Astronomy Without A Telescope – Big Rips And Little Rips

by Steve Nerlich on July 2, 2011

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The concept of accelerating expansion does get you wondering just how fast the universe can end up expanding by. Theorists think that the rate of expansion might become so extreme as to produce a Big Rip. Or, after fiddling with the math a bit, maybe just a Little Rip? Credit: NASA.

One of a number of seemingly implausible features of dark energy is that its density is assumed to be constant over time. So, even though the universe expands over time, dark energy does not become diluted, unlike the rest of the contents of the universe.

As the universe expands, it seems that more dark energy appears out of nowhere to sustain the constant dark energy density of the universe. So, as times goes by, dark energy will become an increasingly dominant proportion of the observable universe – remembering that it is already estimated as being 73% of it.

An easy solution to this is to say that dark energy is a feature inherent in the fabric of space-time, so that as the universe expands and the expanse of space-time increases, so dark energy increases and its density remains constant. And this is fine, as long as we then acknowledge that it isn’t really energy – since our otherwise highly reliable three laws of thermodynamics don’t obviously permit energy to behave in such ways.

An easy solution to explain the uniform acceleration of the universe’s expansion is to propose that dark energy has the feature of negative pressure – where negative pressure is a feature inherent in expansion.

Applying this arcane logic to observation, the observed apparent flatness of the universe’s geometry suggests that the ratio of dark energy pressure to dark energy density is approximately 1, or more correctly -1, since we are dealing with a negative pressure. This relationship is known as the equation of state for dark energy.

In speculating about what might happen in the universe’s future, an easy solution is to assume that dark energy is just whatever it is – and that this ratio of pressure to density will be sustained at -1 indefinitely, whatever the heck that means.

But cosmologists are rarely happy to just leave things there and have speculated on what might happen if the equation of state does not stay at -1.

Three scenarios for a future driven by dark energy - its density declines over time, it stays the same or its density increases, tearing the contents of the universe to bits. If you are of the view that dark energy is just a mathematical artifact that grows as the expanse of space-time increases - then the cosmological constant option is for you.

If dark energy density decreased over time, the acceleration rate of universal expansion would decline and potentially cease if the pressure/density ratio reached -1/3. On the other hand, if dark energy density increased and the pressure/density ratio dropped below -1 (that is, towards -2, or -3 etc), then you get phantom energy scenarios. Phantom energy is a dark energy which has its density increasing over time. And let’s pause here to remember that the Phantom (ghost who walks) is a fictional character.

Anyhow, as the universe expands and we allow phantom energy density to increase, it potentially approaches infinite within a finite period of time, causing a Big Rip, as the universe becomes infinite in scale and all bound structures, all the way down to subatomic particles, are torn apart. At a pressure/density ratio of just -1.5, this scenario could unfold over a mere 22 billion years.

Frampton et al propose an alternative Little Rip scenario, where the pressure/density ratio is variable over time so that bound structures are still torn apart but the universe does not become infinite in scale.

This might support a cyclic universe model – since it gets you around problems with entropy. A hypothetical Big Bang – Big Crunch cyclic universe has an entropy problem since free energy is lost as everything becomes gravitationally bound – so that you just end up with one huge black hole at the end of the Crunch.

A Little Rip potentially gives you an entropy reboot, since everything is split apart and so can progress from scratch through the long process of being gravitationally bound all over again – generating new stars and galaxies in the process.

Anyhow, Sunday morning – time for a Big Brunch.

Further reading: Frampton et al. The Little Rip.

Anonymous July 3, 2011 at 3:26 AM

The FLRW equation for the scale parameter a = a(t) is

(a’/a)^2 = 8?G?/3 – k/a^2

where a’/a = H, the Hubble parameter, and flatness means k = 0, spherical geometry is k = 1 and hyperbolic geometry is k = -1. There is an equation of state for the material in the spacetime

d(?a^3)/dt + pda^3/dt = 0

which is most relevant for the case of radiation and matter dominated universe with p = ?/2 and ? a^3 = constant for radiation. The general equation of state is p = w?. Since we are interested primarily in the cosmological event horizon I will consider the de Sitter spacetime, which has ? = constant. The FLRW equation for k = 0 is then

da/dt = sqrt{8?G?/3}a

which has the solution a = sqrt{3/8?G?}exp[sqrt{8?G?/3}t]. Using the Einstein field equation we then have that the stress energy is T^{00} = 8?G? = ?, which is the cosmological constant. Returning the first equation, the FLRW equation, we then see that H^2 = ?/3, where to make this more complete we use H^2 = ?_DE?, where total Omega is unity, or 1 = ? = ?_DE + ?_DM + ?_M composing the various parts. The de Sitter metric approximates spacetime as ?_DE –> 1. We just set this to unity for now.

