Is the Universe Really Flat?

Reading: Chapter 26: Cosmology

How do we go about determining the ultimate fate of the Universe?

We have gone through this course taking the Universe to be flat. Upon what evidence is this important conclusion based? How solid is this evidence? We now consider these questions.

Tests for the Appropriate Solution

• Dynamical Tests: H_o & Mass, Peculiar Velocities
• Topological Tests: Type Ia SN

  Above: Schematic illustration of how at large redshift z, the Hubble relation deviates from a line. Note that the axes on the plot have been reversed, the Distance is the vertical axis and the redshift is the horizontal axis. Right: Using the bright Type Ia SN as standard candles, the Hubble relation is followed to z ~ 1 to find the deviation from a line.

• Cosmic Microcwave Background Radiation (CMBR) Observations (WMAP):
  Small differences in the CMBR temperature across the sky have been measured by the Wilkinson Microwave Anisotopy Probe (WMAP) and have quantified how much the CMBR departs from a smooth, featureless Universe.

  To remind you, the fluctuations are tiny, much less than 0.001 Kelvin the Dipole Anisotropy.

  The shape of the Universe affects the amount and distribution of fluctuations on small scales in the Universe. This suggests a flat Universe. Further, the sizes of the fluctuations tell us how inhomogenoues the Universe was at Recombination. Given the current size of the structures in the current Universe, this helps to tell us how much Dark Matter there is in the Universe! The fact that the Universe is flat and we can infer the amount in the Universe from the CMBR, any difference must be due to the existence of Dark Energy.

  Further information gleaned from the fluctuations in the CMBR suggest that the inflationary model is correct (and hence the Universe is flat). Below is shown a representation of the evolution of the scale factor of the Universe upon which is superimposed various events of note in the evolution of the Universe.

  

  Best-fit modeling

  ===> 73 % of the Universe is Dark Energy; the luminous galaxy part of the Univese ~ 0.7 %; the baryon part of the Universe ~ 4 %; and the Dark Matter part of the Universe ~ 23 %.