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It is known that all observers will agree on the position of the black hole event horizon. But what about the cosmic horizon of the de Sitter space? Can one say that the horizon of scientist1 is different from the horizon of scientist2?

If so, it turns out that the scientists are researching different universes: the information available for scientist1 is forever lost for scientist2. This may lead to the information loss paradoxes if the observers can communicate.

This question was sparked by the answers to this question: Can matter leave the cosmic horizon?

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Anixx
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Yes, the cosmic horizons are observer-dependent. After all, spaces like de Sitter space are maximally symmetric which means that all of their points are equally good as all other points. There can't be a privileged submanifold.

This observer-dependence doesn't lead to any information loss even if one assumes that there is no physics beyond the cosmic horizon because the information that seems to penetrate the cosmic horizon according to a different observer is really stored at the cosmic horizon itself according to the first observer.

Luboš Motl
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Yes, both scientists have different horizons. But this doesn't lead to information paradoxes, because their ability to communicate will also depend on their horizons.

Let's start with the cosmic particle horizon (the edge of the observable universe). Suppose that there is a distant galaxy near the edge of the current particle horizon of scientist 1, but still outside the particle horizon of scientist 2. For simplicity, suppose that both scientists and the galaxy lie on a straight line.

Now, scientist 1 observes the galaxy, which means that some of its photons have reached him. The exited scientist wants to send his observations to scientist 2. But during that time, some photons of the galaxies have passed scientist 1, and are on their way to scientist 2, ahead of the message. So by the time he gets the message from his colleague, he'll have observed the galaxy himself. That is, the galaxy has entered the particle horizon of scientist 2.

What about the cosmic event horizon? Suppose that a galaxy lies inside the current event horizon of scientist 1, but outside the current event horizon of scientist 2. If that galaxy sends out photons at the current cosmic time, they will reach scientist 1 at some point in the future, but they will never reach scientist 2. Will that lead to a paradox?

No, because when scientist 1 receives the photons, he himself will have moved outside the event horizon of scientist 2. So he'll never be able to communicate his observations to his colleague.

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