... ?

Take a few breaths and ease up a bit, fella; not everyone on /. is being serious or trying to troll.

Where do *you* live? That's a genuine question, because here in the UK, South America is that big southern lump featuring the likes of Argentina and Brazil, Central America is the thin wiggly bit featuring the world-famous Panama Canal which is based in Panama, and North America is the big lump on top which Mexico, the USA and Canada call home.

Actually, sorry, you're wrong about that. The geography skills of the guy who wrote the summary are deeply questionable (Mexico seemed to pull off the trick of joining South America remarkably quietly), but "maths" is the abbreviation of "mathematics" used in the UK. It's not a plural of "math" -- and, after all, we don't call it "mathematic". So I think we've pinned down where "thephydes" is from - he or she is either British, or learned British English.

So I think the main thing we can learn from the summary is that despite the characterisation of Americans has having no knowledge of geography outside their own country, the rest of the English-speaking world is just as bad and should probably stop feeling so damned smug and look at the fucking great log in their own eyes.

I've had to remote Firefox too, chiefly to access papers that are behind paywalls my university has access to but I have no access to at a university I'm visiting, or at home. You're making Firefox over X sound a lot better than it actually is.

Well, I wasn't a particular fan of that comment either... :) But your comments about the conservation of energy are basically wrong -- like I say, the expansion of the universe is governed basically by two equations:

1) The Friedman equation, which is the "Hamiltonian constraint" and which can be interpreted as an energy constraint equation
2) The matter continuity equations, which arise directly from conservation of equation of matter

(Technically, and apologies for the ugly LaTeX notation here, matter is described in relativity by "stress-energy" or "energy-momentum" tensors, which bundle together the classical concepts of energy, momentum flux, energy flow, and momentum flux density. The gradient of the more familiar Momentum flux density produces momentum conservation, while the time derivative and gradient of the energy give, well, energy conservation otherwise known as matter continuity. In terms of the stress-energy tensors, if energy is conserved then the covariant gradient of these is conserved -- written T^{\mu \nu}_{; \nu} = 0 where the \mu and \nu describe the four spacetime coordinates, and the repeated \nu means we sum across them. In Euclidean spacetime this immediately reduces to normal energy and momentum conservation. That semi-colon means "covariant derivative", meaning it has contributions coming from interactions with the spacetime geometry; if instead you insist on writing the conservation equation as a partial derivative (as in familiar classical mechanics and fluid dynamics) then you get T^{\mu \nu}_{, \nu} = [gravitational terms]^\mu and if you were unaware of the form of a covariant derivative this would look like a violation of energy and momentum conservation rather than what it is -- an interaction of the stress-energy of matter with the geometry of spacetime.

(The energy density, with respect to some chosen time coordinate which can be described as the vector n^\mu normal to a purely spatial three-dimensional surface, is found by the contraction \rho = n^\mu n^\nu T_{\mu \nu} which basically just means the scalar product of the stress-energy tensor with the time coordinate, or phrased differently, the stress-energy tensor projected along the time coordinate. This energy is conserved. Similarly, if we take the full Einstein equations they can be written as G^\mu_\nu = 8\pi G T^\mu_\nu where the G^\mu_\nu is the "Einstein tensor" that basically characterises the local gravitational field, and the G is newton's constant which infuriatingly has the same god damned symbol. If we project these equations along the time coordinate then we get out an energy on the right-hand side, and something that therefore can be interpreted as embodying the "gravitational energy" on the left-hand side. The result of this is the Hamiltonian constraint, and in the specific case of a cosmological spacetime the result is the Friedmann equation. Both these equations therefore express energy conservation -- one for the gravitational field, and the other for the matter.)

Said a bit less technically, the second equation is simply what you expect -- for normal matter we except the density changes with scale factor as rho = rho_0 / a^3. That is, the density decays as the volume of the universe increases. For photons we would expect instead rho=rho_0 / a^4, where we've got the normal volume dilution (1/a^3) and, since a photon's energy is proportional to length and the expansion of the universe will stretch that length, we should have an extra decay in the energy of 1/a. So rho = rho_0 / a^4. To a good approximation the same can be said for neutrinos (although to be exact we should make these massive, albeit extremely light.) Put these together and you have rho = rho_matter / a^3 + rho_photons / a^4. This is nothing but what happens when space expands.

