By three independent hints it will be demonstrated that still at present there is a substantial lack of theoretical understanding of the CMB phenomenon. One point, as we show, is that at the phase of the recombination era one cannot assume complete thermodynamic equilibrium conditions but has to face both deviations in the velocity distributions of leptons and baryons from a Maxwell-Boltzmann distribution and automatically correlated deviations of photons from a Planck law. Another point is that at the conventional understanding of the CMB evolution in an expanding universe one has to face growing CMB temperatures with growing look-back times. We show, however, here that the expected CMB temperature increases would be prohibitive to star formation in galaxies at redshifts higher than

The cosmic background radiation (CMB) has been continuously full-sky monitored since 1989 beginning with COBE, continued by WMAP [

At first it is the assumption that all relevant facts determining the global structures of the universe and their internal dynamics have been found at present times. This puts the question what part of the world may presently be screened out by our world horizon, which nevertheless influences the cosmological reality inside? If, as generally believed, the cosmic microwave background (CMB) sky is such a horizon, then everything deeper in the cosmological past must be invented as a cosmologic ingredient that never becomes an observational fact. On the other hand, when inside that horizon only something not of global but of local relevance is seen, then the extrapolation from what is seen to the whole universe is scientifically questionable.

In this paper we start out from a critical look on the properties of cosmic microwave background (CMB) radiation, the oldest picture of the universe, and investigate basic assumptions made when taking this background as the almanac of basic cosmological facts. Neither the exact initial thermodynamical equilibrium state of this CMB radiation is guaranteed, nor its behaviour during the epochs of cosmic expansion is predictable without strong assumptions on an unperturbed homologous expansion of the universe. The claim connected with this assumption that the CMB radiation must have been much hotter in the past may even bring cosmologists in unexpected explanatory needs to explain star formation in the early universe as will be shown.

It is generally well known that we are surrounded by the so-called cosmic microwave background (CMB) radiation. This highly homogeneous and isotropic black-body radiation [

Assuming that at the times before recombination matter and photons coexisted in perfect thermodynamical equilibrium, despite the expansion of the cosmic volume (we shall come back to this problematic point in the next section), then this allows one to expect that these cosmic photons initially had a spectral distribution according to a perfect black-body radiator, that is, a Planckían spectrum. It is then generally concluded that a perfectly homogeneous Planckían radiation in an expanding universe stays rigorously Planckían over all times that follow. At this point one, however, one has to emphasize that this conclusion can only be drawn if (a) the initial spectrum really is perfectly Planckiàn and if (b) the universe is perfectly homogeneous and expands in the highest symmetrical form possible, that is, the one described by the so-called Robertson-Walker spacetime geometry.

Then it can be demonstrated (e.g., see [

Readers should, however, keep in mind that this is only guaranteed, if the universe has isotropic curvature and expands in a homologous, Robertson-Walker symmetric manner. (see, e.g., [

The abovementioned theory of a homologous cosmic expansion then also allows to derive an expression for the cosmic CMB temperature as a function of the cosmic photon redshift

This relation taken together with Wien’s law of spectral shift

Usually it is assumed that at the recombination era photons and matter, that is, electrons and protons in this phase of the cosmic evolution, are dynamically tightly bound to each other and undergo strong mutual interactions via Coulomb collisions and Compton collisions. These conditions are thought to then evidently guarantee a pure thermodynamical equilibrium state, implying that particles are Maxwell distributed and photons have a Planckian blackbody distribution. It is, however, by far not so evident that these assumptions really are fulfilled. This is because photons and particles are reacting to the cosmological expansion very differently; photons generally are cooling cosmologically being redshifted, while particles in first order are not directly feeling the expansion, unless they feel it adiabatically by mediation through numerous Coulomb collisions, which are relevant here in a fully ionized plasma before recombination, like they do in a box with subsonic expansion of its walls. But Coulomb collisions have a specific property which is highly problematic in this context.