The equation of state p = -? corresponds to a case where the total energy is zero and the first law of thermodynamics is dF = dE – pdV = 0 means the energy that is increased in a unit volume of the universe under expansion is compensated for by a negative pressure which removes work from the system. Further pdV = d(NkT), and for a constant thermal energy for the vacuum and Nk = S this is the entropy of the universe. This is due to a negative pressure which “absorbs work” from the universe. As a result the expansion of the universe appears to generate more dark energy, say with the expansion of any volume of space with a constant vacuum energy, but the negative pressure acts as “negative work” to absorb this apparent creation of energy.

The big rip is a case where the w < -1 and the expansion goes crazy. The w = -1 expansion is exponential and so it does ramp up, but it has an unbounded domain. The big rip is a case where there is some asymptote at some time in the future where the expansion accelerates to infinity in a finite time period. There are a number of problems with this, and the big one is that it violates the weak energy condition of Hawking and Penrose. Such violations mean the spacetime admits things like time travel and various pathologies.

LC

Steve_Nerlich July 3, 2011 at 1:16 AM

Thanks – that looks familiar. As much as I can gather the idea is that DE generates expansion and the expansion absorbs the DE – so nett energy production is zero?

Anonymous July 3, 2011 at 12:06 PM

That is basically how it works. I wrote some years ago papers which in this context had a sum(all) = 0, so the net mass-energy content of the universe is zero. This was something I realized after the discovery of the accelerated expansion of the universe.

Energy conservation requires there to be some time translation invariance principle. In the case of general relativity this means there must be some isometry condition for a vector projected on any geodesic or path in spacetime. This vector is called a Killing vector. These vectors are eigenvectors of the Weyl curvature, and for a spacetime one can compute them. As a rule of thumb, if the metric terms contain some dependency on a coordinate then there is no conservation principle which involves translation along that coordinate. So a time dependency on a metric element, such as the exp(t sqrt{?/3}) in FLRW means there is no time-Killing vector, and thus no symmetry for energy conservation. However, the constraint or equation of state p = -? imposes a net energy = 0 condition with regards to dark energy. This is not so much the case with other matter and radiation.

LC

Anonymous July 4, 2011 at 9:30 PM

“the net mass-energy content of the universe is zero” – ?!?

Do you mean the M-E content remains constant or do you really mean total M-E is zero?
Right after the big bang dark energy was ~zero and there was a lot of ‘normal’ energy/mass. Does what you say imply that after the big bang there was a kind of “potential dark energy” just as large as (but opposite or negative in value) the amount of ‘normal’ energy/mass, and that potential dark energy is gradually turning into ‘active’ dark energy?

Anonymous July 5, 2011 at 3:02 AM

Dark energy was 10^{100} times what it is today during the inflationary period. The accelerated expansion of the universe was such that any region with a radius R increased in radius by e^{63}R or 2.3×10^{27}R, or so called 63 efolds. The dark energy “crashed” in the reheating period which generated the matter-energy we observe, and a residual dark energy remains in the cosmological constant. This reheating period is similar to a thermodynamic phase transition with the release of latenet heat of fusion. That latent heat is the thermal form of the big bang.

The total energy of the universe is constant, which is basically set to zero.

LC

Anonymous July 5, 2011 at 9:57 AM

Wow Mr Crowell. I wonder how many people know this. I didn’t.
Is there consensus among physicists that this is how it went, and that if you add up everything in the universe the sum is zero?
If there is, then this is such a fundamental insight, it should be basic education for everyone.
Thank you, and Mr Nerlich, very much for teaching us.

