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Flatness problem questions Big Bang accuracy.


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The flatness problem is an observational problem that results from considerations of the geometry associated with a Friedmann-Lemaître-Robertson-Walker metric. In general, the universe can have three different kinds of geometries: hyperbolic geometry, Euclidean geometry, or elliptic geometry. The geometry is determined by the total energy density of the universe (as measured by means of the stress-energy tensor): hyperbolic results from a density less than the critical density, elliptic from a density greater than the critical density, and Euclidean from exactly the critical density. The universe is required to be within one part in 1015 of the critical density in its earliest stages. Any greater deviation would have caused either a Heat Death or a Big Crunch, and the universe would not exist as it does today.

flat universe.
The overall geometry of the universe is determined by whether the Omega cosmological parameter is less than, equal to or greater than 1. From top to bottom: geometry in a closed universe, an open universe and a flat universe.

A possible resolution to this problem is again offered by inflationary theory. During the inflationary period, spacetime expanded to such an extent that any residual curvature associated with it would have been smoothed out to a high degree of precision. Thus, it is believed that inflation drove the universe to be very nearly spatially flat.

Magnetic monopoles of the flatness problem.

The magnetic monopole objection was raised in the late 1970s. Grand unification theories predicted point defects in space that would manifest as magnetic monopoles with a density much higher than was consistent with observations, given that searches have never found any monopoles. This problem is also resolvable by cosmic inflation, which removes all point defects from the observable universe in the same way that it drives the geometry to flatness.

The flatness problem and Baryon asymmetry.

It is not yet understood why the universe has more matter than antimatter. It is generally assumed that when the universe was young and very hot, it was in statistical equilibrium and contained equal numbers of baryons and anti-baryons. However, observations suggest that the universe, including its most distant parts, is made almost entirely of matter. An unknown process called baryogenesis created the asymmetry. For baryogenesis to occur, the Sakharov conditions, which were laid out by Andrei Sakharov, must be satisfied. They require that baryon number be not conserved, that C-symmetry and CP-symmetry be violated, and that the universe depart from thermodynamic equilibrium. All these conditions occur in the Standard Model, but the effect is not strong enough to explain the present baryon asymmetry. Experiments taking place at CERN near Geneva seek to trap enough anti-hydrogen to compare its spectrum with hydrogen. Any difference would be evidence of a CPT symmetry violation and therefore a Lorentz violation.

The flatness problem and globular cluster age.

In the mid-1990s, observations of globular clusters appeared to be inconsistent with the Big Bang. Computer simulations that matched the observations of the stellar populations of globular clusters suggested that they were about 15 billion years old, which conflicted with the 13.7-billion-year age of the universe. This issue was generally resolved in the late 1990s when new computer simulations, which included the effects of mass loss due to Stellar winds, indicated a much younger age for globular clusters. There still remain some questions as to how accurately the ages of the clusters are measured, but it is clear that these objects are some of the oldest in the universe.


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