This is because Coulomb collision cross sections are strongly dependent on the particle velocity

In the following part of the paper we demonstrate that even if a Maxwellian distribution would still prevail at the beginning of the collision-free expansion phase, that is, the postrecombination phase era, it would not persist in the universe during the ongoing of the collision-free expansion. For that purpose let us first consider a collision-free population in an expanding Robertson-Walker universe. It is clear that due to the cosmological principle and, connected with it, the homogeneity requirement, the velocity distribution function of the particles must be isotropic, that is, independent on the local place, and thus of the following general form:

If we assume that particles, moving freely with their velocity

At the place where they arrive after passage over a distance

This then means for terms of first order that

Looking first here for interesting velocity moments of the function

and

It is perhaps historically interesting to see that assuming Hamilton canonical relations to be valid the Liouville theorem would then instead of (

In that case the first velocity moment is found with

That means in this case an adiabatic expansion is found, however, based on wrong assumptions!

Now going back to the correct Vlasow equation (

In order to fulfill the above equation obviously the terms with

This dependence in fact is obtained when inspecting the earlier found solutions for the moments

With that the above requirement (

This finally leads to the statement that a correctly derived Vlasow equation for the cosmic gas particles leads to a collision-free expansion behaviour that neither runs adiabatic nor does it conserve the Maxwellian form of the distribution function

Let us therefore now look into other basic concepts of cosmology to see whether perhaps also there problems can be identified which should caution cosmologists.

In the following part of the paper we now want to investigate whether or not the cosmological cooling of the CMB photons, freely propagating in the expanding Robertson-Walker space time geometry, can be confirmed by observations. The access to this problem is given by the connection that in an expanding universe at earlier cosmic times the CMB radiation should have been hotter according to cosmological expectations, for example, as derived in [

Assuming that molecular interstellar gas phases within these galaxies are in optically thin contact to the CMB that actually surrounds these galaxies allows one to assume that such molecular species are populated in their electronic levels according to a quasistationary equilibrium state population. In this respect especially interesting are molecular species with an energy splitting of vibrational or rotational excitation levels

The carbon monoxide molecule CO splits into different rotational excitation levels according to different rotational quantum numbers

Here

Usually it is hardly possible to detect these CO-fine structure emissions from distant galaxies directly, due to their weaknesses and due to the strong perturbations and contaminations in this frequency range by the infrared (i.e., ≥115 GHz). Instead the relative population of these rotational fine structure levels can much better be observed in absorption appearing in the optical range. To actually use such a constellation to determine the relative populations of CO fine structure levels one needs a broadband continuum emitter in the cosmic background behind a gas-containing galaxy in the foreground. As in case of the object investigated by Srianand et al. [

Though this clearly points to the fact that CMB temperatures

First of all, observers with similar observations are often running into optically thick CO absorption conditions which will render the fitting procedure more difficult. Noterdaeme et al. [_{2}-column densities, the latter being much better measurable.

CO absorption profiles observed at SDSS-J1-70542 + 354340 (

The second caveat in this context is connected with the assumption that relative populations of fine structure levels are purely determined by a photon excitation equilibrium with the surrounding CMB photons. If in addition any binary collisions with other molecules or any photons other than CMB photons are interfering into these population processes, then of course the fitted

CMB temperatures as function of redshift

Though from the results displayed in the above Figure

it was Planckian already at the beginning, that is, at the recombination phase, and if

since that time a completely homologous cosmic expansion took place till today.

Point (a) is questionable because the thermodynamic equilibrium state between baryons and photons in the early phase of fast cosmic expansion may quite well be disturbed or incomplete (see [

The present universe actually is highly structured by galaxies, galaxy clusters, superclusters, and walls [

Thus it should be kept in mind that a CMB Planck spectrum is only seen with the same temperature from all directions of the sky, if in all these directions the same expansion dynamics of the universe took place. If CMB photons arriving from different directions of the sky have seen different expansion histories, then their Planck temperatures would of course be different and anisotropic, destroying completely the Planckian character of the CMB. This situation evidently comes up in case an anisotropic and nonhomologous cosmic expansion takes place like that envisioned and described in theories by Buchert [

In fact if one hemisphere expands different from the opposite hemisphere, then as a reaction also different CMB Planck temperatures would have to be ascribed to the CMB photons arriving from these opposite hemispherical directions. If, for instance, the present values of the characteristic scale in the two opposite hemispheres are

Stars are formed due to gravitational fragmentation of parts of a condensed interstellar molecular cloud. For the occurrence of an initial hydrostatic contraction of a self-gravitating primordial stellar gas cloud the radiation environmental conditions have to be appropriate. Cloud contraction, namely, can only continue as long as the contracting cloud can get rid of its increased gravitational binding energy by thermal radiation from the border of the cloud into open space. Hence in the following we show that in this respect the cloud-surrounding CMB radiation can take a critical control on that contraction process occurring or not occurring.

