Friday, July 27, 2012

You Don't Have to Blow Up the Universe to Be Cool


This was supposed to be a story about dark energy. It still is -- dark energy is one of the most intriguing mysteries in cosmology, after all -- but it's mostly a story about cosmic doom, why I love theoretical physics, and why you shouldn't believe everything you read on io9.

What goes up...

It's difficult to express to a non-physicist just how weird dark energy is, because most people are used to encountering things that they don't understand in physics, and they generally assume that someone else is on top of the situation. That's not the case with dark energy. Here's an analogy. Let's say you're throwing a ball in the air. There are logically two possibilities: (1) You throw it, it goes up for a while, slows down, and falls back to Earth. (2) If you happen to have superhuman strength, you throw it hard enough that it escapes Earth's atmosphere and then sort of coasts forever through the void. But imagine neither of those things happen. Imagine instead that you toss the ball up in the normal way, and it looks like it's starting to slow down, but just as you think it's about to reach its maximum height and come back, it suddenly speeds up and shoots off into space.

That's not supposed to happen.
[Source: Norwalk Citizen Online, Christian Abraham / Connecticut Post. ]
Dark energy is like that. It's actually the exact same physics. The big bang is like the throw, starting off the expansion of the Universe. That expansion means distant galaxies are all moving away from us, but since all those galaxies have mass and gravity is still always attractive, ultimately everything in the Universe should be pulling on everything else. This should slow the expansion down, through the same kind of attraction that pulls the ball toward the Earth, slowing it down and keeping it from floating away. But a couple decades ago astronomers discovered that the expansion isn't slowing down at all. There's something out there in the cosmos that's acting against the gravity of all those galaxies. It's not just keeping the Universe from recollapsing, it's actually pushing all the galaxies apart faster and faster, accelerating the expansion. And just as physicists would be at a loss to explain why your baseball suddenly went (non-)ballistic, everything we understand about physics tells us this should not be happening to the Universe. We call it dark energy because we have no idea what it is.

The cosmological constant

We have some theories, of course. In fact, there are probably hundreds of theories, many of them difficult to distinguish from one another with the data we currently have. The most familiar and longest-standing idea is that of the cosmological constant -- a sort of fudge factor that Einstein originally put into his equations of gravity. He wasn't trying to explain acceleration -- at the time, he thought the Universe was static, and he needed an anti-gravity term to balance out the pull of all the mass in the Universe. He discarded the extra term in embarrassment when the expansion of the Universe was discovered, but this new acceleration is making many cosmologists now think we need to put it back in.
The equation governing the acceleration of the expansion of the Universe, with a cosmological constant term. The gravity term includes the density (p) and pressure (ρ) of all matter and energy -- the minus sign means this term slows the expansion. The cosmological constant term (with Λ) has a positive sign, and therefore contributes to acceleration. The parameter a is the scale factor measuring the size of the Universe, and the double dots indicate the second derivative (acceleration) with respect to time. 
A definining property of the cosmological constant is, unsurprisingly, that it is constant. In fact -- and this is almost weirder than the acceleration -- the density of the "stuff" described by the cosmological constant stays the same even as the Universe expands. If you have a box filled with cosmological constant, and you suddenly make the box twice as large without opening it or putting anything in, you now have twice as much cosmological constant in your box. As I said: it's weird.

The cosmological non-constant?

Unfortunately, the cosmological constant isn't really that appealing a solution, since it still looks a lot like a fudge factor and it seems somewhat arbitrary. The main alternative is dynamical dark energy, which is any kind of dark energy that can change with time. Most theories of dynamical dark energy (often just called "dark energy" as opposed to a cosmological constant, which is sort of a special case) involve scalar fields. Until recently, we had no evidence whatsoever for scalar fields in nature, even though they were constantly popping up in theories. Now that we think we might have discovered the Higgs boson (yay!), we have evidence for the first scalar field: the Higgs field. The Higgs field itself doesn't have anything to do with dark energy, but it's comforting that at least one example of a scalar field might actually exist. The nice thing about a scalar field is that it can have the same value everywhere in space while varying with time, which is just what you need if you want some kind of time-dependent dark energy that fills the Universe.