Anonymous July 4, 2011 at 9:30 PM

“the net mass-energy content of the universe is zero” – ?!?

Do you mean the M-E content remains constant or do you really mean total M-E is zero?
Right after the big bang dark energy was ~zero and there was a lot of ‘normal’ energy/mass. Does what you say imply that after the big bang there was a kind of “potential dark energy” just as large as (but opposite or negative in value) the amount of ‘normal’ energy/mass, and that potential dark energy is gradually turning into ‘active’ dark energy?

Anonymous July 3, 2011 at 4:03 AM

Consider that “dark energy” may have passed over a (next) dimensional horizon just beyond the distant red shifted galaxies. This curvature could conceal further massive galactic materials (we call “dark energy”) that interact gravitationally with our current visible universe. Imagine the curvature of the Earth stepped up one more dimension. This horizon would exist at the periphery, in all directions, of our currently perceived four dimensional universe.

Multiple dimensions have been foretasted. This simply involves further dimensionality and gravitation. Do the thought experiment: Imagine.

Steve_Nerlich July 3, 2011 at 1:06 AM

Having big chunks of stuff just over the horizon violates the cosmological principle that the universe is homogenous and isotropic:
http://en.wikipedia.org/wiki/Cosmological_principle

If you are going to propose there are big chunks of stuff out there, that’s fine – but you then have to depart from a discussion around Einstein field equations, which accept the cosmological principle as a fundamental assumption.

Anonymous July 3, 2011 at 10:13 AM

If you are assuming that there is a massive hidden sphere of massive amounts of mass just beyond the visible universe then you have to realize that this sphere will collapse on itself and any gravitational effects inside the sphere gets cancelled out by the opposite side jut like a charge inside a metal sphere is zero.

peter fraser July 3, 2011 at 5:32 PM

I expect that there will be an eventual gravitational implosion to singularity followed by a reflective big bang, followed by a gravitational implosion, followed by…

Anonymous July 3, 2011 at 11:18 PM

The de Sitter spacetime will exponentially expand into a vacuum state, which will obtain in about 10^{100} years. There will still be a horizon at r = sqrt{3/?}, which will over a huge period of time quantum mechanically decay and the universe will end up as an empty flat spacetime as time — > ?. The universe does not appear to be such that it will recollapse.
LC

peter fraser July 4, 2011 at 12:31 AM

Is the reach of gravity infinite in time and space? Lets you and I wait this situation out and see what happens and pick up this conversation in a trillion years. We should have some clarity of pattern by then! Thanks for contributing to the thought process.

Raimonds Cirulis July 3, 2011 at 11:30 PM

pls dont forget that gravity/time/space is strongly inerconnected. What we call time, within that time it flows differently,we dont have zero point to measure the real time , and , within zero point, the time even exist in categories we are unable to name it,and non-exist, thanks to the same time/gravity/space interconnections.So the change within universe dont change the universe, we simply are watching a kind of inner changes, it does not mean that universe expands, as is absolute and ended, all what we see is projections

Raimonds Cirulis July 3, 2011 at 11:30 PM

pls dont forget that gravity/time/space is strongly inerconnected. What we call time, within that time it flows differently,we dont have zero point to measure the real time , and , within zero point, the time even exist in categories we are unable to name it,and non-exist, thanks to the same time/gravity/space interconnections.So the change within universe dont change the universe, we simply are watching a kind of inner changes, it does not mean that universe expands, as is absolute and ended, all what we see is projections

Torbjörn Larsson July 5, 2011 at 7:02 PM

What we call time, within that time it flows differently,

Evidently time doesn’t flow, if you take its derivative it is constant: dt/dt = 1.

It is precisely that which general relativity (GR) explains, by taking the idea of local clocks seriously. Time proceeds uniformly (by GR), space is flat (by GR applied as standard cosmology), so instead spacetime has to curve to explain observation (of different reference frames or clocks).