Here we simply start from the gravitational binding energy of a homogeneous gas cloud given by

A contraction of the cloud during the hydrostatic collapse phase (see [

This already makes evident that further contraction of the cloud is impeded, if the surrounding CMB temperature exceeds the cloud temperature, that is, if

To give an idea for the magnitude of this cloud temperature ^{−3} must be adopted. With these values one then calculates a temperature of

This result must be interpreted as saying that as soon as in the past of cosmic evolution the CMB temperatures

If on the other hand it is well known amongst astronomers that galaxies with redshifts

This paper hopefully has at least made evident that the “so-called” modern precision cosmology will perhaps not lead us directly into a complete understanding of the world and the evolution of the universe. Too many basic concepts inherent to the application of general relativity on describing the whole universe are still not settled on safe grounds, as we have pin-pointed in the foregoing sections of this paper.

We have shown in Section

It is hard to say anything quantitative at this moment what needs to be concluded from these results in Section

The critical frequency limit is at around 10^{3} GHz, with effective radiation temperatures being reduced at higher frequencies with respect to those at lower frequencies. The exact degree of these changes depends on many things, for example, like the cosmologic expansion dynamics during the recombination phase and the matter density during this phase. However, the consequence is that the effective CMB radiation temperature measured at frequencies higher than 10^{3} GHz are lower than CMB temperatures at frequencies below 10^{3} GHz. Our estimate for conventionally assumed cosmologic model ingredients (Omegas!) would be by about

Unfortunately CMB measurements at frequencies beyond 10^{3} GHZ are practically absent up to now and do not allow to identify these differences. If in upcoming time periods, on the basis of upcoming better measurements in the Wien’s branch of the CMB, no such differences will be found, then the conclusions should not be drawn that the theoretical derivations of such changes presented here in our manuscript must be wrong, but rather that the explanation of the CMB as a relict radiation of the recombination era may be wrong.

Though indeed, as we discuss in Section

For those readers interested in more hints why the conventional cosmology could be in error, we are presenting other related controversial points in the Appendices.

All massive objects in space have inertia, that is, react with resistance to forces acting upon them. Physicists and cosmologists as well do know this as a basic fact, but nearly none of them puts the question why this must be so. Even celestial bodies at greatest cosmic distances appear to move, as if they are equipped with inertia and only resistantly react to cosmic forces. It nearly seems, as if nothing real exists that is not resistant to accelerating forces. While this already is a mystery in itself, it is even more mysterious what dictates the measure of this inertia. One attempt to clarify this mystery goes back to Newton’s concept of absolute space and the motions of objects with respect to this space. According to I. Newton, inertial reactions proportional to objects’ masses always appear, when the motion of these objects is to be changed. However, this concept of absolute space is already obsolete since the beginning of the last century. Instead modern relativity theory only talks about inertial systems (IRF) being in a constant, nonaccelerated motion. Amongst these all IRF systems are alike and equally suited to describe physics. Inertia thus must be something more basic which was touched by ideas of Mach [

Velocity and acceleration of an object can only be defined with respect to reference points, like, for example, another object or the origin of a Cartesian coordinate system. An acceleration with respect to the empty universe without any reference points does, however, not seem to make physical sense, because in that case no change of location can be defined. A reasonable concept instead would require to define accelerations with respect to other masses or bodies in the universe. But which masses should be serving as reference points? All? Perhaps weighted in some specific way? Or only some selected ones? And how should a resistance at the object’s acceleration with respect to all masses in the universe be quantifiable? This first thinking already show that the question of inertia very directly brings one into deepest calamities. The first more constructive thinking in this respect were started with the Austrian physicist Mach in 1883 (see [

The English physicist Sciama [

In a homogeneous matter universe with mass density

In contrast, for a moving particle the scalar potential

The gravitoelectromagnetic fields

Assuming an additional body with mass

Considering Newton’s second law, describing the gravitational attraction between two masses, it then requires for

To enable this argumentation a Maxwellian analogy of gravity to electromagnetism was adopted. This, however, seems justified through papers like those by Fahr [