So how do we distinguish between a cosmological constant and dynamical dark energy? The usual way is to look at the relationship between the dark energy's pressure (denoted p) and density (denoted, somewhat confusingly, by the Greek letter rho: ρ). One of the key features of any form of dark energy is the fact that it has negative pressure.

In general relativity, pressure is a form of energy, and energy has a gravitational effect -- your pressure adds to your gravitational field. (So, gravitationally, pressure pulls.) Negative pressure, therefore, subtracts from a gravitational field, and counteracts gravity -- it pushes. For a cosmological constant, the pressure is exactly -1 times the density: p=-ρ. (I'm using units where the speed of light is 1. You could also write this as p=-ρc2.) For other forms of dark energy, there could be a different relationship.

We use a parameter called the equation of state, w=p/ρto describe the ratio of pressure to density. All substances have one: pressureless matter has w=0; radiation has w=1/3. For a cosmological constant, w=-1.

As far as we can tell from astronomical measurements, w is pretty darn close to -1. Every measurement we've done is consistent with w=-1, and every time we improve on our measurements, we find a value of w even closer to -1. But it would be hard to say for sure that w is exactly -1, because all measurements have uncertainties associated with them. We may at some point measure a value of w that is infinitesimally close to -1, but, without some other reason to believe that we have a cosmological constant, we'll never be able to say that it's not just very slightly higher or lower.

The importance of asking "What if...?"

Until about 10 years ago, no one really talked about the idea that w could be less than -1. Anything with w<-1 was called phantom energy and was considered way too uncouth to be plausible. There are good theoretical reasons for this: constructing a theory with w<-1 is difficult, and if you manage to do it, you've probably had to do something tricky like introduce a negative kinetic energy, which is the sort of thing that would make a ball roll up a hill instead of down. You might even accidentally invent a theory with time travel and wormholes. So it was generally thought that we should leave w<-1 alone, and people made constraint plots like this:
Fraction of the Universe made of matter (Ωm) plotted against the dark energy equation of state parameter (w). Values in the orange region have a good fit to the data. [Source: Caldwell, Kamionkowski & Weinberg 2003 (PRL, 91, 071301)]
This is a plot of the fraction of the Universe made of matter (Ωm) versus w. The colored swaths are where the parameters are allowed by different kinds of observations. The orange is the most favored region. You can see from the plot that everything converges around w=-1: a cosmological constant.

But a group of theorists at Dartmouth and Caltech (Rob Caldwell, Mark Kamionkowski and Nevin Weinberg) looked at that and thought, "Maybe it's not converging at w=-1 -- maybe it just looks that way because it's really converging at some value of w less than -1. What would happen if that were the case?"
Same as above figure, but with the range extended to allow w<-1.
[Source: Caldwell, Kamionkowski & Weinberg 2003 (PRL, 91, 071301)]
And then they wrote my favorite paper ever [Caldwell, Kamionkowski & Weinberg 2003 (PRL, 91, 071301)].

Theory is awesome

It really is an amazing paper. Honestly, you should check it out. I wouldn't ordinarily recommend a theoretical physics paper to a general audience, but this paper is so well written, so accessible, and so beautiful that I can't resist. And it's only 4 pages long.

The authors start from a very simple idea: "What if some day we look at the data and we find out that w<-1?" It doesn't sound like a revolutionary idea, but no one had ever followed that idea to its logical conclusion. So they do it, and after jotting down just a few fairly simple equations, they discover that the universe would rip itself apart.

How often do you get to invent an ultimate cosmic doomsday in the course of your professional life? This is the kind of work I got into theoretical physics to do. It's awesome.