That's well and good but it doesn't answer your issue with energy conservation, because it seems to violate it. That's where the other equation comes in, because these equations are only *half* the story. In GR (and other related, geometric theories of gravity) gravity also has an associated energy. It's hard to describe where the Friedmann equation comes from in this picture without the full theory, but it's obvious that if the energy density of photons is being diluted there must be some impact on the geometry that underpins what we call "gravity". In cosmology there is basically one quantity that determines that geometry -- the same scale factor, a. So the energy equation should determine how a evolves in time. Given that we can characterise it with the Hubble rate, which is the change in a with time, divided by a. This doesn't have the units of energy which (since we've set the speed of sound equal to 1, meaning we measure seconds and centimetres with the same stick) has units of 1/time^2. So let's square the Hubble rate to get something in the right units to be an energy. That gives us a crude estimate of the gravitational "energy conservation" as H^2 = ?. First guess for the right hand side has to be to slap in something proportional to the matter energy. This then gives us H^2 = \kappa \rho. This isn't a particularly convincing way to justify the Friedmann equation (which is what that is), but it's better than the usual approach which is to assume an expanding sphere of pure dust and which misses the point of gravitational energy completely.

The point of all of that, both technical and ineptly non-technical, is that while if you just look at the matter sector alone and forget that you have to take the geometry into account, you conclude that energy is not being conserved. However, remembering that in the theory cosmology is based on we have to include interactions with gravity (which can also be described as the "energy" of the gravtiational field though I'd advise caution in taking such interpretations too strongly) everything suddenly falls into place -- the apparent loss of energy from matter is balanced by the gravitational field.

Jesus. Sorry for the length of that one, you didn't deserve that. Oh well, hopefully it interested you -- ultimately I'd agree with the statement "physics has problems too" because if it didn't there'd be one hell of a lot of unemployed physicists mooching about looking unhappy.

It's just how gravity works - if you fill a universe with not quite enough matter to make it collapse it will expand. Meaning if the universe was a bit denser it would collapse, but since it's not it's expanding. Then, as Neil Boekend says, due to something we're currently calling "dark energy" for want of a better term, with the amount of matter we've got we would expect the universe to be expanding but slowing whereas it's actually accelerating.

Sorry I can't give a better answer but really no-one can -- just that given the theory we've got, and the starting point we assume (an initial expansion coming from the point at which the theory simply breaks down), that's how it goes.

That's like a description of high energy physics in general, and it's a very good one for M theory, particularly with the elephant's shadow given the AdS/CFT duality....

"Reading for nerds - stuff that matters"

Or in this context "Reading for nerds - matter that stuffs"

Well, we can have a very good bash at it by taking the science we have at the minute, extrapolating back, noting every place where the story seems to get shaky and the edge cases that can arise, and see when things die. Surprisingly, the story of the last five billion years is a hell of a lot shakier than the story from, say, the fifth second up to the ten billionth year. Very early cosmology, yes, I totally agree -- it's speculation, and in particular (the slight overreaction to the BICEP2 results aside) I don't think anyone actually working on inflationary theories would pretend that they are dealing with anything that isn't, strictly speaking, phenomenology. I think most theorists believe something that *behaved* like inflation had to occur, and I would agree with that, but I don't think anyone has made any particularly strong claims for any particular inflationary theory, since they're all by their nature nothing but speculation about how higher-energy theories might act viewed with our current techniques.

But by the time of big bang nucleosynthesis in the first seconds to the first minutes, the science is really well understood -- we have direct evidence from accelerators for how matter behaves at such energy scales, and the very fact that the predictions of the theory based on this match so closely to observation at every point up to (and even beyond) the ten billionth year of the galaxy can give us a hell of a lot of faith that the fundamental picture is (at least phenomenologically) correct. I say this as someone who has chopped away at cosmology's fundamentals for over a decade -- the broad idea of inflation is probably accurate; something that closely resembles a universe composed of "baryonic" (ie normal) matter (about 5% of critical density), cold dark matter (about 25% critical density), photons, and three species of slightly massive neutrinos, *had* to hold between the first few seconds and roughly around the 10th or 12th billionth year, at which point that model breaks down unless one additionally adds in something that looks like a cosmological constant or a dark energy. Whether the physical identifications are actually precise or not is a totally different question -- and they're not, with dark energy on particularly shaky grounds but "dark matter" certainly hiding a world of complication beneath its single boring equation (w = 0) -- but the actual model is far too successful to simply be ignored. And I wouldn't consider using a different model for the period from just before BBN up until around a redshift of, say, 2 or 3, because there would be little to be acheived. Precisely how I generate the different components of course is model dependent, but it will look and act a lot like Lambda CDM.

For lower redshifts, meh, many bets are still off.

