it out. Now, personally, I find closure more aesthetically pleasing than boundedness, but that's a matter of taste, and I don't have much confidence in the universe yielding to my personal preferences.

Rob -
Thanks for a moment of weirdness. I clicked through to your paper and instantly recognized Figure 8 from when I took lower division galaxies and cosmology. (And yeah, I suppose that puts some constraints on where I am in my academic career, such as it is.)

By the way, if you want to read an informed blog post about vacuum tunnelings, bubble universes, and what came before the Big Bang, this post from Sean Carroll at cosmicvariance.com as the place to start.

-Rob

I think the ratio of stuff I understood in that paper to stuff that went over my head is similar to the ratio of oxygen to dark matter in the galaxy. But its a huge paper, so I still learned a fair bit.

I guess my main complaint- and Rob is by no means the worst offender in this sort of cosmology- is when people start talk about the type of universe that they'd like to find- the sort of universe that seems right to them.

To me, the implication of these sorts of statements seems to be that the universe might actually care about the opinion of some self-catalysing speck who is dwarfed by his mid-sized planet, its unremarkable star, and the fairly typical galaxy which it inhabits.

To me, the implication of these sorts of statements seems to be that the universe might actually care about the opinion of some self-catalysing speck who is dwarfed by his mid-sized planet, its unremarkable star, and the fairly typical galaxy which it inhabits.

Why do you draw that inference?

And in inference it indeed is, not an implication, for all of the motive extrapolation is entirely on your side.

What's wrong with people talking about how they'd like things to be? I'm saying, "hey, this would be cool, and it's still allowed via the data."

As long as I don't confuse that with, "this is how it should be, so I'm going to set out to prove that, and put blinders on to ignore what conflicts with it," what's the problem?

And, indeed, reread the last paragraph or two of my post-- I explicitly do not do this. I was explicitly saying what I think I like, not what I think is.

You seem to be reading this post as, "this end in fire is appealing, and the data allow it, so that's probably right."

Find the probably in my post, and it points in the opposite direction.

-Rob

"I could be off here, but I rather think of the latter as more primary physical descriptions. Especially since unboundedness is weaker, I believe."

That's sort of the point I was trying to get at. People get confused when mathematicians and physicists use to same words. Mathematicians study syntactic structures and how they work together in the abstract, physicists study physically real objects. Sort of like when we're talking about "dimensions". Both mathematicians and physicists are talking about the parameters of a space that are perpendicular to all other parameters (most of the time, anyway, this is a bit to simple for rigorous philosophical discussion). The difference is that one is talking about a conceptual space while the other is talking about an objective space. And they aren't necessarily isomorphic, IMO.

Hmm. Re weaker concepts, the epsilon-delta definition of limits would make them close companions with unboundedness of course."

If you're talking about vertical/horizontal asymptotes, I think they are roughly similar conceptually. Not sure though.

Rob, I'm not saying that you allow your aesthetic sense to get in the way of your science. I'm just wondering: Why have a preference at all?

For example, when discussing the origin of life, people trying to find constraints don't talk about some theories as being more attractive than others- at least, not if they want to be taken seriously. In general, people only talk about the coolness of what-ifs in other people's fields.

Back to your paper, what is this extinction that you discussed extensively. And how do you figure out how bright a Ia supernova is without first blowing up a local white dwarf?*

* If you do need to blow up a local white dwarf, I recommend picking Sirius B- because it would be asthetically pleasing.
;)

Lab Lemming -
There's a somewhat less technical, if slightly dated, overview of the original motivations for thinking the universe is accelerating here:
Turner 1999

Admittedly, the CMB angular power spectrum section is liable to cause the MEGO (My Eyes Glaze Over) effect if you've never read this kind of stuff before, but it should at least give an idea of how observations of clusters, SNeIa, and the CMB combine to support the idea that the universe is accelerating. Plus, you can probably skim over the more arcane parts and still get a decent qualitative understanding of what's going on.

And yes, you're right that there are people who will talk about what kind of universe they'd like and pretend that's how the universe is, or ignore the difference between speculative theory and observed fact when talking to a non-technical audience (*cough* Hawking *cough*), but I see a rather explicit avoidance of those follies in Rob's post.

Physicists and mathematicians can't even agree on which angle is φ and which angle is θ in spherical coordinates ... why would they ever agree on something as big as infinity?

Oops, apparently you posted while I was writing, Lab Lemming. Regarding SNeIa, the short answer is that you don't need one nearby, just at a known distance. In fact, you don't want it very close, since if it's close enough to get its distance from parallax, it would not be fun. One way to go about actually finding the intrinsic luminosity is to observe a SN in another galaxy then get the distance to that galaxy by observing Cepheid variables in it, which have a known period-luminosity relation. How do we know that? We find nearby Cepheids and use parallax to get their distance trigonometrically. This is, admittedly, an oversimplification, but the point is that there is a lot of bootstrapping involved.