Anonymous July 3, 2011 at 6:04 PM

As a curious observer with no science credentials I find all of this pretty interesting and at the moment there is a lot of room for imaginative speculation. My main issue is trying to “resolve” the many “supernatural” experiences I have had. I have observed and experienced inexplicable physical phenomena, even in the presence of others, that lead me to wonder whether there is really some form of consciousness holding the universe together. I don’t expect most scientists would like this explanation but even quantum weirdness implies the universe is quirky. And one can never seem to solve the chicken/egg problem of what came first. So to me the universe and all life is based on a contradiction – a paradox that is actually quite lovely and I enjoy thinking of it all as absurd. It makes me smile. I wonder if science will eventually find “god” or some mystical glue holding it all together.

peter fraser July 3, 2011 at 6:46 PM

This reality is big, complicated and shiny; even tending toward blinding. Personally, I would just assert that there is conscientious in this universe and this conscientious is this universe: Full stop.

Steve_Nerlich July 3, 2011 at 3:32 PM

“I don’t expect most scientists would like this explanation…”.

Respectfully you have not provided an explanation. I imagine most scientists would be willing to listen politely and then request you come back when you have some evidence for any ‘supernatural’ phenomena you have experienced.

No-one is obliged to share anyone else’s personal incredulity and it would be a bit unfair to consider anyone else unimaginative for preferring to pursue concrete fact. Scientists are experts at demonstrating genuine quirkiness in nature which no-one had imagined beforehand.

Establishing evidence constrains the room available for imaginative speculation – or otherwise directs it down more useful paths. This does seem to be the most effective way to achieve insight into the true nature of things.

Anonymous July 4, 2011 at 2:21 AM

I don’t believe I have expressed any incredulity or suggested anyone lacks imagination just b/c they haven’t had a “supernatural” experience. But the things I’ve seen came around periods of great relaxation and clarity in my mind so I’ve admitted that i don’t know if they could be scientifically verified under controlled conditions. But if I found someone open to exploring some form of testing with an open mind I’d probably try it. By the way, I have no interest in organized religion and was agnostic before weird things started happening. I couldn’t give you an exact answer on what I think is “out there” other than to say I believe there’s more than we can see and perceive with these senses.

One thing that happened to me when I was by myself came while I was pondering whether there was an afterlife. As the thought pursed my lips I felt an unseen “joyful presence” and had the sensation of being playfully tickled all over. Totally playful, not at all frightening. It lasted intermittently for 90 minutes. I’d ask “it” to stop b/c I was laughing so hard and it would stop. Then playfully start again. Even if someone observed this how could i prove it was real? They’d just think I was nuts. But since I know it actually happened then I’m obliged to consider it as part of reality. This is only one of many “events” in the last 15 years. What do you think you would do with this info if it happened to you? I’ve chosen to share it on occasion so that others can ponder it if they like. If they wish to consider it as a possible reality.

Steve_Nerlich July 4, 2011 at 12:44 AM

Sorry I wasn’t meaning to stomp all over your input – but am advocating science as the way forward. If I felt such an unusual sensation I would see if it could be independently and objectively measured and try and establish the basis of it.

Anonymous July 4, 2011 at 1:01 PM

No problem. No offense taken. Thanks for hearing me out. I do believe this experience, or similar, is available to anyone. If this counts as an ‘experiment’ try posing a question to the universe sometime. Sounds ridiculous I know. (But not really since existence is already pretty crazy.) If you are able to do this under quiet circumstances as a kind of meditation then it would be similar to my ‘test conditions.’ I can’t promise any result since I don’t know how this works. But I think openness to new and far out ideas and a basic humility in the face of creation may be factors.

Taking a scientific approach is perfectly reasonable. I’m intrigued by the possible collision of science and ‘the magical.’ I do not find them at odds in my mind. Cheers.

Torbjörn Larsson July 5, 2011 at 6:56 PM

Unfortunately subjective experience doesn’t count as an experiment in that sense.

If you go by way of biology, it is evident that the brain is a chemical machine which logically can have no “ghost in the machine” soul operating the mind (no substrate; infinite regress) and experimentally is shut down by such things as sleep or narcosis. The question have been posed many times and amply answered; every time you go to sleep for example.

Anonymous July 6, 2011 at 4:15 AM

Actually, I’ve heard of this tickling experience before. I was told it is a very rare and unusual form of restless leg syndrome. From what I’ve heard it’s harmless, but in it’s most extreme form can take the form of a tickling/burning sensation with a duration of minutes. It’s a temporary malfunction of the nervous system.

