Horizon problem
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The horizon problem is a problem with the standard cosmological model of the Big Bang which was identified in the 1970s.
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Since information can travel no faster than the speed of light, there is a limit to the region of space that is in causal contact with any particular point in the universe. The extent of this region is a function of how long the universe has existed. The particle horizon is closely related to this idea and is where the problem gets its name from.
According to Big Bang, the recombining plasma that decoupled from the cosmic microwave background we currently observe was about <math>10^{88}<math> times the size of any causally connected region at that time, roughly 300,000 years after the Big Bang. Problematically, the near uniformity we observe in the cosmic microwave background suggests that this was not the case and that the entire plasma was causally connected.
Inflationary theory allows for a solution to the problem (along with several others such as the flatness problem) by positing a short 10-32 second period of exponential expansion (dubbed inflation) within the first minute or so of the history of the universe. During inflation, the universe would have increased in size by an enormous factor; enough to account for the observed isotropy of today's particle horizon looking back to the time the cosmic microwave background. The universe before inflation is causally connected and doesn't come back into causal contact until a much later time.
One consequence of cosmic inflation is that the anisotropies in the big bang are reduced but not entirely eliminated. Differences in the temperature of the cosmic background are smoothed by cosmic inflation, but they still exist. The theory predicts a spectrum for the anisotropies in the microwave background which is consistent with observations from WMAP and COBE.
Horizon problem in computer programs
The horizon problem in computer programs for playing board games (for example, computer chess) is a problem that arises when search depth is fixed. If one side has many ineffective threats that nonetheless require a response, the consequences of a bad move may be postponed beyond the limit of the search (the "horizon") and so not properly taken into account by the program. There are various approaches to solving the problem, most involving search extension.ca:Horitzó cosmològic