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## A Singular Question

 Quote by mysearch o Is Hubble’s constant [H] primarily established based on observational measurements and then the critical density calculated from Friedmann’s equation?
Yes.

 o Is it true that for the universe to be spatially flat [k=0], the component energy densities would have to be very close to the critical density?
Yes, in total.
 o Is the figure of 4% baryonic matter based on estimates of the amount of observable matter?
I don't know the whole story of how it is estimated. There is a lot of gas and dust. Different kinds of observations (radio telescopes see cold gas clouds, Xray telescopes see hot clouds etc etc) and different kinds of expert inference. A lot of work on this, but ultimately can only involve guesswork. Yes the 4% figure is based on observation.

 o Is the figure of 23% cold dark matter based on estimates necessary to correct gravitational anomalies, e.g. galactic rotations?
Indeed I believe it is largely based on things like galaxy rotation curves and the apparent stability of clusters of galaxies. But it is confirmed on other grounds as well. For instance there is structure formation in the early universe. The models of structure formation work because there is enough dark matter to start the process of coagulation.

In the computer models it is the dark matter that starts the process of clumping and forming cobwebby strands separated by voids. The ordinary matter was too dispersed to get started curdling.

So dark matter actually forms the skeleton of structure in the universe and without it we would not be as well clumped.

This was a bit of serendipity, because they first estimated how much dark matter there would have to be to make presentday galaxies and clusters stable, and then that turned out to be the right amount of dark matter to explain the observed rate of structure formation in the early universe----starting with the amount of irregularity seen in the CMB.

As a rule, no one observation ever clinches an argument, it is always a process of fitting together several pieces.

 o While the figure of 73% is clearly the remaining portion of the critical density; is there any other observational evidence for dark energy other than the acceleration issue?
Same thing here. They got the original estimate (equivalent to 0.62 joule per cubic km) by how much would be needed to explain the acceleration measured with supernovae up to and including 1998.

But then by good luck or serendipity that turned out to be the amount needed to explain spatial flatness, given estimates of the amount of dark and ordinary matter made on other grounds!

And then some other observations also supported that estimate (approx 0.62 joule per km^3) like the integrated Sachs-Wolfe effect, and further, more distant Supernovae.

I think near flatness is an important part. One can check near flatness using galaxy counts and also independently using the CMB. Then one can measure H(t=present) and use that to estimate rho_crit, (about 0.85 joule per km^3) the density needed for spatial flatness. Then one can estimate how much dark and ordinary matter (say 0.23 joule per km^3).
And the rest, needed to get approximate flatness, turns out to agree with what was estimated for dark energy.

The arguments are all a bit guessy and iffy, but they mesh, coming from different directions. So one can provisionally work with the consensus model (as many do) without complete certainty, always keeping an alert lookout for inconsistent evidence that might refute it, or alternatives that might do as good a job at accounting for all the myriad different kinds of data.

Again a web of supporting or consistent observation, no one single clincher. IMHO.

 o Does this imply that the energy of the observable universe is now larger than at earlier times, when the relative density of dark energy falls to ~0%?
I believe is an unresolved puzzle related to this.

However the observable universe is not an isolated subsystem, What it includes changes with time, so perhaps it does not provide the best example of an apparent violation of conservation of energy.

One could try taking any comoving volume. Any volume which expands along with the regular increase of distances (expanding in concert with the Hubble flow) and the energy of all the forms we know about or at least usually measure will be increasing due to the constant dark energy density---always proportional to volume.

Also a comoving volume experiences a net loss of CMB energy due to redshifting, and expansion gradually drains kinetic energy like that of the neutrino background. To me this has always seemed a puzzle. Where does it go?

I hear some people say that the lost energy of the CMB (it's photons have lost 99.9% of their energy) somehow goes into gravitational energy.

Anyway, as far as I am concerned there are unanswered questions about this. One doesn't know the extent to which the universe as a whole conserves energy. It seems one may only have conservation laws in local coordinates and for isolated subsystems. Maybe the total global energy of the universe is not even mathematically well-defined, and a comoving volume isn't adequately isolated and energy can always flow in and out of the box.

