Is The Universe Open or Closed?

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The curvature of the universe is determined by the density of the universe. You can do a cosmic inventory of all of the mass from ordinary matter in a representative region of the universe to see if the region's density is above the critical density. Such an inventory gives 10 to 20 times too little mass to close the universe. The primordial deuterium abundance provides a sensitive test of the density of ordinary matter in the early universe. Again, you get 5 to 15 times too little mass to close the universe. However, these measurements do not take into account all of the dark matter known to exist. Dark matter is all of the extra material that does not produce any light, but whose presence is detected by its significant gravitational effects.

Dark Matter

Orbital speeds of stars in galaxies

1. Flat rotation curves of spirals even though the amount of the light-producing matter falls off as the distance from the galaxy center increases. Remember the enclosed mass = (orbital speed)² × (orbit size)/G. Below is the rotation curve for our Milky Way Galaxy (a typical spiral galaxy).
   

   Also, the orbital speeds of stars in elliptical galaxies are too high to be explained by the gravitational force of just the luminous matter in the galaxies. The extra gravitational force is supplied by the dark matter in the ellipticals.

   

   Faint gas shells around ellipticals

2. Ellipticals have faint gas shells that need massive "dark" haloes to contain them. The gas particles are moving too quickly (they are too hot) for the gravity of the visible matter to hang onto it. However, the number of ellipticals with these faint gas shells is too large to be only a temporary feature of ellipticals. The dark haloes must extend out to 300,000 light years around each galaxy. The extent of this dark matter pushes W up to around 0.2. If the haloes are larger than originally thought, W could approach 1.

   Motion of galaxies in a cluster

3. Galaxy cluster members are moving too fast to be gravitationally bound unless there is unseen mass. The reasonable assumption is that we do not live at a special time, so the galaxies in the cluster must have always been close to each other. The large velocities of the galaxies in the clusters are produced by more gravity force than can be explained with the gravity of the visible matter in the galaxies.

   Hot gas in clusters

4. The existence of HOT (i.e., fast moving) gas in galaxy clusters. To keep the gas bound to the cluster, there needs to be extra unseen mass.

   Quasar spectra

5. Absorption lines from hydrogen in quasar spectra tells us that there is a lot of material between us and the quasars.

   Gravitational Lensing

6. Gravitational lensing of the light from distant galaxies and quasars by closer galaxies or galaxy clusters enables us to calculate the amount of mass in the closer galaxy or galaxy cluster from the amount of bending of the light. The derived mass is greater than the amount of mass in the visible matter.

   Dark Matter separation from ordinary matter

7. The collision of the galaxy cluster 1E 0657-56, called the "bullet cluster", with another galaxy cluster has produced a clear separation of the ordinary matter from the dark matter. The ordinary matter of one cluster is slowed by a drag force as it interacts with the gas (ordinary matter) of the other cluster. The dark matter is not slowed by the impact because it responds only to gravity and is not affected by gas pressure. In the picture below, the ordinary matter is colored pink---it is hot gas imaged by the Chandra X-ray Observatory. The blue areas are where most of the mass in the clusters is found (the dark matter). The dark matter locations were determined by gravitational lensing of light from background galaxies. Select the Chandra link to view animations of how the separation happened.
   
   

Current tallies of the total mass of the universe (visible and dark matter) indicate that there is only 26% of the matter needed to halt the expansion---we live in an open universe. Astronomers and physicists are exploring the possibility that perhaps there is an additional form of energy not associated with ordinary or dark matter, called "dark energy", that would greatly affect the fate of the universe. This is discussed in the last section of this chapter.

Deriving the Geometry of the Universe from the Background Radiation

An independent way to measure the overall geometry of the universe is to look at the fluctuations in the cosmic microwave background radiation. If the universe is open (saddle-shaped), then lines starting out parallel will diverge (bend) away from each other. This will make distant objects look smaller than they would otherwise, so the ripples in the microwave background will appear largest on the half-degree scale. If the universe is flat, then lines starting out parallel will remain parallel. The ripples in the microwave background will appear largest on the 1-degree scale. If the universe is closed, the lines starting out parallel will eventually converge toward each other and meet. This focussing effect will make distant objects look larger than they would otherwise, so the ripples in the microwave background will appear largest on scales larger than 1-degree. Select the image below to go to the WMAP webpage from which the image came.

The resolution of the COBE satellite was about 7 degrees---not good enough to definitively measure the angular sizes of the fluctuations. After COBE, higher-resolution instruments were put up in high-altitude balloons and high mountains to observe the ripples in small patches of the sky. Those experiments indicated a flat geometry for the universe. Cosmologists using the high resolution of the WMAP satellite to look at the distribution of sizes of the ripples confirmed that conclusion using its all-sky map of microwave background at a resolution over 30 times better than COBE. WMAP also gave a much improved measurement of the ripples. The distribution of the ripples peaks at the one-degree scale---the universe is flat. This result from the WMAP satellite and the too meager amount of matter in the universe to make the universe geometry flat is forcing astronomers to conclude that there is another form of energy that makes up 74% of the universe (called "dark energy" for lack of anything better). The "dark energy" is probably the "cosmological constant" discussed in the last section of this chapter.

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last updated: June 2, 2007