The Komatsu et al. paper on parity-violating birefringence that would rotate CMB polarization suggests that the P-violating birefringence occurs in domains similar to magnetization domains for a temperature below the Curie point. This might mean the inflaton settles into different Mexican hat potential configurations or with different vevs.

Lawrence B. Crowell

So “very natural quintessence models” isn’t a contradiction in terms?

Lab Lemming,

You may be confusing terminology, why can’t a flat universe accelerate?
Imagine being a 3dimensional God looking at a 2d sheet of paper universe… there’s no reason that FLAT sheet of paper can’t just expand.

If you look at Friedmann’s equations here: http://upload.wikimedia.org/math/0/e/1/0e14ece5bb6fddb797a9d3c62fc6473d.png
You see the second derivative of the scaling factor; for an accelerating universe that term needs to be positive. For that to happen, lambda needs to be big enough to overcome the combined negative contribution of the gravity and pressure of matter and radiation.

A cosmology can be spatially flat, but the spacetime curved. The spacetime would be flat if the spatial surface and its evolute which foliate the spacetime are constant with no expansion. Some care must be given, for a spatial surface can be arbitrarily chosen. One can easily embed any spatial surface of choice, which is similar to a gauge condition in electromagnetism.

One of the strange consequences of an expanding univerise is that energy is not something which can be globally defined. The energy balance of the universe is a sort of survey based on local measurements. The gravitational mass-energy density of the universe is

$latex
rho_t~=~rho~+~P_z~+~P_y~+~P_z~-~Lambda/(4pi G),
$

for [itex]rho~+~P_z~+~P_y~+~P_z[/itex] due to luminous and dark matter. The dark matter component is some 85% of this portion. The comsological constant term [itex]Lambda[/itex] is modelled as the result of quantum vacuum energy in the universe with

$latex
Lambda~=~(8pi G/c^2)(rho_{vac}~+~3P_{vac})
$

This term appears to have the condition that [itex]P_{vac}~=~-rho_{vac}[/itex] which is the source of this “negative pressure” that causes the universe to accelerate outwards. The cosmological constant defines an event horizon at [itex]r~=~sqrt{3/ Lambda}[/itex], where the finite value of the distance ~ [itex]10^{10}[/itex] ly.

As a caveat, there is potentially a level of abuse here. Assigning the cosmological constant to a source, as I did above, for the cosmological constant is a factor of an Einstein space(time), where the Ricci curvature is proportional to the metric. This is usually thought of as a purely geometric property of the spacetime and not something due to a source of gravity.

It is tempting to think of the universe as having a net zero mass energy. How to get [itex]E~=~0[/itex] is problematic. The metric terms in the deSitter cosmology are [itex]g_{ii}~=~exp(sqrt{Lambda/3}t)[/itex], and it is not possible to find a [itex]K_t[/itex] so that there is a stationary condition [itex]{cal L}_{K_t}g~=~0[/itex], for [itex]{cal L}_{K_t}[/itex] a Lie derivative. This Lie derivative is defined according to brackets so that

$latex
{cal L}_{K_t}g~=~{cal L}_{K_t}g(X,~Y)~=~g([K_t,~X], Y)~+~g(X, [K_t,~Y]),
$

where the brackets [itex][K_t,~X][/itex] are, for [itex]K_t~=~Apartial/partial t[/itex], not zero because the vectors X are functions of time. So there is no involutary system which defines a conservation of energy on the entire spacetime.

Now, the cosmology will in time expand “infinitely,” and the cosmological horizon will also decay in a manner similar to the decay of black holes. Thus the horizon will receed to infinity and the evolution of the universe has as its attractor point a Minkowski spacetime that is an empty flat void with no mass-energy. So in that sense, as defined by the attractor point, the universe has zero net content, and the evolution of the universe from the vacuum, or some set of inequivalent vacua, to this final attractor point is a way that that “nothing” is reshuffled into another form of “nothing.” From a quantum gravitational perspective the Wheeler DeWitt equation [itex]HPsi([g])~=~0[/itex], means that time is not something which is also defined explicitely, but is only a bookkeeping method the analyst imposes to “organize” spatial surfaces, or the wave functional where spatial surfaces are configuration variables.

Lawrence B. Crowell

EDIT: (I submitted the previous comment prematurely by mistake) … Any chance someone can use an analogy to help explain or put in terms that is light on the math … with regard to the universe being flat? I try to imagine flatness in the way we see faraway galaxies appear as two-dimensional. Is that accurate?

CVF, general relativity says that spacetime is curved, and that curvature is what we perceive as gravity. In general the curvature of spacetime is an enormously complicated thing, as we have to keep track of (for example) how different parallel lines diverge or converge in all sorts of directions.

