In a previous paper we postulated that the repulsive force responsible for the universal expansion is associated with the excitation of the empty space (quantum vacuum) and the excitation energy is represented by the energy of the cosmic microwave background (CMB). In this paper, we show that the concept of the repulsive space expanding photon field (i) can successfully be applied to explain the local velocity anomaly of the Milky Way Galaxy as shown by Faber and Burstein (1998) and Tully (1998), (ii) offers a convincing explanation of the still disputed question of the cosmological expansion on local and intergalactic scales discussed by Cooperstock et al. (1998), and (iii) explains the redshift (RS) of the CMB in accordance with the law of energy conservation without the need for dark matter (DM) and dark energy (DE). Probably the most remarkable result of this model (abbreviated as photon/baryon: PB model in the following discussion) is that the individual voids building up the soup-bubble- (SB-) like galaxy distribution are the governing dynamical components of the universal expansion. Further consequence implies that the universe is considerably older than the interpretation of the Hubble constant as expansion velocity suggests.

The cosmological constant

Einstein did not consider the cosmological constant to be part of the energy-momentum tensor [

Because general relativity (GR) never defined the exact nature of matter, in context with GR both interpretations could turn out to be more successful when applying GR to the universe as a whole [

The physical nature of the cosmological constant is still a matter of speculations. In current astrophysics

In order to overcome this problem in recent approaches several forms of varying cosmological constants were introduced in the Einstein equation [

As a new approach to explain the physical nature of the variable cosmological constant we postulated [

Our hypothesis is not without precedent in modern astrophysics and, in a general sense, akin the decay of the false vacuum in inflationary cosmology. Without discussing details of this theory, in quantum field theory a false vacuum is an excited energy state of the true vacuum possessing a unique property [

In both, in case of the false vacuum and in case of the postulated repulsive photon field as well, the source of force, exerting space-time expansion is the excitation energy of the empty space that relaxes to the ground energy state by doing work either in the expansion of the false vacuum bubble or, as in case of the space expanding photon field, against the gravitational attraction of the baryons.

The notion of space expanding photon field is new and, therefore, supporting reference can hardly be found in literature. In a foregoing paper Novello [

Here we describe the expansion of the universe with respect to the repulsive, space expanding property of the photon field that plays the role of a time dependent with

If we in (^{−1}. Its numerical value can be calculated to ^{−1}.

If one is interested in the energy of the photon term at any time

Equation (

The first term on the right hand side is equivalent to Einstein’s matter tensor, containing matter and all forms of energy/c^{2} which are associated with a certain physical state of matter. The second term is a new energy term, containing those forms of energy which are considered to be a property of the excited empty space, the energy of photons, and neutrinos.

Equation (

In (

The major problem with any such stationary state equilibrium is how to start the present expansion process. The PB model provides a plausible mechanism for the expansion started off in an apparently steady-state origin: Primordial underdensities generated during the early stage of evolution represent centers of expansion and are the seeds for formation of the cosmic large-scale structure. Because mass underdensities are regions of suppressed gravitational attraction in underdense regions the repulsive force exerted by the still homogeneous photon field overwhelms the gravitational attraction and such regions accordingly expand. Matter streams away from underdense expansion centers and collects on the surface and in interstices of a close packing of spheres.

The observed large-scale structure of the universe is in support of this expansion mechanism. Measuring the clustering of bright galaxies has shown that the 3-dimensional distribution of luminous matter has a SB-like appearance with the visible galaxies on the surface of the soap bubbles [

In the following discussion we regard a single void as a representative part of the infinite universe and describe the universal expansion by the example of this isolated but representative sample. It is assumed that all voids of the universe expand in the same way.