Here's how it works. I said before that w=-1 is a cosmological constant -- the energy density doesn't increase or decrease as the Universe expands. It turns out that if w>-1, that means that the energy density goes down as the Universe expands (like ordinary matter). Expand a box of matter and you have the same amount of matter, but more space, so your matter is now less dense. But if w<-1, the energy density increases as the Universe expands. Think about that for a minute. If you have a box of phantom energy, and you suddenly make the box twice as big, you now have more than twice as much phantom energy in your box.

Aside from being unsettling, this kind of behavior can actually have some pretty gruesome consequences for the Universe. If we stick with our familiar cosmological constant, then as the Universe expands, even though all the galaxies are moving away from each other, anything that's gravitationally bound stays bound, because there's just not enough dark energy in any bound system (like a solar system or a galaxy) to mess with it. But with phantom energy, the amount of dark energy in any bit of space is increasing all the time, so a planet orbiting a star will actually eventually be pushed away to drift on its own. Everything will become isolated.

And that's not even the worst of it. Caldwell and his colleagues realized that if the density of dark energy is increasing with time, it will eventually be accelerating the expansion of space so quickly that the cosmic scale factor -- the parameter that measures the characteristic size of a region of space -- will reach infinity in a finite time. If the scale factor is infinite, that means that the space in between any two points is infinite, no matter how close they were to begin with. It means that spacetime itself is literally torn apart. When Caldwell and his colleagues realized they'd discovered a new possible end state of the Universe, they dubbed it, appropriately, the big rip.

video
Animation of the big rip (link to original). From Caldwell, Kamionkowski & Weinberg's paper: It will be necessary to modify the adopted slogan among cosmic futurologists — ‘‘Some say the world will end in fire, Some say in ice’’ — for a new fate may await our world.  [Source: NASA/STScI/G.Bacon]


DOOOOM!

Having just invented a new cosmic doomsday, the authors decided to go a step further. They worked out exactly when the big rip would occur for any given value of w, and then, for a specific example (w=-1.5, which would have a big rip about 21 billion years from now), they worked out exactly how long we'd have to wait before all of the cosmic structures we know and love be destroyed. Galaxy clusters would be erased 1 billion years before the end. The Milky Way would be dismantled with 60 million years to go. At doom-3 months, the Earth would drift away from the Sun. With 30 minutes to go, our planet would explode, and atoms would be ripped apart in the last 10-19 seconds. Discussing this handy timetable of doom, the authors state with admirable detachment that, were humans to survive long enough to observe the big rip, we might even get to watch the other galaxies get torn apart as we await the end of days. I'm sure that would be lovely.

io9, you have forsaken me

Given my affection for the original phantom energy paper, you can imagine I was intrigued the other day to see an article on the io9 website proclaiming "The Universe Could Tear Itself Apart Sooner Than Anyone Believed." Could it be some new evidence for phantom energy, I thought? Sadly, no. It turned out to be an utterly overblown scare-piece that had hidden all the beauty of the physics behind false assertions and dramatic flaming-Earth graphics.

The io9 post discusses the work of Li and colleagues, researchers in China who have published an article called "Dark Energy and the Fate of the Universe." The paper isn't bad, or even really wrong (though I don't agree with all of it). But it's really nothing new or interesting. It starts from the assumption that dark energy is dynamic and that it is evolving to have w<-1 in the future. It then uses a new parameterization of the evolution of w to draw conclusions about the fate of the Universe.

I won't go into a lot of details, but the gist is as follows. If you want to determine if w is changing with time, you have to start with some model for how it's changing -- basically, you have to assume a functional form. You look at data from the past, determine what w was then, and choose some function for w that changes with time and try to measure its parameters. In cosmology, we usually discuss time in terms of redshift (denoted by z), which is a measure of how much the Universe has expanded since whatever bit of the past we're observing. The redshift z decreases with time and is zero today; future times have negative redshifts.

