Given our assumption that the universe is exactly flat, the missing mass problem is that there is not enough observable material so that in Newtonian cosmology the gravitational binding energy can exactly balance the kinetic energy, to give total energy zero, as required for a flat universe. Some physicists argue that in general relativity, the gravitational potential energy is just represented by the curvature term. But it is not clear that curvature can balance the much larger rest energy term
E = mc2.
The visible (luminous mass) accounts for only about 4-5 percent of the needed mass. Studying the rotation curves of galaxies and galaxy clusters reveals an invisible mass (called
dark matter) contained inside the galaxies and clusters that amounts to perhaps 5-6 times the visible matter.
Current cosmological theory accounts for the balance of missing mass by
dark energy, also known as
vacuum energy or the
cosmological constant.
An alternative source for the missing mass is that there may be more dark matter
between the galaxies and clusters, in the intergalactic medium. This cannot be detected by rotation curve analysis. Matter distributed outside a sphere enclosing a galaxy cannot affect its interior motions.
The intergalactic medium is assumed to be made of visible filamentary structures made of ionized hydrogen plasma surrounding large empty volumes called voids. If the voids contained dark matter, they would still appear to be empty. We find it plausible that the intergalactic medium contains about 3 times the density of visible and dark matter in galaxies and clusters.
This amount of dark material can close the universe and explain its flatness. But it does not explain the apparent expansion acceleration seen in Type 1a supernovae. This may be an artifact of the assumption they are perfect "standard candles."
Recent evidence suggests that the distant Type 1a supernovae are in a different population than those nearby.
Calculating Missing Mass in the Intergalactic Medium
Given that there is invisible dark matter inside gravitationally bound galaxies and galaxy clusters, amounting to between 5 and 6 times the visible luminous matter, it seems clear there is some of the same dark matter in the intergalactic medium. There are a number of ways we can estimate the intergalactic dark matter.
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We could work by comparison to the dark matter inside the galaxies. It has presumably escaped capture by the luminous objects, for example by accretion to their surfaces. This depends on a balance between stellar winds or radiation pressure that push matter away, and the gravitational pull of the objects.
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We can calculate the depths of gravitational potential wells of objects inside galaxies and compare it to the estimated temperature of the dark matter. The Boltzmann factor
e-E/kT will then show how equipartition of energy has distributed matter into energy levels high enough to escape capture by the objects.
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By comparison, the depths of the gravitational wells of the galaxies and clusters will determine the intergalactic dark matter density, depending on the assumed temperature of the intergalactic medium.
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As a first approximation, if the wells and temperatures are similar, we would expect a similar ratio of the order of 5 times as much dark matter in the intergalactic medium as the combined visible and dark matter inside the galaxies and clusters. This is more than enough to provide the missing mass. Half that amount would be enough.
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A computer simulation of moving dark matter inside galaxies and clusters could then be run for matter outside.
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The visible stellar and galactic objects have significant negative entropy, the result of our cosmic creation process. We might calculate the total negative entropy. The second law of thermodynamics says that an equal or greater amount of positive entropy must have been carried away from the local pockets of low entropy. The positive entropy is presumably in the energy radiated away and matter convected away. The radiation field is known. Can we calculate how much intergalactic matter would be needed to contain the positive entropy required by the second law?
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