Are the Cosmological Coincidences Just a Matter of Chance?

[Wallace]

Thank you,
I now understand what you are saying.

The value of the integral in #19 is a pure number.

It appears from present observations of the parameter set that that pure number is unity, or near unity.

Whether one considers this to be interesting or not depends on whether it is thought '1' is special number or not.

Garth

Pretty much, in the units of Hubble time (not a unique unit to measure the age in) the value is very close to unity. It's somewhat surprising that it would be so close to such a number, but hey it's got to be something!

 

[LeBourdais]

GR is the best thing we have going, however the problems and possible coincidences being discussed here and here may indicate some modification is required.

I absolutely agree with you Garth.

Paul

 

[cosmomath]

Cosmological Unified Mathematics

Fellow Searchers:

Looking to communicate on aunification program of the current theories and states of Mathematics and Cosmology. Specifically, String/Brane Theory, Causal Sets, Percolation, Conceptual Spacetime Geometric Models, Causality Violations, Non-Commutative Geometry, Topology of Spacetime, Algebraic Topology.

Specifics Sought: All and any commonality between LQG, String Theory, and Causal Sets.
Even simple unions and intersections (even basic or conceptual) are of great interest. Also, any areas/fields of mathematics that have been overlooked (or missing) in the above theories.

Thank You...Good Hunting...COSMOMATH

 

[yogi]

Hi Jon,

In the standard model it is Inflation that drives the geometrodynamics of the universe onto near spatial flatness. To say that the universe has no capacity to depart from perfect flatness is contrary to the understanding of GR and would introduce a "personal theory". Do you have a reason why the universe should behave like this?

Actually such a suggestion does nothing to explain the near equality of the calculated Age of the universe and Hubble Time.

However Inflation itself is being questioned by some people, so you could ask:"Given that the universe is observed to be flat, and if Inflation is not 'true', then, as an alternative, is there some as yet unknown other reason making the universe flat?"

It was such a question that gave rise to Inflation theory in the first place!

Garth

One suggestion is that expansion develops sufficient energy in the form of stress. Consequently, the universe is intrinsically flat. Note that the total estimate for the energy of the Hubble sphere is about 10^53kg - the Hubble radius is a about 10^26 KM so the effective energy density is approximately 1 kgm/m^2 if it is realted to a surface density. By this, I do not mean that new particles are created - rather the effective stress between the condensed forms of energy is incresed as the universe dilates

 

[Garth]

Hi yogi!

What model of 'stress' are you referring to?

Or is this just DE by another name?

Garth

 

[Garth]

Fellow Searchers:

Looking to communicate on aunification program of the current theories and states of Mathematics and Cosmology. Specifically, String/Brane Theory, Causal Sets, Percolation, Conceptual Spacetime Geometric Models, Causality Violations, Non-Commutative Geometry, Topology of Spacetime, Algebraic Topology.

Specifics Sought: All and any commonality between LQG, String Theory, and Causal Sets.
Even simple unions and intersections (even basic or conceptual) are of great interest. Also, any areas/fields of mathematics that have been overlooked (or missing) in the above theories.

Thank You...Good Hunting...COSMOMATH

Welcome to these Forums cosmomath!

I must admit I did a Google search for "aunification" before I realized you must mean "a unification"!

Does this post have anything to do with cosmological coincidences? If so, can you be specific?

If you want to ask a more general question along your lines above I suggest you start a thread in the appropriate Forum, paying due regard to the Physics Forums Global Guidelines.

If you are proposing your own theory, not published in a refereed journal, then that can only be done on PF on the Independent Research Forum paying due regard to their even stricter https://www.physicsforums.com/showthread.php?t=82301.

The reason for these rules is to maintain a discipline that filters out the many crackpot ideas and theories that abound on the Internet. Basically this is a teaching site where newbies are to be encouraged but not to be misled, also we do ask intelligent questions about refereed and published research to increase our own understanding.

Garth

 

[yogi]

Hi yogi!

What model of 'stress' are you referring to?

Or is this just DE by another name?

Garth

Stress in the form of tension. In the notions of DE, the usual assumption seems to be that DE in someway creates a positive pressure that drives the expansion - on the other hand if the stress energy is tension, its role in making the universe flat is not causal but consequent. What we observe about gravity, mass and energy is an attraction - to somhow impute a repulsion to matter-energy is IMO a step in the wrong direction.

