How are Cosmic Photons Redshifted?

Abstract

According to present cosmological views, the energy density of CMB (Cosmic Microwave Background) photons, freely propagating through the expanding cosmos, varies proportional to 1/S 4 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.

On the Cosmology of Electromagnetic Wave Energy in Expanding Universes

“…Interestingly enough, this result is identical with the earlier finding by Fahr & Heyl (2017) where the free propagation of light from the recombination period onwards has been investigated on the basis of a "particle point of view", i.e. a cosmic photon view.…”

“…it is conciliatory with the general expectation that the energy density of CMB photons scales with 1/S 4 , since this is what in fact the observer with a present-day spectrometer sees. it also confirms -now regarding wavemodes from a photon view -the recently published idea of [12] that photons in their peculiar photon rest frame do not suffer from the expansion of the universe. and it supports the idea in the above mentioned paper that the total electromagnetic energy density at present times, which is roughly by a factor z = 1100 higher than in the standard model (S −3 instead of S −4 ), is comparable with the energy density of matter and can therefore explain a certain amount of "Dark Matter".…”

“…Treating cosmic photons as particles this would imply that the energy density of such cosmic photons would decrease as S −3 in contrast to the prediction of the standard cosmology saying that it decreases like S −4 . As shown by [12] this result has substantial consequences for the contribution of photons to the cosmic energy-momentum tensor in the present days of the universe. In the following article we want to analyse deeper whether these most relevant implications are only due to the particle view which was applied to photons by [12], or whether these results also find their support when taking as alternative a wave-view to the cosmic CMB photons.…”

“…[7], [8], [9], [10], [11]. Only most recently then a paper was published ( [12]) where the nowadays well accepted canonical GTR interpretation of the cosmic photon redshift was rediscussed and at least rejected in parts. The main point therein was that cosmic photons in their own proper system, while propagating on cosmic light-geodetics, do not experience the touch of the expanding universe and do not change their proper energy, rather the cosmological energy loss is only registered later, when these photons at some later cosmic times are measured, i.e.…”

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“…, 16 but also see alternative views by Fahr and Heyl, 17,18 while, to the contrary, proton and electron temperatures purely reflecting the effect of the Hubble migration, as shown in Fahr, 14 both are increasing, thus creating along the standard view evidently a strange, even escalating NLTE-situation with , .…”