# Advances in Astrophysics

### How are Cosmic Photons Redshifted?

Download PDF (488.4 KB) PP. 1 - 8 Pub. Date: February 1, 2017

### Author(s)

**H.-J. Fahr**^{*}

Argelander Institut für Astronomie, Universität Bonn Auf dem Hügel 71, 53121 Bonn, Germany**M. Heyl**

Deutsches Zentrum für Luft und Raumfahrt (DLR) Königswinterer Str. 522 - 524, 53227 Bonn, Germany

### Abstract

*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

*S*

_{r}was smaller by roughly a factor of

*S/S*

_{r}_{ }= 1 +

*z*

_{r}= 1100 compared to the present scale

*S*=

*S*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

_{0}*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*-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

^{-4}*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*. 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.

^{-3}### Keywords

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