A typical parameterization of dark energy looks like this: w(z) = w0 + wa (z/(1+z)). The form doesn't matter so much except in that w0 is the value of w today, a positive value of wa means w is decreasing with time, and a negative wa means it's increasing. This parameterization has the property that it goes to infinity in the future at z=-1. Li and colleagues don't like this, but it's hard for me to see why it matters. A redshift of -1 corresponds to an infinite scale factor, which is a big rip. If the only problem with the formula occurs when the big rip is actually in progress, it's hard to see why that should be a big deal for determining anything that happens up to that point.

In any case, they have an alternative, slightly more complicated parameterization, for which w doesn't go to infinity at z=-1: w(z) = w0 + wa [ln(2+z)/(1+z) - ln(2)]. In their formulation, a positive wa means w is increasing, and a negative wa means w is decreasing. They run some simulations and find out that the best-fit points for w0 and wa -- the values the data seem to be pointing to -- imply a big rip will occur.
Constraints on wa and w0 for the model by Li and colleagues. The red point indicates their best fit. The green point is a cosmological constant. The brown region is the best-fit region and the blue region is the 95.4% confidence region. [Source: Li X D et al. 2012 (Sci China-Phys Mech Astron 55,1330)] 
Shouldn't I be scared?

The fact that the best-fit point implies a big rip sounds important, but it isn't really. Many of the latest results have a best-fit value for w that's less than -1; the data just aren't yet good enough for us to draw any conclusions. A cosmological constant easily fits the data, and there's no compelling evidence that dark energy is anything more exotic. Also, as Li and colleagues readily admit, all their conclusions are based on the assumption that dark energy follows their own special functional form -- if it doesn't (and there's no reason to think it would), there's nothing they can say about what would happen.

Nonetheless, Li and colleagues go on to calculate when the big rip would occur with both their best-fit value and their worst-case value (the value still allowed by the data in which the big rip happens soonest) and they say that doomsday could be as soon as 16.7 billion years from now. They even include their own timetable of doom, with earlier times than the original one.

It's a reasonable calculation to make, but I wouldn't call it newsworthy. The comparison they make to say it's "earlier than we thought" is with Caldwell's doomsday value, which used an arbitrarily chosen w=-1.5 for illustrative purposes, not from a fit to any data. The io9 people apparently got hooked by an unreasonably enthusiastic press release and ran with it, trying to stir up the paper's conclusions to make it as significant and alarming as possible.

Disappointingly, the io9 article also contains several blatantly wrong statements, such as "cosmologists are pretty sure dark energy has a value less than -1" (not true!) and "a likely value of -1.5" (completely ruled out!) and "the cosmologists are fairly convinced that w will continue to exhibit a value less than -1 well into the future" (also totally wrong!). Phantom energy is truly an awesome idea, but I don't think many cosmologists would say it's especially likely, and certainly none of us would bet the house. The theoretical problems are substantial and the data just aren't good enough yet for us to say anything either way. The big rip scenario is still fun to think about; it's not necessary to think it's actually imminent to appreciate that. Probably dark energy is a cosmological constant -- and plenty weird enough.

Did I mention theory is awesome?

As a theorist, I encounter a lot of really bizarre ideas. Sometimes I encounter an idea like phantom energy, which is incredibly cool and leads to some truly revolutionary possibilities ... but is probably ultimately wrong. Other times, I get to study something like dark energy, which is mind-bending in a totally different way: not because it breaks physics and makes the Universe blow up, but because it is, contrary to all our understanding, actually out there, just waiting for us to figure it out.

16 comments:

  1. This is a very good post, Katie; thanks for writing and sharing this with the world!

    I met Caldwell in 2001 when I was choosing a grad school, and Dartmouth actually wound up as #2 on my list after that visit. I am personally much more pessimistic about a time- (or z-, or a-) varying equation of state than you are, but ultimately the data will decide, and it's important to keep entertaining all the possibilities as *possible*, but not as equal.

    And FWIW, I'm glad that you, too, recognize that io9 is a site to be very wary of when it comes to any actual science.