There are a couple other explanations I’ve heard for this but they are a bit more exotic and less reliable.

Anonymous July 3, 2011 at 11:25 AM

You can get the feel that we are narrowing in on what holds the universe together. However, I recently came across a reminder of how close people thought they were to a solution over a hundred years ago. The book was W.W.Rouse Ball’s “Mathematical Recreations”, reprinted in 1905, and now on Project Gutenberg.

The last chapter is called “Matter and Ether theories”. This has lovely descriptions of how the ether may be a membrane in 4-space, with fundamental particles as perpetual vortex loops. The idiom feels surprisingly modern, bearing in mind we haven’t yet got to relativity or quantum theory. Here’s a quote (page 329)…

“It is alleged that the theory accounts for the known phenomenons of gravity, electricity, and light, provided that the size of the grains is properly chosen. Reynolds has calculated for this purpose their diameter should be rather more than 5 x 10^-18 centimetres, and the pressure of the medium would be about 10^4 tons per square centimetre.”

It all sounds quite precise and measurable. You can feel the breakthough is just around the corner. Only, there was no Luminiferous Ether, with a pressure of about 10^4 tons per square centimetre, or otherwise. I wonder how this web page will look in a hundred years time.

Anonymous July 3, 2011 at 12:16 PM

Raleigh, Reynolds and others worked on a proposal with loops and knots in aether, and tried to show that different knot topologies corresponded to different particles or atoms. Interestingly there have been some developments analogous to this in recent times, which were worked by Witten. The Yang-Baxter equations and Jones polynomial for knots has been employed to characterize certain amplitudes.

The dark energy is “dark” because we do not know how to characterize the quantum vacuum for it. We know that dark energy, or at least the phenomenology it induces, exists. However, a complete description of the eigenstates does not exist as yet.

LC

Torbjörn Larsson July 5, 2011 at 6:50 PM

I am not particularly worried that any kind of “rip” will be the result, though it can’t be excluded as of yet.

One reason is because when you relax the requirement that w = -1 it naturally comes down on the shy side. (Though when all observations are included, WMAP 7 year sets it plunk on -1 and with symmetrical uncertainties.)

Another reason is because rips injects all sorts of problems such as problems with universal energy (can it then be defined), problems with singularities (the mentioned circumventing of cyclical cosmologies natural problem), problems with the nature of dark energy (if not vacuum energy, what then), problems with vacuum energy (if not dark energy, why is it then so low).

One of a number of seemingly implausible features of dark energy is that its density is assumed to be constant over time. So, even though the universe expands over time, dark energy does not become diluted, unlike the rest of the contents of the universe.

As the universe expands, it seems that more dark energy appears out of nowhere to sustain the constant dark energy density of the universe.

As usual lcrowell makes a hole-in-one on these things. I would add that if dark energy is not constant it would put implausible notions on the vacuum and its energy.

Vacuum energy should be there (zero point energy of fields), it should be constant and it should naturally be much higher. The coupling to cosmology explains all this. (Even if it doesn’t explain the finetuning of the vacuum energy right away.)

It is also exciting physics. By way of dark energy, quantum physics and cosmology meets as much as in the ripples of the microwave background.

I would add the zero energy result I described in another comment to that quantum – cosmology tie. The hamiltonian relies implicitly on general relativity, and the similar action principle of the lagrangian is what is used to derive the perfectly valid low energy quantum relativity theory that is the simplest way to get you gravitons. So there is a birds eye view that action principles makes ties between classical and quantum physics in cosmology, as long as standard cosmology holds sway.

Anonymous July 4, 2011 at 3:10 AM

It is similar to escape velocity. For the Earth with mass M a projectile moving out at v > sqrt{2GM/r} will escape Earth. The expansion of the universe is similar, and further with the de Sitter metric it keeps accelerating.

LC

Torbjörn Larsson July 5, 2011 at 7:17 PM

Is the reach of gravity infinite in time and space?

Classically long-range forces like EM and gravity has to be exactly infinite (r^-2 dependence). That is one of the few things that can be “proved” by math – if the theory is tested as valid already. =D Of course there is no guarantee that this is a fact of an actual universe, since there are constraints such as cosmological scales.

