Why is the age of the Universe the reciprocal of the Hubble constant?

[twofish-quant]

Viewpoint 1: If one assumes that the Universe is homogeneous and isotropic then the net proper acceleration of any particle is zero due to the spherically symmetric distribution of mass around it.

And the acceleration of a particle is zero in it's own reference frame. However, because the reference frames are themselves accelerating, when you switch reference frames you end up with acceleration.

If I'm in an accelerating or decelerating universe then it looks to me that I'm not moving but everyone is either accelerating or decelerating with respect to me.

If Melia's argument is valid then no other cosmologies are possible (!)

Right. But the argument is not valid and from a point of view of strategic marketing or a new idea, it would be a good idea to stay away from theory.

 

[twofish-quant]

Also one of the great examples of scientific writing were the accelerating universe supernova papers. The first reaction that anyone has when coming up with a nutty idea is "this is obviously wrong because of X." In the case of the supernova papers, this was fun because you went

This accelerating universe is obviously stupid because of ... Oh, they thought of that... Well then it's a dumb idea because of... Oh, they mention that. Well, it's wrong because of... Oh, they got that too... (thinking for a day) Wait, they didn't consider ... Oh... That's there. Well...

Once you get to that point then anything that you want to do to argue against the paper would be something subtle.

And it's not a coincidence, before they published they showed it to a bunch of people, and beat up the papers really good.

 

[johne1618]

And the acceleration of a particle is zero in it's own reference frame. However, because the reference frames are themselves accelerating, when you switch reference frames you end up with acceleration.

I think Melia's argument for a linear cosmology requires Mach's principle.

Mach's principle assumes that inertial frames are defined in relation to the "fixed stars" or the rest of the Universe. Thus all observers have an inertial frame from the same family of inertial frames each only differing from the other by a velocity defined by Hubble's law. Thus an object that is not accelerating according to one observer should not be accelerating according to any observer. This condition naturally implies a linear cosmology.

 

[Garth]

twofish-quant Thank you for your detailed and reasoned reply, I was thrown off originally by your use of the words "crank" and "nutty", I prefer the terms 'maverick' and 'heterodox' for serious thinkers who question orthodoxy and their hypotheses!

Which gets you to another problem with slow growth models. Mella claims to have solved the horizon problem. The trouble is that he solves it too well. The universe is very smooth but we do see lumps, and if the universe was always causally connected, it would be a lot smoother than we see.

One way of thinking about it is that the big bang is like a "cosmic clarinet". A clarinet works because you have a reed that produces random vibrations. These vibrations then gets trapped in a tube which sets up standing waves that amplify those vibrations at specific frequencies. The big bang works the same way. You have inflation which produces the initial static. At that point the vibrations get trapped in a tube. What happens with the universe is that there is a limit to which vibrations can affect each other. If the universe is five minutes old, then bits of space that are more than five light minutes apart can't interact. This "cosmic horizon" creates a barrier that enhances some frequencies and not others.

So the universe works like a clarinet and produces a specific "sound". You can then figure out lots of stuff from the "sound of the big bang". If you grow the universe slowly then the "cosmic horizon" is much further way, and I doubt you'd get much in the way acoustic oscillations.

Density inhomogeneities in the CMB are limited by sound speed not light speed, the 'cosmic horizon' for these inhomogeneities is a 'sound horizon' and the maximum speed of sound, which is in a radiation-dominated fluid, is c/√3. The 'lumps' grow continuously and 'slowly', with no Inflation, resulting in the same size as the smaller primordial 'lumps' in the standard model after being inflated.

Having too **little** lithium isn't a huge problem. You can easily imagine lots of things that could burn lithium and you can also question the accuracy of the stellar measurements.

And yet it seems we can't: The cosmic lithium problem: an observer's perspective Memorie della Societa Astronomica Italiana Supplementi, 2012 Vol. 22, pag. 9

Using the cosmological constants derived from WMAP, the standard big bang nucleosynthesis (SBBN) predicts the light elements primordial abundances for 4He, 3He, D, 6Li and 7Li. These predictions are in satisfactory agreement with the observations, except for lithium which displays in old warm dwarfs an abundance depleted by a factor of about 3. Depletions of this fragile element may be produced by several physical processes, in different stellar evolutionary phases, they will be briefly reviewed here, none of them seeming yet to reproduce the observed depletion pattern in a fully convincing way.

T = \frac{1}{H_0} \int_0^1 \frac{da}{\sqrt{ \Omega_{k, 0} + \displaystyle \frac{\Omega_{m, 0} }{a} +\displaystyle \frac{\Omega_{r,0} }{a^2}+ \Omega_{\Lambda,0} a^2 }}.
The coincidence therefore means the integral is unity, within observational error, with no mention of LCDM. The cosmological parameters determined in the LCDM model coincidentally result in the integral having a value of 1, in and only in the present epoch, but in the FC model they do so necessarily because the EOS is ω = -1/3.

Except that in the standard cosmology, the integral "magically" becomes one because we've calculated the various omega's and by some cosmic coincidence that happens to be one. If you toss out the calculations of the omegas, then there is no "magic". The omegas are bogus and so is the integral, and you have nothing to explain.

The integral gives the age of the universe in a general cosmological model, the Omegas are not 'bogus', with the density made up of different species: matter (baryonic and non-baryonic) , radiation, dark energy and a component for curvature where \Omega_{k, 0}=1−\Omega_{m,0}−\Omega_{\Lambda,0} in a flat universe.

I am not 'tossing out the calculations of the Omegas', they exist (at least most of them) in any model and there may well be something to explain: the fact that the integral appears to be very near unity.

The other thing is that we are in "adversarial boxing mode" and not "teaching mode." If I had a student write a research paper about slow growth cosmologies, and then they talk about deuterium spallation, then I'd mention to them that they should include some references to the work in the 1970's

Such as: The Formation of Deuterium and the Light Elements by Spallation in Supernova Shocks Where Colgate finds that if 1% of galactic matter has been processed through Type II S/N then that would explain observed deuterium abundance.

The existence of ionisation and high metallicity in the early universe suggests that in fact there were a lot of supernova, even hyper-nova, from Pop III stars, so deuterium production from spallation in their shocks could have been efficient enough.

Garth