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Originally Posted by AntonioLao  One of the objectives of the mission of the satellite named WMAP/NASA launched in June 30, 2001 was to measure the mass contribution from positive curvature of space-time as well as the contribution from the negative curvature. See http://map.gsfc.nasa.gov/. What it found is that these contributions, within 2% accuracy of the measurements, exactly cancel each other. The clincher is that the universe is flat. From theoretical considerations it has been known for a long time that a particular solution of Einstein’s field equations of general relativity described a Euclidean four dimensional space-time flatness model. See http://en.wikipedia.org/wiki/Einstein_field_equations |
Solutions (that are useful) to the Einstein Field Equations are Lorentzian. This means that the signature is (-+++). A Euclidean metric would have signature (++++). What you mean is a 3 dimensional euclidean metric with a time component to make up the 4D spacetime. I presume you are talking about Minkowski spacetime here. Note that, since we know space is expanding, we cannot live in a Minkowski spacetime. If the universe is (globally) flat, then we will adopt the Friedmann Robertson Walker spacetime, with k=0 (i.e. zero curvature).