 

[Garth]

Actually it is the other way round, a positive pressure, such as that of the primordial plasma, and then gas, before large scale structure formed, or the radiation pressure of the CMB at an earlier age, increases the deceleration of the expansion.

This is because such pressure acts in the same way as 'extra energy' and adds to the mutual gravitational attraction within the universe.

In order for DE to cause acceleration it must have negative pressure, which is indeed the case for false vacuum energy, for example, so it would introduce tension.
In order for the universe to accelerate the total pressure must be less than minus one third the total density:p < - \frac{1}{3}\rho and false vacuum energy has: p_fv = - \rho_{fv}.

I hope this helps.

Garth

 

[yogi]

Garth

Thanks for your response

I am familiar with most of the models - and disagree with the notion that increased tension in the form of stress energy will affect the expansion rate one way or the other. Basically, I doubt weather we have a viable theory as to what causes expansion - and probably further from a theory that would explain acceleration or deceleration, if such is the case. The major efforts are directed to tinkering with different types of energies, vacuum states and ratios that are adjusted to match flatness. The motivation for my post 34 was post 21. IMO expansion generates the G field and the consequent stress follows as a product thereof - not as causal but as resultant. That is what I was attempting to state in answer to the question as to why the universe could not deviate from perfect flatness (your post 23)

You had apparently pondered a similar notion at one time - as I recall in the old model of SCC, the product GM was constant - but not in your revised model?

regards

yogi

 

[Garth]

You had apparently pondered a similar notion at one time - as I recall in the old model of SCC, the product GM was constant - but not in your revised model?

That is correct, in SCC it was the condition GM = constant that yielded \lambda = 1, which GP-B has proved cannot be the case. In the General theory, GSCC, this condition has been dropped, and \lambda has to be determined empirically.

Garth

 

[Garth]

An eprint in today's physics ArXiv Age of the Universe, Average Deceleration Parameter and Possible Implications for the End of Cosmology develops the coincidence of the equality of the universe's age and Hubble time, a coincidence I was discussing in this old thread.

The author, Jose Ademir Sales Lima, is a professor at the University of Sao Paulo, Brazil, and his approach is described in this web page The daringness of challenging Einstein.

The factor AH₀, where A is the age of the universe, is given by the integral in this post:

All I am pointing out is that in the present epoch, with the observed values determined by the 'precision cosmology' mainstream model,

\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 \right)}}}\approx 1 .

We note that according to that mainstream \LambdaCDM model this near identity with unity (\pm0.6%) did not hold at various earlier epochs and indeed it need not hold in the present epoch. Depending on the mix of DE and matter, and the equation of state of DE, the integral could have a value between 0.66 and \infty. It therefore seems a suspicious coincidence that the present value of the integral should be so near to unity.

Furthermore there is a related coincidence in the near equality of density of the components of that DE/DM/Matter mix in the present epoch.

Further thoughts?

Garth

 

[hellfire]

I came across this topic again and I have calculated the integral

\mathcal{I}(\Omega_{m,0}, \Omega_{\Lambda,0}) = \int_0^1 \frac{da}{\sqrt{ \Omega_{k, 0} + \displaystyle \frac{\Omega_{m,0} }{a} + \Omega_{\Lambda,0} a^2 \right)}}}

with \Omega_{k, 0} = 1 - \Omega_{m,0} - \Omega_{\Lambda,0}

The surface

\mathcal{I}(0 &lt; \Omega_{m,0} &lt; 1, 0 &lt; \Omega_{\Lambda,0} &lt; 1)

is depicted this graph.

The values of \Omega_{m,0} and \Omega_{\Lambda,0} that lead to

\mathcal{I}(\Omega_{m,0}, \Omega_{\Lambda,0}) = 1

are depicted in this other graph.

I minimized my efforts with a very simple numerical integration and making the graphs with excel. If someone would be interested in having the excel-macro please contact me via PM.

 

[Garth]

Another paper on the intriguing coincidence H₀t₀ or H₀A = 1,

THE ARCHAIC UNIVERSE: BIG BANG , COSMOLOGICALTERM AND THE QUANTUM ORIGIN OF TIME IN PROJECTIVE COSMOLOGY.

