Cosmology, Inflationary

The Flatness Problem

Numerous observational hints independendy suggest that the density parameter of the universe is Ω = 1 with tight tolerance. That is to say, the mean density of the universe is close to a value known as critical density, which separates a universe of eternal expansion (Ω < 1) from one that is to turn its expansion to a collapse in a remote future (Ω > 1) due to the gravitational deceleration effect of its high mass content. In terms of Einstein's general theory of relativity, the cosmological classification according to the mean density is identical to 1, according to the intrinsic geometry of space: While a density parameter Ω > 1 comes along with a “closed” geometry (the three-dimensional equivalent of a spherical surface), the under-critical “open” Ω < 1 universe is affected by the intrinsic geometry of a saddle. The limiting special case Ω = 1 finally accords to a flat (“ Euclidean”) geometry of a plane surface. The cosmological standard model predicts that any small deviation from Ω = 1 in the early universe will be amplified massively in the course of time. Thus the universe should have a density parameter that is orders of magnitude larger or smaller than 1. Or, on the other hand, Ω has to be extremely close to 1 right after the big bang. This is a classical problem of fine-tuning.

The Horizon Problem

In theories of time and space one frequently uses the term past light cone of an event. An event is a point that determines a “here and now” in spacetime. The past light cone of an event E contains all events (points of spacetime) E, in the past of E from which light or information could have reached the event E. An event E is able to influence a (future) event E only if E lies within the past light cone of <>

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