Sure but you know what I'm meaning. In physics we have a very distinct hierarchy of descriptions. At the base are the "fundamental" theories, which are assumed to hold for point particles and fundamental forces (ie forces that don't reduce to different ways of viewing another force). These are the likes of the electroweak theory, the strong theory, and any random speculation about quantum gravity that you choose to believe (or not - I don't believe any of the theories of quantum gravity at the minute, though the approaches of loop quantum gravity, dynamical triangulations, or non-commutative geometries are to my mind a lot more promising than the approach of superstring theories; less ambitious and following more closely the ethos that lead to QED in the first place). Above that is the emergent theory of quantum mechanics, which in principle should arise out of QED but which in practice is a staggeringly successful and ultimately phenomenological theory. The two are related, however, and both involve similar quantisations of classical concepts - a Lagrangian density in the case of the "fundamental" theories which are therefore quantum field theories describing the fundamental forces; and a Hamiltonian or Hamiltonian density in the case of quantum mechanics which is therefore a direct quantum theory of particles.

Then above that, quite a long way, sit the likes of thermodynamics and fluid mechanics. Thermodynamics arises by describing a system of interacting particles -- atoms, molecules, what have you -- through a Hamiltonian and then applying a statistical average of this. What emerges is a simple description of the behaviour of vast numbers of particles which is coincidentally the phenomenological theory developed in the 19th century, except that entropy is now a determined quantity rather than defined only to within an additive constant. Fluid mechanics can be recovered by setting up a Boltzmann equation, which is itself a statistical quantity, and then integrating out the lower moments, which become density, momentum, momentum flux etc. Similarly chemistry in principle can be recovered by modelling atoms with Schroedinger equations, and that's certainly done but it's computationally expensive.

Then above *that* (which holds on our scales) lies cosmology. Cosmology is the extrapolation to gigaparsec scales, of all things, of a force known to operate on scales between a millimetre and, with mounting inaccuracy in the measurements, solar system scales. It seems likely to hold on at least parsec scales but the extrapolation to kiloparsec scales is questionable, and the application in galaxies is actually ill-defined (meaning that it is impossible with current knowledge to calculate the mean-field of a galaxy due to the numerous gravitational lenses a galaxy is filled with, and the fact that such lenses break any spatial average we've currently been able to define in metric-based theories; we're also still working on straight statistical averages for gravitating systems). The application up to first mega- and then gigaparsec scales is subject to similar caveats.

So yes, in principle I totally agree wtih you that ultimately all numerical science is phenomenology, but the way the word is typically used in physics is slightly different -- a phenomenology is a theory that is not assumed to be related in any direct way to the theories that are assumed to hold on laboratory or, particularly, atomic scales and below.

I absolutely agree with your first paragraph. (Actually with pretty much your entire post.)

For the record, my feeling on dark energy is that it's a mirage caused by analysing recent (highly inhomogeneous) cosmology through a model that at its base assumes homogeneity and isotropy, which a hunch would suggest is liable to cause odd effects, and which closer study through inhomogeneous models imply that at the least the effects of dark energy can be generated in pure dust (ie baryon + CDM) universes. My own research focusses on another, related issue -- cosmology is a theory built on averages, but that average *is never defined anywhere*. An average over a tensor field is ill-defined, and any average that we've been able to write that more or less makes sense relies on a globally-hyperbolic spacetime, meaning no geodesic crossings. Alas, the universe is full of gravitational lenses which are nothing but massive regions where null geodesics cross, so we have an inbuilt issue with the idea of mapping up from small-scale (well, galaxy scale) objects to an entire cosmology -- it's currently quite impossible.

Dark matter is a slightly different topic. You can argue that the effects of dark matter might also arise from averaging effects (ie constructing a model which is after all nothing more than a homogeneous and isotropic solution fitted to the inhomogeneous reality), and some have attempted to do so, with a bit more success than with dark energy. (Practically every attempt to find a dark component from averaging has found dust, except the most refined and plausible which have found curvature.) I suspect that's a part. You can also argue that GR simply does not operate on such large scales, and that even GR should be modified on large scales before we apply an average, and I suspect that's a part, too. Then we have particles that can act as a dark matter -- neutrinos are massive, and as you point out definitely contribute, but they certainly can't be the whole answer because they imply a washed-out structure because they're relativistic for too much of the universe's evolution, meaning that they tend to propagate out of gravity wells rather than falling into them. There are other, speculative, particles that could contribute; if SUSY has any basis in fact (and I hope not but even now it may still do) then there's a lightest supersymmetric particle, which would be stable and massive and act as a dark matter. We *also* have that gravity may not be described by GR, and may not map up to cosmological scales with a simple average, but also that since it's geometric, attempting to describe smaller scales on which evidence much of the basis for dark matter rests is a bit suspect: we have to check what the dynamics of stars are in the geometry produced by a galaxy. That's basically impossible (and is linked to the averaging issue, since we'd be wanting a mean-field, along with the backreaction of the star itself on the mean-field) but it's also got to be done before we believe particle physicists when they blithely declare that they've found "the" dark matter.