In other words, the relation H₀ t₀ =1, which is exactly true for Milne kinematic relativity formulated for an empty Universe, remains exactly true in the LCDM model where it leads to the same results confirmed by WMAP. In addition, it has been observed [2] that, even though data relating to Ia supernovae are better reproduced by the LCDM model, agreement with the Milne model stays good up to a distance of 8 billion light years.

Garth

 

[jonmtkisco]

Hi Garth,

Of course the coincidence remains perplexing, and both the Lima paper and your note reinforce that point. I like Lima's approach to the math.

However, it seems unlikely to me that one can validly project past changes in the deceleration rate to predict future eras which must oscillate around a long term deceleration rate of 0. In the past, each change of era resulted from the expansionary dilution over time of a component characterized by a relatively higher deceleration parameter, thereby unmasking a new dominant component characterized by a lower deceleration parameter (first radiation domination, then matter domination), and then by an even lower, negative deceleration parameter (cosmological constant). This historical trend has been all in one direction.

Moreover, while radiation and matter were subject to expansionary dilution over time, the cosmological constant (in its vanilla form) is not, which implies that it is the "final" and "permanent" era. So presumably Lima is implying that the cosmological constant must be an exotic form which also becomes diluted by expansion or by time, making way eventually for some unknown, but presumably less energetic unknown source of deceleration. (Of course if the cosmological constant goes to 0 eventually, the universe could simply revert to being matter dominated again, albeit at a very dilute level of gravity.)

Interesting stuff.

Jon

 

[Garth]

Interesting stuff.

Indeed Jon, but is it true that "This historical trend has been all in one direction"?

The Inflation era unmasked an extremely higher acceleration (negative deceleration) parameter, followed at a later epoch by the gentler acceleration of DE...

The thought in the back of my mind is that if DE fixed the total equation of state at \rho = - \frac{1}{3} p (see Kolb) then that would deliver the Milne model, with no Inflation era and which would explain the "intriguing coincidence" nicely. I know there would be other problems fitting the model but it is just a thought...

Note the paper I cited, and the quote from it that I posted has confused Milne Kinematic Relativity with the Milne model, (\Omega = 0, k = -1, R(t) = t.

The Milne model is simply the empty GR universe, whereas Kinematic Relativity was Milne's attempt to produce a cosmology based on SR alone. (I have his 1935 and 1947 books)

Garth

 

[jonmtkisco]

Hi Garth,

The Inflation era unmasked an extremely higher acceleration (negative deceleration) parameter, followed at a later epoch by the gentler acceleration of DE...

Yes, I agree that inflation would be the exception to the one-way trend I described towards lower (absolute) deceleration parameters. Maybe what we should take away from this is that inflation theory is the odd man out! I don't like the inflation theory, although I know of no better alternative currently.

Even including the inflation era, there is also a one-way trend toward lower energy density in each succeeding era. Which suggests that if there is a new era after the DE dominated era, the energy density will be so low that an enormous amount of time will be required for anything noteworthy to happen.

The thought in the back of my mind is that if DE fixed the total equation of state at \rho = - \frac{1}{3} p then that would deliver the Milne model, with no Inflation era and which would explain the "intriguing coincidence nicely. I know there would be other problems fitting the model but it is just a thought...

I'm all in favor of that if it fits as well with the various observations as the concordance model. I assume that's what Lima refers to as "K-Matter".

The Milne model is simply the empty GR universe, whereas Kinematic Relativity was Milne's attempt to produce a cosmology based on SR alone. (I have his 1935 and 1947 books)

Which of Milne's models is the one that has the annoying comoving coordinates for privileged observers? That's the part of Milne that tends to mess up discussions.

Jon

 

[Garth]

I'm all in favor of that if it fits as well with the various observations as the concordance model. I assume that's what Lima refers to as "K-Matter".

Yes, it was Kolb in his 1989 paper (linked to above) that coined the word "K-matter" which he suggested might be a universe dominated by cosmic strings.

Which of Milne's models is the one that has the annoying comoving coordinates for privileged observers? That's the part of Milne that tends to mess up discussions.

Jon

Kinematic Relativity.

You might find Matt McIrvin's web page http://world.std.com/~mmcirvin/milne.html illuminating. It is a fair description of Milne's theory as far as I can see.

Garth