The numerical value of ^{−1}) amounts to

The gravitational self-energy of the corresponding thin spherical shell (void) with mass

The expansion velocity is given by

The structure or morphological factors ^{−1} in the interior of a thin spherical shell with wall thickness

The Local Void was identified in the Nearby Galaxies Atlas [

The local velocity anomaly was first noticed by Faber and Burstein [

The observation is the following [

However, after subtraction of the velocity components caused by the nearby galaxies, the residual pattern of motion reveals an extra component. The Milky Way moves away from the Local Void with a velocity of 260 km/s in direction close to the supergalactic South Pole. This movement is not toward anything substantial, but it is directly away from the Local Void, orthogonal to the disk of the Local Sheet [

It was suggested that this offset might be the consequence of a push from the Local Void [

Using (

The linear relationship between expansion velocities with increasing radii of the voids is shown in Figure

Expansion velocity of voids with increasing radii. The triangle represents the local velocity of the Milky Way Galaxy orthogonal to the disk of the local sheet.

Results for voids with radii of 33, 50, 66, and 80 Mpc, ^{−3} are summarized in Table

Expansion velocity ^{−1}) of voids with radii 33, 50, 66, and 80 Mpc.

33 | 50 | 66 | 80 | |

^{−1}) | 183 | 277 | 366 | 444 |

The expansion velocities in Table ^{−1} Mpc^{−1}.

It can be seen from Table

This result could have far-reaching consequences for our understanding of the universal expansion. Regarding voids as the dynamical component of the expansion, the large-scale structure can be thought of as a close packing of expanding spheres of different sizes and the linearity of the individual expansion rates with distance makes it impossible to differentiate local void expansion from a global cosmic expansion.

The PB model implies a spectacular outcome for the age of the universe. The time necessary for the expansion of a primal void with ^{26} cm can be obtained by integration of ^{−3} the time necessary for expansion to a radius of 10^{26} cm can be inferred to about 115 Billion years. The PB model, predicting an age of the universe of ≫115 billion years, could help to solve the age problem of galaxy formation by using the idea that the universe is much older, and so they may have been evolved over time in some regular way without the need for DM or DE.

The question as to whether the universal expansion affects local systems is still a matter of debate and during the last decades several papers appeared in scientific literature dealing with this issue. On basis of a detailed quantitative analysis, Cooperstock et al. [

In a more recent paper, Gentry [^{26} cm is 10^{10} times stronger than that between the solar system and the Milky Way galaxy. With this objection the question of global expansion remains obscure and a definitive answer to this issue is still lacking.

The PB model offers a more convincing explanation of the expansion on intergalactic and on local scales. We have shown that according to the PB model the universe can be thought of as consisting of underdense, expanding, and overdense, contracting, regions. An important feature of the SB universe is that due to its still homogeneous and isotropic large-scale structure, the amount of mass

With the postulate of the PB model the energy decrease of the CMB is equal to the work done by the photons in the expansion of the universe versus the gravitational attraction of the baryons:

However, the value of the Hubble constant of 5.54 km s^{−1} Mpc^{−1} is far not enough to explain the RS of atomic spectral lines. A resolution of this problem might be found in the hypothesis that the RS of spectral lines is composed of a velocity and a superimposed RS component of as yet unknown origin and the rate of expansion is much lower, say, the universe expands according to the prediction of the PB model. A new RS mechanism based on the process of energy equilibration of starlight into the equilibrium blackbody radiation for explaining the Hubble relation is developed in order to explain the RS of atomic spectral lines [

The results presented in this paper have demonstrated that the PB model, describing the evolution of the universe from the interaction of attractive and repulsive forces, can explain (i) the fine-tuning or flatness problem, (ii) the age problem in galaxy formation without the need for DM and DE, and (iii) the loss of energy of the CMB in accordance with the law of energy conservation. One advantage that the PB model would have over ΛCDM is that it works with constituents that are known to be present in the universe today. Probably the most remarkable cosmological implication of the results presented in this paper is that the individual voids building up the SB-like galaxy distribution are the governing dynamical component of the universal expansion. Voids expand and the overdense regions collapse.

An observational test of this model could be made by determining the radial velocities of galaxies situated on the border of voids and comparing these velocities with those obtained from our model.

The author is grateful to Professor Rainer Mattes from the Westfälische Wilhelms-Universität, Münster, Germany, for proofreading and for his continuous interest in this work.