But in cosmology, where we start by assuming that matter is distributed uniformly through space (but expanding with time), things simplify a great deal. The curvature of spacetime comes uniquely from two contributions: the curvature of space all by itself, and the fact that space is expanding as a function of time. A certain density of matter spread uniformly through the universe implies a certain total amount of spacetime curvature, but that can be distributed in various ways between spatial curvature and the expansion rate. So you can have a “flat universe,” which means zero spatial curvature, even though spacetime overall is curved because of the expansion.

More at Ned Wright’s cosmology tutorial.

Sean,

What do you think are the prospects for very informative, qualitatively new results to come from the Planck telescope? Will there simply be more precision of existing data, or do you think they’ll be able to elucidate previous foggy regimes of the parameter space?

CVF: Trying using a balloon. When no air is blown into the balloon, it’s flat(2-d). Yet when the first breathe is pushed into the balloon, it expands(3-d). So, using this as an illustration, now picture the universe being the balloon. There is your common english, with light of math, explaination to the expansion of the universe.

What you actually get is a limit on the sum of the neutrino masses; you can’t tell which individual ones are massive etc. From here, the limit on the sum of the masses is 1.4 eV at 95% confidence.

Brian, it’s just the standard error of the mean:

http://en.wikipedia.org/wiki/Standard_error_(statistics)

The more data points you have, the broader the distribution looks to your eye, but the better-determined the mean of the distribution actually is.

I guess I missed this one:

Adam on Mar 5th, 2008 at 10:45 pm
@ Mr. Crowell:

Have you considered that the stochastic nature of the parametrically-driven electron birefrigence would circumvent the dynamic Curie threshold and instead oscillate unstably until (pi/d^2) – 1 converges on infinity, thus causing the universe to implode?

————-

I am trying to figure out what you are meaning here. The result seems to point to some analogy with the T

Did you read about the latest measurements of spatial curvature? It is now firmly established that the radius of our Universe is greater than the size of our observable universe a fact which will make it even harder for advocates of non-trivial topology to hang out onto their “small universe” hypothesis….

Secret American Planck Basher,

Well, the free parameter in question is a pretty important one, in my view: the energy scale of inflation. Pinning down the energy scale of inflation is a pretty big step in making any significant statements about what inflation actually is. There are also measurements of the CMB out to smaller scales, which will provide further, much more significant constraints on various other inflationary parameters. It’s also a big help to make use of the same instrument for both the large angular scales and the small angular scales, as there are always uncertainties that crop up when combining different experiments. Then there’s the fact that additional sky coverage improves measurements at all angular scales, and so Planck will be able to do better out to somewhere around 10-20 arcminutes or so than any ground-based instrument can possibly do.

Energy scale of inflation. Is it really “important”? Yes, in the context of inflation models, but I don’t see it as having much of an impact beyond the “conclusions” section of Yet Another Inflation Paper. It will kill 60% (? — high side) of models on a good day, but it won’t open up vistas. Once upon a time there was the consistency relation, a lot harder to check, but today even that’s old hat.

Measurements to smaller scales. Once past 10 arcminutes or so, you’re in the damping tail and will learn nothing more of the early universe. Getting l of 700 won’t really help much with l of 3000 except you might know the input cosmological parameters a bit better.

As for the other benefits you mention. Yes, of course there will be a lot of data. I just don’t see it as really changing things, pushing the field, in new directions. And I say that as a guy with Kolb and Tuner on his desk and a couple of early universe ideas out in the literature and in my head. I wish there was a measurement from Planck that I’d be truly excited about, but right now it’s a grab bag of things that other places will cover as well.

Spaceman,

According to Inflation theory, it is many, many times the size of the visible universe. To the point that, from our perspective, it is just about spatially infinite. Curvature seems mostly a function of the time dimension, in that the analysis of redshift and CMBR says it is only13.73 billion years old.

http://en.wikipedia.org/wiki/Cosmic_inflation

“Cosmic inflation has the important effect of smoothing out inhomogeneities, anisotropies and the curvature of space.”

Basically it explains how the factors which suggest an infinite universe can exist in a finite model.

Lawrence,

Doesn’t the Uncertainty Principle essentially show that some information is destroyed in the very process of measuring other information?

Since I view time as a consequence of motion, rather than the dimensional basis for it, I think monumental amounts of information are destroyed and replaced every moment. I would posit the current credit meltdown, as well as the rest of history, as proof.

Lawrence,

If time is a measurement, than what physically exists is perfectly conserved, as it passes from one macro-state to the next. It is only these macro states that are created and consumed.