mathman said:There is a parameter Ω, which is related to the total mass + energy of the universe. A flat universe is given by Ω =1. Current estimates of baryonic matter + dark matter + dark energy add up to Ω = 1.
Calimero said:By measuring distance and redshift to type Ia supernovae we can track expansion history. Since expansion depends on density we see that observations fit with omega=1.
The best current evidence stems from the combination of CMB and BAO data.TrickyDicky said:Yeah, but that estimates are mainly from the CMB angular power spectrum, my question was what other observational evidence is there?
I should mention that the supernova measurements are almost completely degenerate with the curvature (this is because for supernovae, the curvature is almost completely degenerate with the intrinsic brightness, which is not very well-known and is fit as a free parameter for most SN data analysis computations). But they do constrain other cosmological parameters, in particular the ratio between matter density and dark energy density.Ich said:For illustration, see http://supernova.lbl.gov/Union/figures/Union2_Om-Ol_systematics_slide.pdf" . Any two of the three (BAO, SN,CMB) indicate flatness, but only combinations including CMB give strong constraints.
When we say that the observable universe is spatially flat, it means that the universe has a flat geometry on a large scale. This means that the angles of a triangle drawn on the surface of the universe would add up to exactly 180 degrees, just like in Euclidean geometry. This is in contrast to a curved or non-Euclidean geometry, where the angles of a triangle would add up to more or less than 180 degrees.
Scientists have used various methods to measure the curvature of the universe, such as studying the cosmic microwave background radiation and observing the distribution of galaxies. These measurements have consistently shown that the universe is very close to being spatially flat, with a margin of error of less than 1%. This indicates that the observable universe is indeed flat on a large scale.
A flat observable universe has significant implications for our understanding of the cosmos. It suggests that the universe is infinite in size, has always existed, and will continue to exist forever. It also supports the idea of the universe undergoing a period of rapid expansion in its early stages, known as inflation. Additionally, a flat universe is consistent with the theory of dark energy, which is thought to be responsible for the accelerated expansion of the universe.
There have been some competing theories to the idea of a flat observable universe, such as the idea of a closed universe with positive curvature or an open universe with negative curvature. However, these theories have largely been ruled out by observational evidence. One alternative theory is the idea of a "bumpy" universe, where there are small fluctuations in the curvature of space, but overall it is still considered to be flat.
The concept of a flat observable universe does not necessarily imply the existence of an "edge" to the universe. In fact, the idea of a flat universe suggests that it is infinite in size, with no boundaries or edges. However, our observable universe is limited by the distance that light has had time to travel since the beginning of the universe, so we can only see a certain portion of the entire universe. This can sometimes be confused with the idea of an edge, but in reality, the universe may extend infinitely beyond what we can observe.