# The cosmological horizon problem

In GR cosmology, there is a big bang singularity. For every particle, there was only a finite time in the past. During this finite time, only a finite distance may have been reached. This allows to define a horizon of influence for each event — all events which may have had a common cause in the past, after the big bang itself.

Now, in standard GR cosmology this horizon is small. Too small to explain some observable facts:

• First, the horizon is too small to explain why the background radiation is homogeneous. Usually one would use thermodynamics to explain such a homogeneous temperature distribution. But thermodynamics would require enough time, enough causal connection, to become established. Such causal interaction is, unfortunately, forbidden by the quite small cosmological horizon.
• Moreover, in this homogeneous background radiation are inhomogenities — the origin of the inhomogenities we observe today as galaxies, galaxy clusters and other big structures. To explain all these observable inhomogenities, we have to assume some initial small fluctuations. But the size of the fluctuations which are required for this purpose is much greater than the horizon size in the early universe.

The second problem is much more serious. That some completely homogeneous distribution may have been caused by something else, last but not least homogeneous initial values, seems to be a meaningful assumption, based on Ockham's razor. But if initial fluctuations are greater than horizon size, this requires a very strange conspiracy, forbidden by current physics.

### GR solution: Inflation theory

The GR solution of this problem is inflation in the early universe. That means, some additional mechanism (with some hypothetical origin in particle physics) has to give an additional term in the early universe. This additional term leads to an acceleration of the expansion of the universe ($$a''(\tau)>0$$).

That inflation solves this problem seems to be the main reason why it is widely accepted in cosmology.

### GLET solution

In GLET we have, for the choice $$\Upsilon>0$$, no big bang singularity and therefore no horizon problem.

In some more general, technical meaning of the word "inflation" (meaning only a period where $$a''(\tau)>0$$ or the expansion is accelerating) for $$\Upsilon>0$$ the related terms of GLET leads to inflation if the state of the universe is sufficiently dense.

### Comparison

Thus, to sove the horizon problem, GR needs some additional mechanism, which has to be originated in something else, like particle physics. GLET cosmology does not require such an additional mechanism. Instead, the GLET parameter $$\Upsilon$$, which solves the horizon problem in GLET, follows from completely independent axioms of GLET.