I don't know whether this has much general interest. I am interested by communication horizons in cosmology, or causal horizons if you prefer. This paper claims to study several cases including how far apart two quasars would have to be to have been out of contact ever since the end of the putative inflation epoch. That is very far back---the very start of post-inflationary expansion. It struck me as impressive to attempt to calculate these things, especially if they can do a creditable job. So here's the paper:(adsbygoogle = window.adsbygoogle || []).push({});

http://arxiv.org/abs/1305.3943

The Shared Causal Pasts and Futures of Cosmological Events

Andrew S. Friedman, David I. Kaiser, Jason Gallicchio

(Submitted on 16 May 2013)

We derive criteria for whether two cosmological events can have a shared causal past or a shared causal future, assuming a Friedmann-Lemaitre-Robertson-Walker universe with best-fit ΛCDM cosmological parameters from the Planck satellite. We further derive criteria for whether either cosmic event could have been in past causal contact with our own worldline since the time of the hot "big bang", which we take to be the end of early-universe inflation. We find that pairs of objects such as quasars on opposite sides of the sky with redshifts z ≥ 3.65 have no shared causal past with each other or with our past worldline. More complicated constraints apply if the objects are at different redshifts from each other or appear at some relative angle less than 180 degrees, as seen from Earth. We present examples of observed quasar pairs that satisfy all, some, or none of the criteria for past causal independence. Given dark energy and the recent accelerated expansion, our observable universe has a finite conformal lifetime, and hence a cosmic event horizon at current redshift z = 1.87. We thus constrain whether pairs of cosmic events can signal each other's worldlines before the end of time. Lastly, we generalize the criteria for shared past and future causal domains for FLRW universes with nonzero spatial curvature.

38 pages, 16 figures, submitted to Physical Review D

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# Criteria for causal independence (new paper, Planck data)

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