What is the mass equivalent of all forms of energy in the universe?

According to Einstein's famous equation E = mc^2, every form of energy is equivalent to a certain amount of mass. This mass is subject to the force of gravity, and it is natural to ask how much mass is present in the universe in all known forms of energy. There are believed to be several important kinds of sources of energy in the universe in addition to the protons, neutrons and electrons that make up all the known forms of matter. All of the following estimates are with respect to the critical density of the universe which is set by its expansion rate. For a 'Hubble constant' of 50 km/sec/megaparsecs, the critical density in equivalent grams per cubic centimeter is 5 x 10^-30 grams per cubic centimeter; about equal to one hydrogen atom in a container 130 centimeters on a side averaged over the entire visible universe. This defines the co-called Critical Density of the universe.

Cosmic Background Radiation: The famous microwave 'fireball' radiation contributed by about 10 billion photons for every quark in the universe, at a temperature of 2.7 K. If we add up the energy per photon in this radiation field, we would arrive at a density of energy that is less than 1 percent of the Critical Density. The following are off the top of my head rough estimates for the different contributions:

Neutrinos If lab experiments are correct, electron neutrinos have a small but finite rest mass between 5 - 10 eV which would be enough to provide at most about 20 percent of the Critical Density of the universe for an expansion rate of 50 kilometers/sec/megaparsec.

Cosmological Constant In every cubic centimeter of space there may exist a new physical 'scalar' field that contributes to the energy of the vacuum state. Based on a variety of upper limits set by astronomical observations, the magnitude of this contribution to the universe is probably less than 20 percent of the Critical Density.

Baryonic matter Of course all of the luminous matter we can see, and all of the matter glowing in intergalactic space via x-rays, contribute to the total mass of the universe by definition. Currently, we seem to be able to find about 1 percent of the Critical Density in this form of mass, and the cosmological deuterium abundance is a very sensitive barometer of just how much baryonic matter there can be. Too much, and the density of the universe a few minutes after the Big Bang would have been high enough to cook all the deuterium into helium. Too little, and the deuterium abundance would be much higher than what we now seem to find. The bottom line seems to be that not more than about 10 percent of the Critical Density can be in the form of baryons of ANY kind, including forms that are undetectable by direct observation.

Gravity In order for the universe to be 'critical', meaning that it is exactly 'flat' and destined to expand indefinitely, the sum of all of the above forms of energy has to equal the effective rest mass of the cosmological gravitational field, which can be thought of ( though not meaningfully) as having negative effective mass. The goal is to balance the total gravitational energy of the universe against its internal energy in all forms. We don't know, a priori, just how much gravitational energy the universe has, and we are trying to get a handle on this by adding up all of the known forms of contributions to it, and then assuming a particular global geometry to space time. The calculation of the Critical Density assumes a globally flat, Euclidean space-time which is infinite and requires the universe to expand indefinitely. A hyperbolic, negatively-curved geometry requires for the current expansion rate, that the density of mass be less than the critical amount for a Euclidean space-time. And for a closed universe destined to recollapse in the future, the density of mass must exceed the Critical Density.

Which one of these is correct is largely a matter of philosophical choice. If you believe that the universe ought to be open, infinite and 'critical' then the various contributions to the observed density of the universe fall short of the Critical Density by factors from 2 to 5. The difference is made up by what astronomers call 'missing mass'. If you believe that we have already itemized all of the significant forms of mass and prefer ao open, infinite but hyperbolic global geometry, then your work is done and you can go home. If you want the universe to be closed, finite and destined to recollapse, then you have some work to do to find more than 2 - 5 times the mass we can now identify in known forms of mass and energy ( and their upper limits ).


Copyright 1997 Dr. Sten Odenwald
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