As I mentioned in another comment here, FLRW universes are zero energy objects so guaranteed existence for infinite time, and standard cosmology which belongs to that class looks to specify that explicitly.

It also looks like the natural state of inflationary universes are infinite volume, and again our standard cosmology which belongs to that class looks to specify that explicitly.

To top it off, another natural state of inflationary universes seems to be multiverses, which opens up the areas of backward eternal multiverses and infinitely fecund multiverses.

And there are many results in quantum physics which doesn’t seem to make sense unless you allow for infinite degrees of freedom of physics.*

It would be interesting to know if infinities are allowed by global properties and/or by local singularities as much as it seems to be built into quantum physics. I would bet “yes” on the former and by symmetry “yes” on the latter. That isn’t how I would have bet a few years ago…
———–
* Say, by the procedures for using hamiltonians, but also such results as Woit’s paper on time. I’m too lazy to dig up that ref right now, so ask if you are interested.

Jamie Kitchen July 4, 2011 at 2:47 PM

Hello Icrowell. I am trying to follow your mathematics and it has been a long time since college for me. One way out question I have is that is there any way that the Dark energy that is being created (And cancelled out by negative work) could potentially turn into the equivalent mass? I remember that energy and mass are equivalent from a universal content perspective and can be converted under the correct conditions.

Anonymous July 4, 2011 at 3:40 PM

The dark energy of the universe does bleed away. It quantum tunnels into the formation of nascent cosmologies. Eventually the de Sitter vacuum will decay into a Minkowski spacetime. Attempting to mine dark energy will prove to be tough. In a cubic meter of space there is about one proton equivalent of dark energy. This is about 10^{-11}joules, which would not be enough light the smallest spark. Trying to “grab” that energy would be tough, for it would require some “unobtainnium” field which couples to it strongly.

LC

Anonymous July 5, 2011 at 12:22 PM

I should say that the mass-energy associated with the de Sitter vacuum is a new zero. Other mass-energy is a perturbation on the de Sitter spacetime, and the conservation of this can’t be established by general relativity. However, it may be that this is a “frozen” quantum fluctuation on the de Sitter spacetime, which will attenuate away over a long time period. This gets into deeper issues, for the de Sitter vacuum or spacetime is actually a boundary for an anti-de Sitter space of one dimension higher, and this gets into string & M-theory of Dp-branes.

The observation that the universe is a net zero was first mentioned by E. P. Tyron back in 1973, who argued that the negative potential energy of stuff in the universe cancelled out the positive mass-energy of that stuff. I worked up a paper I published in GRG last decade where I extended this to the de Sitter vacuum.

LC

Torbjörn Larsson July 5, 2011 at 6:15 PM

Hold your galloping universe! =D I don’t think there is a generally agreed on test for this as of yet.

I come from this with another perspective than lcrowell, because the inner workings of general relativity is unfamiliar to me. However, a few years after standard cosmology was more or less accepted (with the WMAP 2004 results, I would say), I heard about this idea in a cosmological setting.

The reference is work by Faraoni et al on the energy of FRW universes as dynamical systems. It turns out Minkowski and inflationary de Sitter spaces are zero energy. So our universe is too. Note that this is a general result and on the resulting total energy.

Now this procedure uses an action principle on generalized coordinates so on generalized kinetic and potential energies. The condition is that Einstein’s equivalence principle holds, for example by general relativity. However they note some similar results: pseudotensor based results, the Wheeler-deWitt equation on the universe, thermodynamical results (universe as isolated system).

As long as standard cosmology is with us I would add suggestive things like flat space (locally zero energy density on average) and, absent “rips”, infinite time in at least the forward direction (classically only zero energy objects are guaranteed existence for infinite time). Maybe so suggestive they will constitute bona fide predictive tests one day.

Anonymous July 5, 2011 at 7:57 PM

So my galloping universe probably has zero energy.
It does seem to be real and it is galloping like mad. I don’t know how to hold it… Perhaps it would annihilate when it would stop – the only way to maintain the sum at zero

peter fraser July 7, 2011 at 12:40 AM

Thank you for your response.

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