*"Solution to the Dark Energy Problem".*

Single author, Paul Howard Frampton. Hmmm. A thought crossed my mind at the very start. Was this the work of a crackpot, sneaked into the arxiv while nobody was looking ?

The tentative answer, before reading the text, was "No". Professor Frampton is a distinguished scientist with an excellent record, and although I know at least one distinguished scientist who has apparently lost his mind, this did not appear to be the case.

But wait. What was the date of publication ? April first ? No, April 11th. Okay, it looked like I would need to read the article to find out!

Fortunately, the paper is just 9 pages long, and it contains a mere seven (7) formulas -not even quite hard to decypher! For a paper allegedly solving a long-standing puzzle in contemporary physics and cosmology, this must be a record. But let me discuss the contents, with the explicit caveat that I am not an expert and my judgement is as good as yours.

**The paper**

The paper is extremely colloquial and simple to read. The author start with a brief section containing a description of the problem of the accelerated expansion of the universe. This effect is with us since 1998, when it was recognized by the scientific community that the distant stars producing type-1A supernova explosions were increasingly receding from us as a function of their distance.

Type-1A supernovae are like "standard candles", because the mechanism that ignites them guarantees that they have all the same intrinsic luminosity: thus their systematic study in distant galaxies provided the necessary input.

The evidence for an accelerated expansion of the universe was later confirmed by independent observations. One may be thus led to speculate that a sort of "negative pressure" pervades the universe, causing it to expand at an increasing rate. This works out easily like an addendum to the equations governing the universe expansion. Frampton explains clearly how a solution of the problem can be worked out adding a "dark energy" to the energy density in the Friedmann equation.

Section two is titled

*"Solution to the Dark Energy Problem"*. And since the statement of the problem took five formulas in section one, we are left with two formulas... Enough of a task to make a theorist's nerves stretch beyond the breaking point. But let us follow Frampton -section two is only two pages long!, so we can afford to be analytical.

He starts with the holographic principle: all the information about the universe is encoded in its two-dimensional surface. If this is so, it allows us to consider the universe in a different light.

A dimensionful parameter of importance in cosmology is the Schwarzschild radius of a body: it is the radius which constitutes the event horizon for the mass possessed by the body. Most heavenly bodies have a Schwarzschild radius much smaller than their real dimensions: for instance, the sun has a radius of 800,000 kilometers, but its Schwarzschild radius is of just 3 km. When the physical radius is much larger, objects are quite different from black holes.

If one considers the whole visible universe, on the other hand, one gets a visible mass equal to about 10^23 solar masses. Its Schwarzschild radius is thus of 30 billions of light years, while its physical size is of 48 billions of light years. The universe does not seem much different from a black hole!

The above observation provides the hint to Frampton's solution of the problem of dark energy. Quite simply, a relation can be written between the temperature at the event horizon (the second-to-last equation) and the acceleration (last equation!), and this agrees with experimental measurements of the expansion rate of the universe. Thus the apparent dark-energy effect may be just interpreted as a thermodynamical effect for this giant black hole.

Frampton discusses the results in a separate section. I can only quote a most meaningful statement:

My result calls into question almost all of the work done on quantum gravity, since the discovery of quantum mechanics. For gravity, there is no longer necessity for a graviton.In the case of string theory, the principal motivation for the profound and historical suggestion by Scherk and Schwarz that string theory be reinterpreted, not as a theory of the strong interaction, but instead as a theory of the gravitational interaction, came from the natural appearance of a massless graviton in the closed string sector.I am not saying that string theory is dead. What I am saying is, that string theory cannot be a theory of the fundamental gravitational interaction, since there is no fundamental gravitational interaction.

I confess that my understanding of the whole picture is too sketchy to allow me anything but the above summary -no insight, no extrapolations, no comment. For the little I know about the matter, I found no flaws in the reasoning described in the paper. So, before I leave the debate to the experts, all I can say is that the very concept of an accelerated expansion driven by a negative energy density has always looked a real stretch to me, and I never believed in the "official" explanation of the cosmological evidences that have piled up in the last dozen years.

I am now eager to read more about this article elsewhere. I will add links here if I find anything worth reading!

The numbers work out because the dark energy parameter is at the same scale as the observable universe. It is the same conincidence that has been used in anthropic arguments and would probably work in many other arguments. It is not convincing unless the theory is good. In this case I can see any real explanation of why the temerature or entropy should produce an acceleration on the same scale.

It also works only if you assume that the observed homogeniety of the universe stops at the current scale of the observable universe, otherwise the "black hole" would be bigger. Or he could be saying that the cosmological constant varies with the scale of the universe, but the required relationship is probably not consistent with observation.