One way to think about it is this: Laws should have an operational definition. Energy conservation law basically prohiibits someone from building a perpetual motion machine? Can you think of a way to harness the dark energy (the amount of which grows as the volume expands)? If no observer can harness it, then maybe it is not violating any law.
 Recognitions: Gold Member Science Advisor When space expands, a photon redshifts. This nicely fits the conservation of energy principle. The total energy of the photon is diluted across a larger volume of space. Incidently, this phenomenon refutes the notion of space as a propogation media for photons [i.e., aether]. If space were such an entity, photons would blue shift when it was tensioned - like the note emitted by a guitar string being tightened. If space behaves more like a fluid, you should get shear when it is stretched. In that sense, dark energy could be equated with turbulence.
 Recognitions: Gold Member Marcus, I hope you don’t mind, but I thought your previous response was so useful I made a reference to it in the sticky thread at the beginning of this forum. See following link: http://www.physicsforums.com/showpos...9&postcount=51. As implied, I found this to be a very useful summation of the state-of-play concerning what appears to be some of the more critical assumptions of the LCDM model. I might still be a little sceptical of the serendipity theory regarding the energy density of dark energy at this time, but need to research some of the background issues a little more before commenting. Therefore, started to do some figures on the energy issues related to the observable universe now and at CMB decoupling, i.e. z-1090, as the following figures can be checked against the cosmological calculators. However, I was wondered if anybody had any comments on the results so far? Energy Density at z=0; Observable radius = 4.558e10 LY = 4.312e26 m Observable volume = 3.965e32 LY^3 = 3.358e80 m^3 Baryons = …4%; ……….3.41e-11 joules/m^3; …1.145e70 joules CDM = …...23%; ………1.96e-10 joules/m^3; …6.581e70 joules Radiation = 0.00824%; …7.03e-14 joules/m^3; …2.360e67 joules Lambda = …73%; …...…6.23e-10 joules/m^3; …2.092e71 joules Total = …..100%; ……...8.53e-10 joules/m^3; ….2.864e71 joules Energy Density at z=1090 Observable radius = 4.180e7 LY = 3.954e23 Observable volume = 3.059e23 LY^3 = 2.589e71 m^3 Baryons = ..11%; …4.53e-2 joules/m^3; ….1.172e70 joules CDM = …..64%; …2.60e-1 joules/m^3; …. 6.731e70 joules Radiation = 25%; …1.02e-1 joules/m^3; …. 2.640e70 joules Lambda = …0%; ….6.23e-10 joules/m^3; …1.612e62 joules Total = ….100%; ….4.08e-1 joules/m^3; ….1.056e71 joulesSo we are considering a comoving volume expanding from 41.80 million lightyears to 45.58 billion lightyears. Therefore, we can estimate the unity change in energy of this volume as follows: Baryon:… 1.145e70 / 1.172e70 = 0.977 CDM: .…. 6.581e70 / 6.731e70 = 0.977 Radiation: 2.360e67 / 2.640e70 = 0.00089 Lambda:…2.092e71 / 1.612e62 = 1.297e9 Total: ……2.864e71 / 1.056e71 = 2.712So under expansion and within the limits of accuracy of the calculation, the baryon and cold dark matter energy within this comoving volume remains unchanged, as we would expect. The radiation energy falls due to the additional (1/a) wavelength expansion factor, while there is an exponential increase in dark energy because it scales with volume. However, the bottom line appears to be that our comoving volume now has 2.7212 times the energy at decoupling, i.e. +370,000 years! I guess one immediate question that comes to mind is whether this energy analysis should consider any change the gravitational potential energy due to expansion? I haven’t really had time to consider this issue, but as a generalisation, any increase in potential energy would be negative, therefore I was wondering if this might, in any way, offset the apparent positive increase in energy?After reading Chronos` post could I clarify a few points: In the context under consideration, the expansion of space, wherever that means, leads to an increase in the wavelength of a photon in transit. As frequency is the inverse of wavelength, it falls as a function of expansion and so does energy by virtue of E=hf? Irrespective of the guitar string analogy, the expansion of space does seem to affect the photon. If we assume that the speed of light [c] doesn’t change, then I assume we must assume the product of permittivity and permeability of space doesn’t change. So what caused the photon to change frequency?

 Quote by mysearch Marcus..... I thought your previous response was so useful I made a reference to it in the sticky thread at the beginning of this forum.
Hear! Hear!

 Is Hubble’s constant [H] primarily established based on observational measurements and then the critical density calculated from Friedmann’s equation?
and Marcus replied simply "Yes"---- which is quite true ---- as far as it goes. But adopting a different perspective warns of how incomplete our present understanding of cosmology still is:

The actual observational measurements are (a) H now (finally well-established by observation at 72 Km/sec/Mpc) (b) the Universe's flat spatial geometry (inferred from the WMAP power spectrum) and (c) the observed matter density (via the complex of observations discussed by Coles and Ellis in Is the Universe Open or Closed?; C.U.P. 1997), together with more recent observations of gravitational lensing caused by dark matter).

When these observations are interpreted in the usual way with GR, assuming the isotropic-everywhere cosmological principle, they determine the present value of Lambda --- and rightly focus attention on the puzzle of why that most mysterious quantity (or H, if you prefer) has the value it does.

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 --- and rightly focus attention on the puzzle of why that most mysterious quantity (or H, if you prefer) has the value it does.
More by way of a footnote: If, as indicated, H is primarily determined by observation and measurement, then it would seem the Friedmann’s equation does not really explain the value of H, only how the corresponding critical density is calculated from its value at any point in time. While the positive or expansive nature of H may be obvious from observation, what still puzzles me is why the Friedmann equation implicitly assumes that the value of H is positive, i.e. an expansive velocity, when the component energy densities of this equation only seem to suggest a universe that must collapse under gravitation, prior to +7 billion years. The following thread provides my rationale for asking this question: http://www.physicsforums.com/showthread.php?t=267808