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    1. Thanks, Ethan!

      Caldwell is a very cool guy. I saw him at a conference a year or so ago and I couldn't resist telling him that he wrote my favorite paper ever. It was kind of amusingly awkward. :-)

      I think I actually agree with you about time-dependent equations of state. Personally, I think it's probably going to end up being a cosmological constant. But I also think that possibility is the most boring and maybe also the least elegant, so it's fun to think about alternatives.

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  2. Awesome post, Katie!

    Tho you breached a pet peeve of mine : ) What does it mean for a scalar field to exist? Would it not be more accurate to say that something exists that we model with a scalar field?

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    1. Thanks!

      I guess it's hard for me to see much difference between saying "a scalar field exists" and saying "something exists that we model as a scalar field." A scalar field is defined as something that has a magnitude (but not a direction or polarization) at every point. It also has to be invariant under Lorentz transformations, which means that it has the same value for all observers. The usual example people use to illustrate the concept a scalar field is the temperature in a room -- it has a magnitude, but not a direction, at every point. But you could say that it's not *really* a scalar field in the purest sense because it's not fundamental (it's a description of some other underlying physics). (I'm not sure whether it would be considered Lorentz-invariant -- I think it depends on how you define it, but certainly if you measure the temperature at a point by using, e.g., the frequency of its thermal radiation, you'll get a different measurement if you're moving with respect to it.)

      Anyway, the point is, if there's "something" in the Universe that is a fundamental physical object and has all the properties (transformations, couplings, etc) of a scalar field, it's hard to see why you would have to say it's not *really* a scalar field, but just acts like one.

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    2. Maybe you have some other nomenclature, but my understanding is that scalar fields are mathematical entities. They model some physical phenomena quite well. It's particularly important, in my opinion, to keep this clear when dealing with the most abstract physics so as to not to confuse the public or yourself : )

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  3. Hi Katie,

    This is a spectacular post and concept that you describe, and I found it by reading a comment from Ethan on his blog. What interests me the most is Dark Matter and Dark Energy, and I'm commenting on your post because I have an idea that is similar to this Doom-scenario that you present, only a bit more down to earth.

    The 'Big-Rip' that you present here, comes down to the idea of what happens when the pressure-equation of the thing that makes up empty space (DM & DE) changes, 'the cosmological non-constant(?)' and w=p/ρ that describes the ratio of pressure to density.

    In this Doom-scenario it is a matter of time, if I'm correct, whereby the universe would rip itself apart at w=-1.5 in about 21 billion years from now.

    For the scenario that I have in mind, I like to ask the question what would happen if we would build a machine that could change this w-parameter on a local scale? Would atoms within that local area start to 'Rip-up' and release their bonding energy, would there be a 'turn-over' state for this to happen?

    It's clear that DM & DE seems to influence Luminous Matter and visa versa, so for such a device I'm thinking of a high-energy particle collider that generates lot's of energy (heat/pressure) for a long period of time into 1 focus point, and thus continuously influencing the state of the w-parameter, of the DM & DE (Dark Liquid), within that collision area.

    The DOOOOM that might happen would come from the fact that the atoms that find themselves within that area collision area, would find themselves continuously in a situation with a highly varying w-parameter, and they could start to rip-up, losing their composition, and combust! This group combustion at a sub-atomic level, would cause for the expansion of the area/field with a differing w-parameter, and this would set of a chain-reaction. Similar to how a forest-fire can take off from; a magnifying glass that bundles a normal amount of light into one focus spot (collider), that 'lights' up one tree, and that for its part generates enough heat to get the next one going, and so forth … So I'm not thinking here of a 'Big Rip' of the Universe, but a relative 'Small-Rip' that could turn our planet and Solar system into a Supernova where everything in this area is boldly ripped apart.

