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Hubble’s Law

Hubble's law» states that the redshift, z, of light coming from a galaxy is proportional to it’s distance, r. The constant of proportionality, H₀, (in units in which lightspeed = c = 1) is Hubble’s constant. Hubble’s law applies to galaxies at small cosmological distances, but outside of the local supercluster». Light from a galaxy at a small cosmological distance, r, at seen at cosmic time t on earth, was emitted at cosmic time t − r. The teleconnection replaces the standard linear redshift law with a square law. So,
From which we read the value of Hubble’s parameter,


This differs by a factor of 2 from the standard formula. It follows immediately that the rate of expansion of the universe is half, and that (for given cosmological parameters) the universe is twice as old as would be indicated by the standard redshift law.

Cosmological Parameters

The teleconnection redshift relation alters cosmological parameters but otherwise leaves the established equations of general relativity unchanged. Friedmann’s equation is
Normalising, such that Ω = 1 is critical density for closure in a no-Λ model, Ω takes on four times its standard value.


With these definitions, Ω + Ω_k + Ω_Λ = 1 as usual, but critical density for closure is a quarter of the standard value. The baryonic density, Ω_B is four times greater on this scale. It follows that that missing mass can be made up by neutrinos. There is thus no reason to introduce exotic missing matter.

The table used Ned Wright»’s Cosmology Calculator» to compare the properties of the standard model with those of the teleconnection, based on an adjustment of the local distance scale predicted by analysis of local stellar motions under the teleconnection, and on the values of Ω found from analysis of supernova data, below. The data supports a closed no-Λ model with no time scale problem and no requirement for exotic cold dark matter (a time scale problem means that the age of processes taking place within the universe are greater than that of the universe itself).

Observations of the Early Universe

If observations at high redshift had revealed the expected activity of the early universe it would have falsified the square redshift law; in fact observations of galaxies with redshifts up to about z = 6 have shown a much more mature universe than had been expected, and much faster apparent formation of large galaxies than can be accounted for by theoretical models of galaxy evolution (Glazebrook et al», Cimmatti et al»). The teleconnection presents an alternative. A square redshift law means we have to revise the ages of redshifted galaxies. At a redshift of 3 the universe would have been a quarter of its current size under the standard law and only 2.1 Gyrs in age. Under the teleconnection it would have been half its current size and 4.5 Gyrs in age, thereby alleviating pressure on the theory of galaxy evolution.

The James Webb Space Telescope», scheduled for launch in 2013, and the Extremely Large Telescopes», currently under design and development and due to come into service around 2018, will give a clear view of the universe at much higher redshifts. If we find mature galaxies at very high redshifts, it will be firm evidence that the universe the age of universe at at a given redshift is much greater than predicted by standard general relativity.

Supernova Redshift

Type 1a Supernovae» are formed when matter is sucked into a carbon-oxygen white dwarf» from a companion star (normally a giant). A white dwarf supports no nuclear fusion, and is maintained against gravitational collapse by electron degeneracy». When the mass of the white dwarf reaches the Chandrasekhar limit», approximately 1.4 solar masses, electron degeneracy can no longer support it against further gravitational collapse. The core heats and when it reaches the ignition temperature for carbon fusion» a runaway» reaction begins. The result is a supernova explosion». Because this process is almost identical in every case, all type 1A supernovae have almost exactly the same intrinsic brightness, or absolute magnitude». As a result, type 1A supernovae are the best available standard candles» from which we can determine cosmological parameters.

Redshift and magnitude each give a measure of the distance of the supernova. A plot of magnitude against redshift follows a curve which can be calculated from the cosmological parameters. We find the best fit to the data by adjusting the parameters so as to minimise the χ² value (the sum of normalised squared differences between the data points and the curve). The Union compilation», prepared by the Supernova Cosmology Project» contains, at the time of writing, the most up to date supernova data from different sources, prepared in as uniform a manner as possible, from which 307 type 1A supernovae pass usability tests.

Data on the cosmic microwave background» (CMB) determined from the Wilkinson Microwave Anisotropy Probe» (WMAP») indicates a flat space (Ω_k = 0) model with non-zero cosmological constant, known as the concordance model». For 307 SNe in the Union compilation, the best fit concordance model gives Ω = 0.29 and χ² = 311.0. The best fit teleconnection no-Λ model gives Ω = 1.92 and χ² = 309.4. The difference in χ² values is too small for comparison of the quality of the fits, as can also be seen in the plots. The predicted curves for the teleconnection no-Λ model and the standard concordance model are sufficiently close that it would only be possible to distinguish them by taking a large sample of supernova with redshifts greater than about 1.4. The Joint Dark Energy Mission» is currently considering three concepts for space telescopes intended to collect the sort of data which would be required, with projected launch dates before 2020.


Magnitude plotted against redshift for 307 supernovae from the Union compiliation. The theoretical curves for the best fit concordance and teleconnection models are green and red respectively.


Residuals to the best fit concordance model.

The calculation of luminosity distance under the teleconnection follows the same pattern as in the standard model, but using the squared redshift law. The coordinate distance from emission at time t_e to detection at time t₀ is
The angular size distance is a₀sin2ρ, taking into account the doubling of angles required by the non-physical metric. Then, observing that energy and rate of photon emission are shifted by 1 + z, the luminosity distance is
The distance modulus is μ = 5logd_L + 25, as usual.

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