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 15 to 20 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

There is much more dark matter mass than visible, glowing matter. Some of the dark matter is regular sort of matter (atoms) that is too faint for us to detect such as dead burned out stars, planets, brown dwarfs, gas + dust clouds, etc. The rest of the dark matter is made of material that is not made of atoms or their constituent parts. This strange material has a total mass about five times more than the total mass of the ordinary matter. Some evidence for the presence of dark matter has already been presented in the previous chapters. The list below summarizes the evidence for dark matter's existence.

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).

    the Milky Way's rotation curve

    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.

    velocity dispersion of elliptical galaxies

    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 be around 0.3.

    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. Inventorying all of the ordinary matter in the lensing galaxy clusters (those that lens the light from distant galaxies) and comparing it to the total mass of the galaxy clusters gives a five-to-one ratio of dark matter to ordinary 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. The more recent observation of the MACS J0025.4-1222 cluster collision has shown the same sort of separation of dark matter from ordinary matter.

    Bullet cluster shows dark matter separating from regular matter

Current tallies of the total mass of the universe (visible and dark matter) indicate that there is only 32% of the matter needed to halt the expansion---we live in an open universe. Ordinary matter amounts to almost 5% and dark matter makes up the other 27%. One possible dark matter candidate was the neutrino. There are a lot of them, they have neutral charge and photons do not bump into them. Unfortunately, their mass is too small and they move much too fast to create the clumpy structure we see of the dark matter and ordinary matter. The universe would not have been able to make the galaxies and galaxy clusters if the dark matter was neutrinos. To create the lumpy universe, astronomers are looking at possible massive neutral particles that move relatively slowly. Various candidates fall under the heading of "WIMPs"—weakly interacting massive particles (sometimes, astronomers & physicists can be clever in their names). Another possible dark matter candidate was simply ordinary matter locked up in dim things like white dwarfs, brown dwarfs, neutron stars, or black holes in the halos of the galaxies. These massive compact halo objects ("MACHOs") can be detected via microlensing like that used to detect exoplanets. Some MACHOs have been found but the number (and resulting mass) of them appears to be much too small to account for the dark matter. Big Bang nucleosynthesis and the microwave background radiation (as described below) also provide a strict upper limit on the amount of ordinary matter that could produce the MACHOs in any case. Astronomers and physicists are also exploring the strong possibility that 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.

how angular size of fluctuations depends on geometry of universe

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 (to within 0.4% uncertainty). 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, a result confirmed by the even higher precision Planck satellite with over 2.5 times higher resolution than WMAP. This result from the WMAP and Planck satellites and the too meager amount of matter in the universe to make the universe geometry flat along with the observed acceleration of the universe's expansion rate (discussed in the last section of this chapter) are forcing astronomers to conclude that there is another form of energy that makes up 68.3% 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. Furthermore, the distribution of the sizes of the ripples shows that some sizes are preferred and other sizes are damped out as would be the case if the dark matter was different from ordinary matter. The size distribution, the spectrum of sizes, gives the ratio of dark matter to ordinary matter. Dark matter not made of atoms or other particles in the Standard Model makes up 26.8% of the critical density, leaving just 4.9% of the universe with what the rest of the previous chapters of this website have been about (ordinary matter). That ratio matches up very nicely with the ratios found using the other independent methods of Big Bang nucleosynthesis and the motions of galaxies.

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last updated: May 11, 2013

Is this page a copy of Strobel's Astronomy Notes?

Author of original content: Nick Strobel