    I know it is a very unlike scenario cause we can observe Cosmic Rays with very high energies, but I would like to point out that the LHC combines these single collisions into 1 spot, like a magnifying glass, with a rate that is a billion (10^9) times higher than in nature. So if the local w-parameter would be influenceable by particle collisions, than the statistics of the field, that also contains atoms that surrounds the collision-area, would be far beyond a 'flexible' normal w-parameter. All matter within that area would be in a continuous state of extreme pressure and tension, and for a much longer period than what is normal or even the most extreme setting in our solar system. There's only one except and that's a supernova, no?

    Looking forward to hear your opinion,

    Yours truly,

    Victor Von Doom

    aka Dr. Doom
    --
    http://youtu.be/NcsQ4Z9tSV0

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  4. Hi Victor/Chelle/Dr. Doom,

    Thanks for your comment! There has of course been a lot of doomsday talk surrounding the LHC, but there's really no way a high-energy particle collision (or even many at once) could destroy the Universe. As for the scenario you describe: The local equation of state depends on the relationship between pressure and density in that region. Matter and radiation have equations of state either 0 or positive, and adding more matter and radiation and pressure can't make the equation fo state negative, and certainly can't push it to less than -1. To push w below -1, you'd have to somehow reduce the density of matter and radiation to virtually nothing, and then you'd have to somehow add in a lot of phantom energy (dark energy with w<-1). We have no way to do that -- we don't even know what dark energy is, and from what we know about dark energy now, it seems to be entirely homogeneous and smooth. If you could make a perfect vacuum, and if dark energy already intrinsically had an equation of state w<-1, then that region would expand, but only if it stayed a vacuum, and you know what they say about nature and vacua. And it wouldn't expand very fast, either. The current expansion rate of the universe (for w really close to -1 as far as we can tell) is about 70 km/s/Mpc, which means that two galaxies a megaparsec (about 3 million light years) away from each other are only moving apart at 70 km/s, and more closely spaced points are moving apart more slowly. So even if you *could* build a machine that could reduce the value of w locally (by making an insanely huge vacuum and also having a really low value of w in the universe generally), it wouldn't have a very dramatic effect. Particle collisions certainly can't reduce w -- if anything, they locally increase it -- and they really can't do anything particularly exciting outside the particle detectors in which they occur. High energy particle collisions do, as you say, occur all the time from cosmic rays etc, and in cosmic explosions such as supernovae and gamma-ray bursts, and they were even more common in the early universe, and none of those things has ever caused a small-rip type event as far as we're aware.

    I hope this answers your question!

    -Katie

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    1. Hi Katie,

      Yes, this answers my question, thanks. I'm now starting to see why a 'Small Rip' theory is doomed to fail, I've been mixing up some things.

      Ethan said this about Dark Energy:

      ”I think of it as a fluid that permeates throughout all of space with a positive energy density and a negative, outward-pushing pressure.”

      So I wrongly guessed that by putting heaps of energy into a collision box, parts of the scattered Luminous mass & energy would be transferred onto the Dark Liquid, and this energy input would be translated into a higher negative outward-pushing pressure, and also a higher above normal excitation level. Here I mistakingly made the link that a transfer of energy into the phantom-world, would be the same as making 'w' go below -1

      And there's also, like you point out, the expansion rate of the Universe that messes up my scenario. Back to the drawing board. Dr. Doom will have to come up with something new that makes the Universe static again, just like Einstein's first impression ...

      best,

      m.

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  5. Nice demasking of the phantom at the opera!

    As for the fate of the universe, these scenarios seem to come and go (collapsing universes, cycling universes, unstable protons). It looks likely, I take it, that the standard cosmology will win out as regards the geometry of spacetime. Even so, I read that the standard 126 GeV higgs, if it is indeed a standard higgs and no other physics pops up, is currently estimated to have a quasistable vacuum at the known parameter values (needs better LHC data) at ~ 3 sigma. So it would be replacing the Big Rip with the Big Pop in ~ 10^100 years as the universe transition to a new vacuum.

