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How are Cosmic Photons Redshifted?
Authors: H.-J. Fahr, M. Heyl
Number of views: 486
According to present cosmological views, the energy density of CMB (Cosmic Microwave
Background) photons, freely propagating through the expanding cosmos, varies proportional to
1/S4 with S being the scale factor of the universe. This behavior is expected because General
Theory of Relativity, in application to FLRW- (Friedmann-Lemaitre-Robertson-Walker) cosmological
universes, leads to the conclusion that the photon wavelengths increase during their free passage
through the spacetime metrics of the universe by the same factor as does the scale factor S. This
appears to be a reasonable explanation for the presently observed Planckian CMB spectrum with
its actual temperature of about 2.7 K, while at the time of its origin after the last scattering during
the recombination phase its temperature should have been about 3000 K, at an epoch of about
380 ky after the Big Bang, when the scale of the universe Sr was smaller by roughly a factor of
S/Sr = 1 + zr = 1100 compared to the present scale S = S0 of the universe. In this paper we start
from putting the question whether the scale-behavior of the CMB energy density that enters the
energy-momentum tensor of the field equations describing the expanding universe is really falling
off like S
−4
and, if in fact a deviation from a behavior according to S
−4 would occur, why do we
nevertheless presently observe a CMB energy density which appears to be in accordance with such
a S
−4
-scaling? This question arises from another basic and fundamental question, namely: Can we
really assume that the wavelength of the freely propagating photon during its travel all the way
along its light geodetic is permanently affected by the expansion of the universe, i.e continuously
recognizes the expansion of the cosmic scale S? With other words: Do freely propagating photons
really undergo a permanent change of their wavelengths when freely traveling through cosmic
space-time or is the observationally apparent energy loss of cosmologically red-shifted photons an
effect which only occurs just in the moment of photon registration at some specific world point? If
the latter would prove to be true , then it would mean that the energy density of freely propagating,
non-interacting CMB photons, due to non-changing, conserved wavelengths, is behaving with respect
to cosmic scale variation different from conventional expectations, but rather would turn out to
behave just like the energy density of matter, namely according to S
−3
. Hence the photon part of
the energy momentum tensor would become different and associated solutions of FLRW-equations
would undergo corresponding modifications. In consequence, the CMB energy density as far as
it enters the energy-momentum tensor generated by freely propagating CMB photons during the
expansion period of the universe after the recombination era would no longer become negligible for
the cosmic dynamics, since its value would stay in the same order of magnitude as that of baryonic
or dark matter.