It furthermore appears that mass constellations in the universe do also play the decisive role at centrifugal forces acting on rotating bodies. Accelerations are not only manifested, when the velocity of the object changes in the direction parallel to its motion (linear acceleration), but also if the velocity changes its direction (directional acceleration) without changing its magnitude (e.g., in case of orbital motions of planets). Under these latter conditions the inertia at rotational motions leading to centrifugal forces can be tested. The question here is what determines the magnitude of such centrifugal forces? Newton with his famous thought experiment of a water-filled rotating bucket (see, e.g., [

According to Mach the reaction of the water in the rotating bucket in forming a parabolic surface is an inertial reaction to centrifugal forces due to the rotation with respect to the whole universe marked by cosmic mass points, the so-called cosmic rest frame (see, e.g., [

Thus, whether one describes the earth as rotating with respect to the universe at rest, or the universe as counterrotating with respect to the earth at rest, should lead to identical phenomena, that is, identical forces. To test this expectation Thirring [

Within a Newtonian approximation of general relativity he could show that a rotating universe at the surface of the earth leads to metrical perturbation forces which are similar to centrifugal forces of the rotating earth. For a rigorous identity of both systems, (a) rotating earth and (b) rotating universe, a special requirement must, however, be fulfilled (see Figure

The universe as a mass-shell.

To carry out his calculations he needed to simplify the mass constellation in the universe. In his case the whole universe was represented by an infinitely thin, rotating spherical mass shell with radius

However, this request would have very interesting consequences for an expanding Hubble universe with

If now in addition with Thirring’s relation in a homologously expanding universe one can adopt that

Following Mach [

As we have shown above Thirring’s considerations of the nature of centrifugal forces were based on the concept of the mass of the universe

Fahr and Heyl [

The space-like metric in this cosmic case is given by an inner Schwarzschild metric, however, with the matter density given by the actual cosmic density

Then the above expression for

This result is very interesting since meaning that this mass horizon distance

This not only points to the surprising fact that with the use of the above concept for

The correct treatment of empty space in cosmology needs an answer to the following fundamental problem: What should a priori be expectable from empty space and how to formulate uncontroversial conditions for it and its physical behaviour? The main point to pay attention to is perhaps that the basic mechanical principle which was pretty clear at Newton’s epoch of classical mechanics, namely, “actio = reactio”, should somehow also still be valid at times of modern cosmology. So if at all the energy of empty space causes something to happen, then that “something” should somehow react back to the energy of empty space. Thus an action without any backreaction contains a conceptual error, that is, a misconception. That means, if empty space causes something to change in terms of spacegeometry, because it represents some energy that serves as a source of spacetime geometry, perhaps since space itself is energy-loaded, then with some evidence this vacuum-influenced spacegeometry should change the energy-loading of space (see [

The cosmological concept of vacuum has a long and even not yet finished history (see, e.g., [

The above term for

Under this convention then the following interesting chance opens up, namely, to fix the unknown and undefined value of Einstein’s integration constant

Very interesting implications connected with that view are discussed by Overduin and Fahr [

If vacuum is addressed, as done in modern cosmology, as a purely spacetime- or volume-related quantity, it nevertheless is by far not evident that “vacuum energy density” should thus be a constant quantity, simply because the unit of space volume is not a cosmologically relevant quantity. It may perhaps be much more reasonable to envision that the amount of vacuum energy of a homologously comoving proper volume

In case of a Robertson-Walker geometry this is given by

Here

If

The invariance of the vacuum energy per comoving proper volume,

If, on the other hand, work is done by vacuum energy influencing the dynamics of the cosmic spacetime (either by inflation or deflation), as is always the case for a nonvanishing energy-momentum tensor, then automatically thermodynamic requirements need to be fulfilled, for example, relating vacuum energy density and vacuum pressure in a homogenous universe by the most simple standard thermodynamic relation (see [

This equation is fulfilled by a functional relation of the form

The exponent

As evident, however, now the above relation is only fulfilled by

If we then take all these results together, we see that not only the mass density in the Robertson-Walker cosmos but also the vacuum energy density should scale with

With the additional points presented in the Appendices it may all the more become evident that modern cosmology has to undergo a substantial reformation.

The authors declare that there is no conflict of interests regarding the publication of this paper.

_{CMB}at high redshift from carbon monoxide excitation