_{1}

This work briefly reviews and extends the author’s three previous works (2015),
* Journal of Modern Physics*, 6, 78-87, and 1360-1370; (2016), 7, 1829-1844 that propose as an alternative to the accelerating ΛCDM universe, the decelerating Einstein de Sitter (EdS) universe, in which dark energy is a different phase of dark matter located only in intergalactic space (IGS), and that instead of a negative pressure, it has an index of refraction n
≈1.50, and hence a reduced speed of light c / n through it. This allows the EdS universe to expand the extra distance necessary to obtain the diminished brightness of the Type Ia supernovae. In view of the recent suggestion that the universe is not accelerating, but possibly expanding uniformly, a table is given comparing both the accelerating and uniformly expanding universes with the EdS universe supplemented by the reduced speed of light. It is shown that fitting the uniformly expanding universe leads to a smaller value of
*n*, and hence too short an age for the EdS universe, unlike the case with fitting the accelerating universe. The main result is that the proposed reduced speed of light in the IGS predicts discordant redshifts. It is shown that the current explanation of “accidental superposition,” is most likely insufficient to explain the number of observations, and that the present proposal could make up the difference. It can be tested astronomically, as illustrated in a figure.

Recently the author has published three papers [

As mentioned, dark energy in this model does not have a negative pressure, or indeed any pressure at the level of approximation used here, but instead, has an index of refraction n that reduces the speed of light through it to c / n. Because of this reduction, it obviously takes longer for light to reach the Earth from the SNe Ia than it would if the speed of light remained c. This in turn gives the decelerating, but still expanding, EdS universe the additional time needed to further expand, so as to result in there being a greater distance to the SNe Ia, and hence a greater diminution in brightness, than if light traveled with speed c. This additional distance also shows up in the verification of the ΛCDM model by Anderson, et al. [_{A}, and luminosity distance D_{L}, as discussed in [

On the other hand, since the speed of light within the galaxies is taken to be c, the model effectively assumes that the speed of light reduction is only occurring within the intergalactic space (IGS), and therefore that dark energy is only in the IGS. Since it was noted by Riess, et al. [

However, for some purposes, it is more convenient to convenient to work with the logarithmic measure of the fractional distance increase given by

(2)

which will be done here. The above corrections do not depend on the kind of universe that is being compared with the accelerated universe; all that is required, in addition to the independence of n on z, is that the expansion parameter satisfies

Thus, as was shown in [

In [_{i}, for i = 0.1 to 1.0, was obtained that made

In [

one has finally that

Calculations were made in [

In [

Although much of the following analysis is standard, it is necessary to present it here so as to make clear the meaning of the terms in

Upon introducing the Hubble parameter

Since the CDM obeys the conservation law

ducing the standard definition:

Upon making use of

Now for the

Thus the above ratio becomes

For the

which has to be evaluated numerically. For the EdS universe, for

In [

Under the uniform expansion scenario suggested in [

where u is some constant speed of expansion whose value is left open, since it will drop out. Then it follows that

Where, since the universe is expanding, the positive root has been chosen. Then, from

Once again,

and hence

To compare

z | |||||||||
---|---|---|---|---|---|---|---|---|---|

0.1 | 0.0208 | 0.0194 | −0.0014 | −6.7 | −2.9 | 0.0103 | 0.0106 | 0.0003 | 2.9 |

0.2 | 0.0387 | 0.0364 | −0.0023 | −5.9 | −2.1 | 0.0196 | 0.0201 | 0.0005 | 2.6 |

0.3 | 0.0539 | 0.0515 | −0.0024 | −4.5 | −0.7 | 0.0282 | 0.0287 | 0.0005 | 1.8 |

0.4 | 0.0671 | 0.065 | −0.0021 | −3.1 | 0.6 | 0.0360 | 0.0364 | 0.0004 | 1.1 |

0.5 | 0.0786 | 0.0772 | −0.0014 | −1.8 | 2.0 | 0.0433 | 0.0435 | 0.0002 | 0.5 |

0.6 | 0.0885 | 0.0883 | −0.0002 | −0.2 | 3.6 | 0.0500 | 0.0501 | 0.0001 | 0.2 |

0.7 | 0.0972 | 0.0985 | 0.0013 | 1.3 | 5.1 | 0.0564 | 0.0561 | −0.0003 | −0.5 |

0.8 | 0.1048 | 0.1079 | 0.0031 | 3 | 6.8 | 0.0623 | 0.0618 | −0.0005 | −0.5 |

0.9 | 0.1115 | 0.1166 | 0.0051 | 4.6 | 8.4 | 0.0678 | 0.0670 | −0.0008 | −0.5 |

1.0 | 0.1175 | 0.1247 | 0.0072 | 6.1 | 10.0 | 0.0731 | 0.0720 | −0.0011 | −1.5 |

It will now be shown what (14) entails about the energy density and pressure for the uniformly expanding universe, from the standpoint of the field equations. Upon rewriting the line element as

and

Since for uniform expansion

Although it is clear from

with

In contrast to the above results, based on the value of n derived from the fit to the accelerating universe, if one uses n = 1.26 that was found in fitting the uniformly expanding universe, one finds for the age of the EdS universe

Although the least squares fit yielded

In [

Thus, as a test of the proposed alternative model, since the location of the discordant redshift galaxies are known, astronomers should undertake to see whether there are any higher redshift galaxies that are suitably located off to the side of the lower redshift galaxies with the same morphology and spectral signature that could alternatively be responsible for the discordant redshift images. The failure to find any appropriate candidates, would rule out the proposed model, since the probability for this scenario would seem to be about the same as for the case when there is an actual galaxy at

In regard to this issue, Bahcall [

where ^{-3} sq. degrees. He sets ^{th} magnitude, as determined in the Lick survey [

This smaller, but still highly uncertain, value for N suggests that about one- half of the 64 cases listed by Arp are due to something other than accidental superposition, and could instead be due to the reduced speed of light in the IGS, and the refraction scenario proposed in the highly simplified ^{ }

The decelerating EdS universe, supplemented by the proposed reduction of the speed of light by the dark energy, can fit the increased distances to the SNe Ia, and hence their diminished brightness predicted by the accelerating

Tangherlini, F.R. (2017) A Possible Alternative to the Accelerating Universe IV. Journal of Modern Physics, 8, 622-635. https://doi.org/10.4236/jmp.2017.84042