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 TITLE: Relativistic Radial Expansion: Do we need Dark Energy?
 AUTHOR: Ben-Amots, N.
 SOURCE: J. Phys.: Conf. Ser., v. 330, 012018 (2011)
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 ABSTRACT: The Hubble law, for which the radial expansion velocity is linear in the distance r, implies a visible Universe limited to a horizon at r=c/H. No information beyond this horizon can reach us.
Here we suggest a modified Hubble law for the measured radial expansion velocity that does not put a limit on the radius of the visible Universe. The modified Hubble law is based on Einstein's well-known addition of relativistic velocities, and differs from the (conventional linear) Hubble law in orders of Hr/c that are higher than the first order. The modified Hubble law solves Olbers's paradox (as the linear Hubble law does), and the existence of dark energy becomes unnecessary for explaining existing astronomical data on the dependence of luminosity as a function of redshift for type Ia supernovas.

 INTRODUCTION: The linear Hubble law (in some references referred to as the Hubble-Humason law) implies a horizon. See, for example, Rindler [1] and others [2-6]. Ellis and Rothman [5] named their paper on the subject of cosmological horizons: "Lost Horizon."

Here we present a modified Hubble's law so that no horizon exists or is necessary.

Our formulas indicate that Perlmutter's interpretation of data of luminosity versus redshift of type Ia supernovas as demanding an accelerating expanding Universe is not correct. Analyzing the data with the modified Hubble law, shows that no cosmic acceleration is present, so that invoking Dark Energy is superfluous.

 SUMMARY: The linear Hubble law leads to a visible Universe limited in radius.

Here we suggested a modified Hubble law that does not limit the visible radius of the Universe, thus enabling a Universe without a horizon. The linear Hubble law may be viewed as an approximation of the modified Hubble law for small expansion velocity of relatively close galaxies.

We showed that the modified Hubble law, like the linear Hubble law, solves Olbers's paradox.

This paper shows that if the origin of Hubble's redshift of galaxies is the Doppler effect, (caused by the receding velocity of the galaxies), there exists a modified Hubble law that fits the present observations for small Hr/c -- yet without exhibiting a horizon at large Hr/c. Further, we suggested an explanation for Perlmutter et al.'s (1999) and others' observations by the non-linear, modified Hubble's law (8),
v(r)=c tanh(H r/c)   (8)
without needing dark energy.

The originally suggested Hubble law (1)
v(r)=H r    (1)
is arbitrary, while the modified Hubble law (8) suggested above obeys the correct relativistic addition formula (3):
v = (v_1+v_2)/(1+v_1 v_2/c^2)   (3)

Thus we derived a new formula for the Hubble law, which contains the existing as a special case for small expansion velocity of relatively close galaxies.

So, using our formula (8)

a) No horizon is needed,

b) Olbers's paradox is explained by both Hubble formulas.

c) We find that Perlmutter et al.'s and others' interpretations of accelerating expanding universe may be incorrect. We suggest that analyzing the phenomenon with the modified Hubble law, will find that no cosmic acceleration is present, so that also Dark Energy may be superfluous.

 30 references


 COMMENT: Lectured at IARD2012 Conference, Firenze 2012.
Lectured at Marcel Grossmann Conference MG13, Stockholm 2012

Kadin, A.M., "Variable mass cosmology simulating cosmic acceleration,"
viXra (2012)

Shimojo, Mastaka
"Problems in size expansion analysis based on hypothetical relationships between scale factor, exponential function and Bondi K-Factor,"
J. Fac. Agr. Kyushu Univ., v. 60(2), pp. 390-403 (2015)

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