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 universal 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.
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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 lP=c.tP=G.mP/c2,
and rs=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, "universal" is not a great word to have in the middle of the definition of the initialism "FUGE". 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 could also be rendered as "flat uniform granular expansion", but this only works when one already knows that we are talking about the universe, so it could apply only when one were to talk about "the FUGE cosmological model" (as per the title of this post) or something similar. And the uniformity that we are talking about only applies at a sufficiently large scale, as per discussions of homogeneity and isotropy.
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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.
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