"AA" == Allan Adler writes:

AA At the risk of uttering complete nonsense, I'd like to describe
AA something I've been wondering about for a while, namely whether
AA the density of light in the universe might be related to the
AA problem of dark matter and dark energy.

AA If one takes all of the light in the universe, it has a certain
AA mass and therefore it exerts a certain gravitational force on the
AA matter in the universe. I don't know how much that force is taken
AA into account in computations of the rate of expansion of the
AA universe. For example, what is the total gravitational attraction
AA exerted by the light from the cosmic background radiation?

A better way to state it (so as to avoid the endless discussions about
whether light has mass or not) is to note that light has energy.
Gravitation depends upon the total energy density, which of course
includes the rest-energy (i.e., mass) of an object but is not limited
to that. Thus, the light in the Universe contributes to an energy
density, which will affect the Universe's expansion.

The crucial aspect for the Universe's expansion is the critical
density. This is the density at which gravitation can just balance
the expansion. If the Universe's density is above the critical
density, it recollapses; if it is below, it expands forever. (This
all assumes that the cosmological constant is zero or that there is no
dark energy, but it is still a useful way of characterizing the
problem.)

The critical density of the Universe is about 1E-29 g/cm^-3, or
equating mass and energy, about 1E-8 erg/cm^-3.

The energy density of the cosmic microwave background is
4.2E-13 (1+z)^4 erg/cm^-3 at a redshift z. At the current epoch
(z=0), the ratio of the energy density of light in the Universe to the
critical density is about 1E-5.

We think that the total mass density (from both dark and luminous
matter) is within 30% or so of the critical density. Thus, in the
current epoch, radiation (in the form of the cosmic microwave
background) is about 10,000 times too rarified to explain dark matter.

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