# Space flatness

1. Jul 29, 2010

### TrickyDicky

Besides the power spectrum from the CMB, what other observational evidences suggest that our observable universe is spatially flat?

Thanks

2. Jul 29, 2010

### mathman

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.

3. Jul 29, 2010

### TrickyDicky

Yeah, but that estimates are mainly from the CMB angular power spectrum, my question was what other observational evidence is there?

4. Jul 29, 2010

### Calimero

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.

5. Jul 29, 2010

### TrickyDicky

I believe is the other way around, we assume a flat model first (later confirmed by CMB) and we fit the SN observations in that model, getting as a result an accelerated expansion that introduced a new parameter, dark energy. So the SNIa observations fit the model, they are not in itself evidence of flatness.

6. Jul 29, 2010

### Calimero

No, you got it wrong. It is flat because omega is 1. For some other value it will not be flat. In addition you can calculate it as (3c^2Ho^2)/8piG, and many measurments confirmed Hubble parametar to Ho=71 km/sec per mpc.

7. Jul 30, 2010

### Chalnoth

The best current evidence stems from the combination of CMB and BAO data.

The CMB sets a length scale of our universe at a redshift of $z=1090$. Baryon Acoustic Oscillations, on the other hand, set a length scale of our universe around roughly $z=1$ to $z=2$. This extremely long lever arm lets us do the equivalent of drawing a huge triangle across the universe, a triangle that we can then check the angles of and see if they add up to 180 degrees.

8. Jul 30, 2010

### Ich

For illustration, see http://supernova.lbl.gov/Union/figures/Union2_Om-Ol_systematics_slide.pdf" [Broken]. Any two of the three (BAO, SN,CMB) indicate flatness, but only combinations including CMB give strong constraints.

Last edited by a moderator: May 4, 2017
9. Jul 30, 2010

### Chalnoth

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.

It's also worth mentioning that as you can see from that plot, CMB alone doesn't actually constrain curvature all that much. But all you need to do to get it to constrain curvature is add a measurement of the nearby Hubble expansion rate. This anchors the CMB observations, allowing curvature to be tightly constrained.

Last edited by a moderator: May 4, 2017