The horizon problem (homogeneity problem) arises due to the difficulty in explaining the observed homogeneity of casually disconnected regions of space in the absence of a mechanism that sets the same initial conditions everywhere. The size of the universe is too large for homogeneity, since thermalization faster than the speed of light is considered impossible.
I propose the simplest solution of this problem based on the proposal that the universe in its early stages was not in a hot state but in a pure, metastable quantum state:
Melkikh A.V. A pure quantum universe as an alternative to inflation
Article A pure quantum universe as an alternative to inflation
If the moving particles of the universe were entangled with each other, then these particles will simultaneously transit into their mixed state, no matter how far apart they are. This means that their further thermalization (associated with the creation and annihilation of other particles) will depend on the degree of entanglement of the initial state, but not on the size of the system.
Dear Alexey,
The existance of the horizon problem in cosmology is due to have a finite velocity of light and no due to initial metastable states. Notice that even a metastable state, which may be considered a kind of temporary energy trap or a somewhat stable intermediate stage of a system the energy of which may be lost in discrete amounts is very difficult to justify.
The horizon problem (also known as the homogeneity problem) is a cosmological fine-tuning problem within the Big Bang model of the universe. It arises due to the difficulty in explaining the observed homogeneity of causally disconnected regions of space in the absence of a mechanism that sets the same initial conditions everywhere.
Greeting
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