My suspicion is that dark energy doesn't exist and is a mirage, while dark matter is a combination of all the above: modifications to GR, effects of averaging GR, the related effects of stellar motion in realistic geometries, massive neutrinos, perhaps even sterile neutrinos, some currently unknown particle or particles that arise in high energy particle physics... and given the number of parameters that are introduced from all of that, also probably impossible to constrain. Hey ho.

There doesn't seem to be any actual news here - just a link to someone's post about the hydrogen content of the universe.

Time, yes. Not sure what you're referring to with thermodynamics - it's just a statistical theory that emerges when you deal with vast numbers of particles. (And if I did want to treat thermodynamics as inviolate, which it basically is for large enough systems of particles, there is no issue with conservation of energy with the loss of energy due to cosmological expansion. I'm not totally sure why you'd think there is: energy conservation is inherent in the system. There's nothing controversial about the idea that if you work in an expanding spacetime then photons that are not being pumped by an external source of energy will be stretched. Similarly if you work in a collapsing spacetime then photons not being drained with be blue-shifted. The Friedmann equation can ultimately be interpreted as an energy conservation equation if one is so minded, it just comes from the Hamiltonian constraint.)

Eh?

"If there is more dark matter in the universe than ordinary matter (by a factor of 4:1 they say), wouldn't you expect it to somehow figure in the "calculations" going back to the big bang?"

Yes. And yes, it does, it "figures" right from the start.

"I saw no mention of it in the article."

Who died and made this article God?

"In fact, come to think of it, you seldom hear much about that big elephant dark matter in the room in the first minutes after the bing bag."

That's chiefly becase in the first few minutes after the big bang the universe was radiation dominated, meaning that the density of photons (and neutrinos) was vastly greater than that of dark and normal matter. The transition between radiation and matter domination is governed by the density of dark matter just as much as baryons. Where on Earth are you getting this idea that dark matter is an "elephant in the room"? Here's an interesting fact for you - you know there are waves imprinted both on the CMB and on the large-scale structure of galaxies, right? If you "love reading about cosmology" you must, right? Those waves are the result of oscillations while the universe was radiation-dominated, caused by baryons tending to cluster together under gravity, and a restoring force introduced by radiation pressure, which set up ringing oscillations across the universe. Without dark matter to provide extra clustering under gravity those waves are at totally the wrong wavelength. From the CMB *alone* you can find how much dark matter there has to be relative to normal matter. How's that for an "elephant in the room"?

"I think readers should be warned this is a very speculative field of study."

As is all theory. However, I think readers should be warned that the fundamentals of cosmology are very far from speculative - even if the results might in principle be phenomenological, they will not change. Cosmology, particularly in the early universe but after the first microsecond, say, is based on well-understood science and is anything *but* speculative, and questions about whether dark matter or dark energy are physical quantities or are emergent in one way or another are not unique to cosmology but also arise on astrophysical scales. (And in some ways are irrelevant, since whatever dark matter and dark energy actually are, they have to work as cosmology describes them anyway. Small changes to the Lambda CDM model cause large disagreements with the data.)

"I'm reminded of my physics professor of many years ago who claimed "Cosmology is as mature as botany was before Darwin." "

Err, yeah. How many years ago? If he held the same opinion now I'd be surprised. If he held that opinion after the late 90s then he was ignorant of the field. That's OK, my Masters supervisor, in the early 2000s, is a brilliant physicist and held a similar opinion (although not stated quite so... badly, with a lousy analogy that could never work), and he was wrong too, increasingly so as the datasets grow ever huger and the tools with which to analyse them evermore sophisticated. This kind of view is untenable, and I say that as a man who has gone on record repeatedly with statements such as "cosmology is wrong. It is demonstrably wrong, it is wrong in its fundamentals and it is wrong in its principles" - because that's a statement I also surround with caveats. Cosmology is "wrong" in the same way that thermodynamics is "wrong", or that much of chemistry is "wrong", or much of biology is "wrong", in that it's at heart a descriptive, phenomenological theory. (Before chemists or biologists come to me to scream, those fields are typically phenomenological, although both contain subfields that are avowedly not so; but ultimately if you're not mapping up from the behaviour of the individual atoms you're dealing with phenomenology, and I'm well aware of how brutally difficult it is to do chemistry directly from the Schroedinger equation, which is what that implies. 'Phenomenology' is not a criticism, unless it's taken as so by people who mistakenly think they're dealing with the underlying science directly.)

Sorry, it was a throwaway remark - I was referring to Poul Anderson's "The Stars are Also Fire" which won the Prometheus Award back in the 90s. I spent seven years as a professional cosmologists so I'd be extremely worried if I didn't know that stars run on fusion :)