trained target value, adopted from direct measurements).

The most uncompromising answer to explain the disagreement would be that something is wrong with the basic assumptions of the cosmological models, the interpretation of the CMB, or the model itself. Another possible conclusion could be―although this would be likely to seriously undermine faith in the reliability of observational data―that measurement errors in determining the RS are responsible for the discrepancies in the data [6] .

Although none of above mentioned grounds can be definitely excluded, such assumptions appear unlikely. The gap between h = 0.726 and h = 0.30 is too wide; it seems unrealistic that it could be bridged by supposing systematic measurement errors. The theoretical background of understanding the CMB anisotropy is conclusive and the experimental data measured with COBA, WMAP, and Planck are consistent.

It seems justified to assume that both the direct measurement of H0 and the indirect calculation on the basis of the CMB are correct. If so, the disagreement between the two results is real.

3. Possible Resolution to the Problem

As a straightforward explanation for the above disagreement I consider the case that the RS of starlight and the RS of the CMB have different physical origins. The dilemma is that the H0 from the CMB and the H0 from the direct RS measurement cannot mean recession velocity within the same theory.

3.1. The Redshift of the CMB Calculated from EdeS Models Is Due to Expansion

1) “Ockham’s Razor” or the simplicity principle is one of the key criteria for choosing between rival theories. The principle states that simpler theories should be preferred to more complex ones. A theory is simpler than another if it contains fewer adjustable parameters in order to account for the empirical data. This criterion speaks clearly for the preference of h = 0.3 as the true velocity of the universal expansion.

2) Simplicity can also be understood in terms of the explaining potential of competitor theories.

The h = 0.3 with Ω(DM+B) = 1 from EdeS is, not unexpectedly, close to the value that naturally follows from the original Einstein Equation [7]

v 2 = 8 π G 3 ρ B , o b s (5)

with ΩB = 1, ρB ~ 10−30 g∙cm−3.

With ΩB = 1 and h = 0.3 the missing mass and the age problems would not arise.

3) Low-h models are also consistent with Big Bang nucleosynthesis, cluster baryonic fractions, the large scale distribution of galaxies and the ages of globular clusters, although in disagreement with direct determination of the Hubble constant [5] .

4) Different tests based on observational data have been performed to provide evidence for the expansion hypothesis. Recently, Lopez-Corredoira [8] [9] and Crawford [10] critically reviewed the results of these tests and concluded that the expansion tests do not support models with h = 0.7. Static [10] and slowly expanding universe models fit the observational data better than the ΛCDM model with h = 0.7 [11] , although―without DM and DE―cannot account for the baryonic acoustic oscillations (BAO) and the integrated Sachs-Wolfe effect. Low h EdeS models with DM and zero cosmological constant, however, are expected to show not only a better agreement with the expansion tests but, in addition, they perfectly fit the BAO power spectrum and as pointed out by Blanchard et al. [6] have no strong integrated Sachs-Wolfe effect and are in better agreement with the low quadrupole seen by WMAP.

3.2. The Redshift of Atomic Spectral Lines

Strong support in favor of a non-velocity interpretation of the RS of spectral lines comes from the exponential slope of the Hubble diagram. Harrison [12] has shown that that the relation v = H0d in an expanding homogeneous and isotropic universe must be a linear velocity/distance function.

It has been shown [13] that the RS/d diagram of 280 supernovae and gamma ray burst RSs can be fitted exactly with the function

z = e 2.024 × 10 18 × t s 1 (6)

as shown in Figure 1(a), or, equivalently, with the analytical function

μ = 25 + 5 log ( c / H 0 ) + 5 log ( ( z + 1 ) ln ( z + 1 ) ) (7)

[14] . Here, tS is the flight time of a photon from the co-moving radial distance to the observer and μ is the magnitude. These results have been confirmed [15] [16] [17] .

As can be seen from Figure 1(b) (results are taken from [14] ) ΛCDM models show a poor agreement with the observed data: the ΛCDM model with H0 = 62.5 km∙s−1∙Mpc−1 (bottom line) departs from the best-fit curve for z + 1 < 6.5 to the bottom, for z + 1 > 6.5 to the upper side of the trend-line (middle line). The deviations are of a systematic (non-statistical) nature and, therefore, the model cannot reflect the exponential slope.

In the range of z > 3 the ΛCDM model with H0 = 72.6 km∙s−1∙Mpc−1 (upper line) shows a sharp increase in slope and departs considerably from the observed exponential function. ∑χ2-test in the high RS range of tS × 10−14 = 6000 - 11,000 including 41 data points leads to a statistical significance between the observed tS/z and the calculated ΛCDM data of P = 0.053, indicating that from the statistical point of view, the two data sets are essentially different.

The exponential slope of the Hubble diagram provides a clear indication for an energy decrease with a constant rate. However, it is not the aim of this paper to identify a specific energy decay mechanism I want only to point out that the disagreement between the two methods of determining H0 is a real problem that needs explanation. With this, the Hubble diagram test could prove to be the most important cross check in identifying the true physical nature of H0 (CMB) and H0 (spectral lines). For further confirmation of the exponential slope of the

(a)(b)

Figure 1. (a) Solid line: potential μ = a × zb best fit RS/μ data; (b) RS of type Ia supernovae and gammy ray bursts as a function of tS = DC/c.

Hubble diagram, more accurate data and more data points in the RS range of z > 3 are necessary to ensure a 4σ confidence level.

4. Conclusions

I have shown that the assumption of different physical origins for Hubble’s constant of starlight and of the CMB represents a plausible explanation for the disagreement of the RSs obtained from the EdeS model without the cosmological constant. It also explains the results obtained by the determination of H0 from atomic spectral lines. This conjecture is admittedly radical, but it is a logical conclusion if we refuse to believe that something is fundamentally wrong with the interpretation of the CMB anisotropies, or even with the concordance cosmological model itself.

There are only two possibilities to resolve the problem. Either we assume that the underlying ΛCDM cosmological model is in fact incomplete, or the distance measurements of H0 are wrong. Alternatively, the presented interpretation, namely that the RS of starlight and RS of the CMB have different physical origins, is correct. At present, there is no third position. Currently, it might be too early to consider the ΛCDM model as definitely proved and confirmed by independent probes.

Cite this paper
Marosi, L. (2017) Is the Velocity Interpretation of the Redshift of Spectral Lines in Accordance with Astronomical Data?. International Journal of Astronomy and Astrophysics, 7, 248-254. doi: 10.4236/ijaa.2017.74021.
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