Actually, the truth is, you don't need to know the true luminosity at all to measure the acceleration of the Universe; you only need it to measure the current expansion rate.

In the fits done in that paper, the current expansion rate and the intrinsic luminosity of the supernova are combined together into a single fit parameter. That fit parameter is, oversimplifying a bit, primarily constrained by the "nearby" (z<0.1) supernovae, and the difference from the straight extrapolation of those and the measurements of the distant supernovae is what gives you the acceleration/deceleration.

-Rob

True enough, Rob, but you do need to know that SNe Ia are, in fact, standard candles, i.e., that they are all close to the same intrinsic luminosity, right?

What does the 'e' in SNe stand for?

Also, are there any good basic papers on Ia nucleosynthesis? Is that as constant as the light curve?

'cause isotopes are way more interesting than the fate of the universe.

You guys should check out science channel this week. They are doing some kind of space week, basically a space programming all week

True enough, Rob, but you do need to know that SNe Ia are, in fact, standard candles, i.e., that they are all close to the same intrinsic luminosity, right?

Yes, definitely. But you can get that from their residuals around the expansion of the Universe when you're looking at "nearby" objects (i.e. no more than a billion or so light-years away). You may not have the absolute scaling, but you can see that they're always consistent with each other. (In fact, there's a leftover intrinsic scatter of something between 10 and 20 percent, but we take that into account in our error budget.)

What does the 'e' in SNe stand for?

SN=Supernova, plural supernovae... SNe.

In common conversation, you are allowed to pronounce it "snee" if you're with people who know what you're talking about :)

Also, are there any good basic papers on Ia nucleosynthesis? Is that as constant as the light curve?

Almost certainly; I don't know what they are, though, I fear.

-Rob

In common conversation, you are allowed to pronounce it "snee" if you're with people who know what you're talking about :)

Ah, so that's why the Klingon language has word roots for things like "neutron star"! I have always wondered. :-)

I'm fascinated by different physicists' ideas of what the teliology of the universe "should" be. In the end I suppose it boils down to religious preferences. Ask an atheist, and they'll say the Big Bang wasn't a beginning; it's just where our theories break down and eventually we'll understand what went on before that time. (This philosophical bias--that there should be no beginning (or end)--is of course what caused the Big Bang theory to be so slowly accepted in the first place.) And then ask a religious fellow like Rob Knop, and it's taken for granted that the Big Bang was a beginning, and he'll even go so far as to say there is (or at least he prefers) an end.

Personally, I'm pretty neutral on religion, so I'm interested in beginnings and ends to help me decide if there's a God or not.

And then ask a religious fellow like Rob Knop, and it's taken for granted that the Big Bang was a beginning, and he'll even go so far as to say there is (or at least he prefers) an end.

Er, no.

Taken for granted that there was a beginning? I don't do that. Scientifically, all I can say is that there is an early moment where our theories break down and which we can't look before. That's not an atheistic statement, that's an accurate statement of the state of science. Despite what Dawkins and PZ and Moran may have told you, "accurate about science" and "atheistic" are not synonymous. I have written about this at length before, and refer obliquely to it here. I find it very curious that you're ascribing to me a view that there is a definite moment of beginning... what I see happening, in fact, is you projecting your preconceptions on what certain sorts of people think on to those people without evidence.

Philosophically and religiously, I personally don't have a bias. "A moment of beginning" isn't part of my own personal religious faith.

Also, the "end" provided by the Big Rip isn't an end any more than the Big Bang is a beginning. It is something you can call the end of our Universe, much as the passing of a star to a white dwarf can be described as the end of a star's life, but that doesn't mean that time itself must really end there.

-Rob

I imagine I have indeed unduly stereotyped you (such things always happen when one tries to draw conclusions from limited data). But you've now done the same to me :). "Accurate about science" doesn't mean "antiest", of course--it actually comes closer to nihilist. Because "accurate", in science, is always "we don't know". That's what you've retreated to--but if that were the kind of thinking that motivates you, I doubt you'd be posting at all about beginnings and ends. The point is that taking the "beyond the equations and expeirments" step of saying something interesting about teliology, or whatever, brings in personal bias, and I think, at the very least, openness to religion is commonly a prerequisite to accepting the
"big bang is a beginning" interpretation, which I still claim your original post is predicated on.

But--I didn't mean for this to be an argument; iteresting stuff!

Because "accurate", in science, is always "we don't know".

I disagree with that.

There is a difference between "not knowing everything" and "knowing nothing."

We do know something. Being accurate in science means stating what our best understanding is, and stating our best understanding of our uncertainties about that. That's better than just saying "I don't know."

Yes, this is qualitatively different about what you think "must" be right, of course.

I have no philosophical or aesthetic problem with future infinity - it makes such a nice top-off to a Penrose diagram - but it is necessary that the Universe should have an end, because otherwise there could be no Restaurant At it.

That's an excellent point.