Problems with the FUGE cosmological model

After having written much about the problems that I see with the standard cosmological model, I thought it would be fair to talk about the problems with the FUGE (flat uniform granular expansion) model.

Fundamentally, all the FUGE model is saying is that:

• for every unit of Planck time, the radius of the universe increases by one unit of Planck length, and
• for every unit of Planck time, the mass-energy in the universe increases by half a unit of Planck mass.

---

First off, why the units of Planck time and Planck length and half a unit of Planck mass?  In Half a Problem Solved?, I discuss how our universe could be one of a matched pair.  In the update, I refer to a paper in the Annals of Physics (reported at Live Science) which details a theory involving a mirror universe which runs “backwards in time”.  Each of these mirror universes would receive (or generate) half a unit of Planck mass per delta unit of Planck time (even if these delta units are in opposite directions), summing to a total of one unit of Planck mass per delta unit of Planck time.

And secondly, given that l_P=c.t_P=G.m_P/c², and r_s=2GM/c², which indicates a linear relationship between all the key elements, there is no particular issue if the implied granularity is at the Planck scale, or smaller, or even larger.  I prefer the Planck scale, but I am not irrevocably wedded to it.

Thirdly, in the original meaning of FUGE, it had "universal" in the middle of the definition, which wasn't great.  I actually started with flat, granular and expansion, which suggested FUGE, so the insertion of "universal" is actually somewhat akin to what happens with a backronym.  Recently I realised that FUGE is better rendered as "flat uniform granular expansion", applying when talking about "a FUGE universe" or "the FUGE cosmological model" (as per the title of this post) or something similar.  Note that the uniformity that we are talking about only applies at a sufficiently large scale, as per discussions of homogeneity and isotropy.

---

There will be some who will point out issues additional to those that I go through below, of that I am certain, but the major problem that I see is that I have no good explanation for why mass-energy enters the universe.

I have previously suggested that it could be because there was a black hole in a precursor universe, and all the mass-energy from there is entering our universe, but that just kicks the problem down the road – where did the mass-energy from that universe come from?  From an earlier precursor universe perhaps, but that results in an endless regression.  Additionally, an inherent feature of that model is that there are two mirrored universes each going off in different temporal directions (negative and positive) each of which gets half the mass-energy, as mentioned above.  So this sequence of universes implies that they would be halving in mass-energy each time a new universe branches out of an old one.  Do that a few dozen times and you start getting sparsely populated universes (2⁴⁸≈10³⁵).  With the quantity of mass-energy in our universe, there’s a hint that either there was a tremendous amount available at the very beginning or we are one of the very earliest iterations of universes.  Unless, of course, there’s some mechanism by which the mass-energy in both the positive and negative temporal directions recombine when a new pair of universes is generated, in which case a new complication is added because we don’t have anything close to a mechanism for explaining that.

A better explanation, albeit one lacking in key detail, is that expansion itself results in the creation of mass-energy, if the universe is flat.  The tiny detail missing is … what causes the expansion?  The positive aspect here, however, is that we merely have an absence of explanation.  What cannot be denied, at least not reasonably*, is that we observe expansion, even if we may not be able to explain its origin.  The creation of mass-energy is a fundamental requirement of the standard cosmological model even if it is rarely (if ever) stated as such.  The notion of dark energy includes an assumption that there is a background of invariant energy density in the universe, indicating that a universe with increasing mass-energy is not inherently impossible (because, if so, that should have been raised an objection to this explanation for dark energy).

Another problem is that it is not immediately obvious that the universe ought to be flat.  Once we have expansion and the notion that the universe is flat, and therefore has critical density, the quantity of mass-energy entering into, or being created by the expansion of the universe follows naturally.  But why would the universe be flat?

I think it is useful to consider the notion that there are reasons that mitigate against the universe not being flat.

There are only two non-flat options – either the universe could have greater than the critical density, or less than it.

In the first option, the density would be greater than that of a black hole with the radius of the universe.  The densest type of black hole is a non-rotating black hole (like a Schwarzschild black hole) and, if our universe were ever denser than that, then … well, what I would expect to see would be similar to the notion of inflation, massively rapid expansion, until such time as the density was no longer greater than that of a black hole, becoming flat or overshooting into sub-critical density.  While this might sound like an explanation for inflation, we would still have a question as to why the initial density was greater than critical.  And it would also mean that, today, we would only see either a sub-critical or critical density.

Which leaves only the second alternative, the universe having a density that is less than that of a black hole of similar dimensions – or sub-critical density.

The universe as a whole is entirely composed of gravitationally uncoupled systems (uncoupled from each other, or at least only coupled to such a relatively negligible extent that the systems do not collapse into each other).  Each of these systems are less dense than a black hole.  The solar system is an example, or just the Sun itself, or the galaxy, or galaxy cluster (or superclusters).  It is certainly possible to imagine a universe that is less dense than a black hole.

However, remember that we are trying to understand why mass-energy is entering the universe – this is associated with a universe that is flat and we are now considering a universe that would not be flat, so there is no reason to assume that mass-energy would enter it over time.  We have only three options in this sub-critically dense universe:

• there is an invariant quantity of mass-energy in the universe,
• mass-energy is leaving the universe due to some unexplained mechanism,
• or mass-energy is entering the universe at some reduced rate than for a FUGE universe due some other unexplained mechanism.

In the first option, we would have a situation in which – until right now, due to expansion – the density was higher than a Schwarzschild black hole with a radius of 13.77 billion light years, and it will later have a density that is lower.  Nothing is denser than a non-rotating black hole, so we can eliminate this option.

The second option is worse, since in the past the universe would have been even denser, and it too can be eliminated as an option.

The third gets us nowhere, since we still have mass energy entering the universe, we just have a situation in which rate no longer makes any sense.

There is a possible fourth option, being a combination of two or three of the options rejected above, in phases, perhaps also incorporating a flat phase, and a super-critical phase.  Such an option would have the same problems as the Standard Cosmological Model (and indeed could be equivalent to the Standard Model).  

At the risk of sounding Zen, the universe itself seems to be telling us that it is not possible to have less than critical density.

Then there is the fact that the FUGE model deviates from standard cosmology.  I have discussed this in The Problem with the Standard Cosmological Model.  To the extent that there are problems with standard cosmology, the fact that the FUGE model deviates from standard cosmology is not really a problem.  If the FUGE model were shown to not reflect the facts of the universe, then that would be a problem.  But it does not, so far as I can tell, it just results in the universe as it is today, with a lot less faffing about.

---

* Maybe there is reasonable denial after all - as reported by Live Science.  However, this paper does not deny the appearance of expansion (per red shift).  Note also that it removes dark matter (as a form of mass-energy) and also dark energy.  I suspect that Lombriser's model introduces gravitational and cosmogenesis-related issues, but given the complexity of the theoretical underpinnings, it's entirely possible that it doesn't and I just cannot see it.