    Speaking of pops, if multiverse vacuum bubbles transits the neighborhood we won't even see the doomsday coming. But if the likelihood is constant (at a naive guess), as it hasn't happened in 13 Ga it seems rather remote too.

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  6. It occurs to me I forgot two reactions:

    - I like how the article is explicit on Einstein's "anti-gravity" (curvature) term. I think that is less intuitive today than the modern opposite sign energy cosmological constant.

    - I don't see how dark energy can be any weirder than redshift decreasing energy of photons, that shows how energy conditions doesn't really apply to non-local (large) spacetime volumes. You still see objections to redshift, but not as many as they used to be.

    The weird process is that spacetime can expand out of spacetime in the first place. General relativity, what a funny idea. (O.o)

    I imagine that since space dilutes to flat, nearly empty space eventually, the small or non-existent difference to zero energy density means one can see dark energy as the needed deficit without worry too much about its dynamical effects.

    Or perhaps abstract it to the analogous situation of potential energy balancing kinetic (say) energy. (Which seems weird too when you first study it, not the concept but its non-tangible characteristic.)

    Am I saying that general relativity is weirder than the standard model? Must be the tensorial stress on the brain.

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  7. Standard cosmology. What a place to confuse those two!

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  8. Hi Torbjörn,

    You mention a lot of different things, but I can try to respond to a few of them at least.

    As for the Higgs metastability issue, there's some information on that here: http://blog.vixra.org/2011/12/04/what-would-a-higgs-at-125-gev-tell-us/ but personally I haven't been following the discussion much. As that article states, there may be a high energy at which the vacuum is unstable, but "such energies are found in the more extreme parts of the universe and nothing bad has happened."

    To me, dark energy is a LOT weirder than redshift decreasing the energy of photons, if only because doppler shifts are quite familiar in other contexts. I think the idea of the expansion of space stretching out photons to make them longer wavelength is reasonably intuitive. There's a bit on the energy conservation issues here: http://scienceblogs.com/startswithabang/2011/12/02/dark-energy-accelerated-expans/ that might answer your question about that.

    Hopefully this is helpful, and thanks for the comments!

    -Katie

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  9. Greetings, is this your one and only blog or you also own some more?

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  10. Antigravity is the source of dark energy
    ========.
    The force generated from positive gravitational potential energy by antigravity can be indicated like
    F= +(1/3)ΛMc^2r
    shaped,
    ========
    http://www.sciforums.com/showthread.php?133579-Antigravity-is-the-source-of-dark-energy-(accelerating-expansion)

    or
    http://vixra.org/abs/1110.0019 chapter IV

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  11. AstroKatie,

    I read your post recently and from what I understand about dark energy from your post is that the cosmological constant is -1, which causes the density of dark energy to remain constant regardless of expansion. If this is the case, dark energy must therefore not be in a self contained system. That would mean that the universe is not a self contained system, which could mean that dark energies a consequence of the larger process than the universe or the "Big Bang." The larger system might be exchanging dark energy for the time dimension, which means our universe is expanding so that time can continue to propagate and the universe can age. The other part of this system could be an inert universe with nothing in it but dark energy, and is colliding into our universe causing our universe to expand, and it the same time causing that inert universe colliding into us, to contract as it loses dark energy and gains the imprint of our past universe frozen in an inert time state.

    I am thinking of getting into astrophysics to do theoretical research to follow through with this hypothesis.

    Thanks,

    John Theibert

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  12. Hi John,

    If you're interested in how energy conservation works in the context of dark energy, check out these blog posts for some more info: http://scienceblogs.com/startswithabang/2011/12/02/dark-energy-accelerated-expans/ & http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

    I hope you do end up studying astrophysics, but don't do it just to follow up on an idea you have before you got the necessary background! Whenever you start to pursue a new course of study, you'll find that nearly all your previous ideas were either wrong or incomplete -- and that will be terrific, because you'll be in the right place to replace those misconceptions with solid, mathematically rigorous results. Good luck!

    Best,
    Katie

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