In the SCM there is redshift, popularly (but not quite correctly) explained as a Doppler effect. There is also time dilation, which diminishes the photon arrival rate and further reduces the observed flux. The EST line element may be transformed into a line element of the FRW (Friedmann-Robertson-Walker) type (Masreliez,1999), which models expanding space rather than expanding space and time (scale) and therefore is similar to the SCM line element in that it exhibits both redshift and time dilation. Since all line elements that can be derived via continuous variable transformations are equivalent in General Relativity, the observed luminosity in the EST universe should diminish not only by the redshift, which contributes with a factor 1/(1+z), but there should also be additional cosmological extinction, which contributes by the same factor.

The EST line element is (setting c=1):

This can be transformed into a FRW line element by:

At *t=0* and *u=T* both line elements are Minkowskian and we have *dt=du*.
Since these line elements are physically equivalent the photon arrival rate should
be the same and since there is both redshift and time dilation in the FRW line element
the same is true in the EST universe.

Another way to see this is to use the transformation:

Here *r *and *t* in the last term are implicitly defined by the two relations
above. In this line element there is neither redshift nor time dilation for radial
light propagation, but the received light intensity is diluted inversely proportional
to the surface element:

This agrees with the EST luminosity relation (c=1).

However, the luminosity relation presented in Masreliez 1999, which is the traditional
relation for tired light redshift, is incorrect since the second factor *1/(1+z) *
is missing. Also, since there are two dimming factors *1/(1+z)* in the EST
model, there is both redshift and time dilation, like in the SCM model.

(Also, relation 12.14 in Masreliez 1999, for the coasting distance traveled by a
particle with initial velocity *v _{0}=c· β_{0},* is not
correct; it should be

In the EST universe the cosmological scale expansion does not change the average distances between galaxies or their angular sizes, since both space and time expands.

The EST distance-redshift relation is:

*H _{0}* is the Hubble constant,

The corresponding expression for distance in the SCM with flat spacetime is the Mattig distance:

These two expressions for the apparent luminosity agree within 0.03 magnitudes in
the range 0<z<1 if Ω_{M} =0.54 and Ω_{Λ}=0.46.
The EST luminosity prediction agrees well with the SNe Ia observations as can be
seen in Figure 1. It is remarkable that this good agreement
with the EST model is obtained without any adjustable parameters (other than the
matching at low z-values).

Based on supernovae Ia, CMB temperature anisotropy and galaxy clustering observations
the current consensus is that Ω_{M} =0.3 and Ω_{Λ}=0.7
(Perlmutter, 2003, Tegmark et. al., 2003). These are also the values that
minimize the least square magnitude difference between the SCM and the EST luminosity
relations in the range 0<z<10.0. The maximum magnitude difference between
the two models is now 0.25 dB.

Since the parameters Ω_{M} and Ω_{Λ }are selected
to make the SCM agree with observations the unexpected dark energy in the SCM might
be a consequence of using an inferior cosmological model. The EST model agrees
with observations without adjustment. However, the EST model implies that
the vacuum energy density does not disappear. It is given by the energy-momentum
tensor for the EST line element:

Note that Omega equals one *by design* since *T _{00}* is the Critical
Density. Furthermore, the net gravitating energy is zero in the EST because the
sum of the diagonal elements is zero.

The Surface Brightness test (Tolman, 1930) uses a test statistic formed by dividing
the estimated absolute luminosity *L *by the estimated surface area of a distant
galaxy. The test uses three observational measurements, the apparent luminosity
*I*, the angular size* θ *and* *the redshift* z*. The angular
size is used together with an estimated distance, that depends on the redshift and
the assumed cosmological model, to estimate the surface area of a galaxy; the area
is proportional to (*θd) ^{2}*, where

Let the distance when the light was emitted from a test galaxy be *d _{1}*
and the distance when the observation is made be

Define the surface brightness test statistic, *SB*, at the time of emission
by:

* SB=L/( θ d _{1} )^{2}*

For the SCM* *we then have* SB = L(1+z) ^{ 2}/( θ d_{0})^{2}.*

The apparent luminosity is given by:

*I=L/[ d _{0}∙(1+z)]^{2}*

This implies* SB _{SCM}= (I/ θ^{2})*

Since both the apparent luminosity and the area depend quadratically on the distance, the test statistic is independent of the particular distance gauge used.

For the EST model the apparent luminosity is also given by:

*I= L/[d _{0 }(1+z)]^{ 2}*

However, the distance measure *d _{0} *differs between the SCM and the
EST models.; Also, distances remain constant during scale expansion

*SB _{EST}* /

This shows that the test statistic strongly depends on the model.

Define *<SB>=2.5 log(SB)*

We get:

*<SB _{EST}> - <SB_{SCM}>= 2.5∙log (1+z)^{ -2}=
-5.0 ∙log(1+z)*

The difference amounts to about 1.4 magnitudes at z=0.9.

The radial distance used in estimating the surface brightness at the time of emission
is *θ·d _{1}*.

We have for the SCM, with the Mattig distance used by Lubin and Sandage:

And for the EST model:

With *q _{0}=0.5* the difference between the logarithms for these two
radial distances is about 0.3 dB at z=0.90 (The EST distance is larger).

The open circles in Figure 2 are similar to figure 2, η=2.0, in Lubin and Sandage IV (astro-ph/ 0106566). The filled circles are the corresponding EST estimates.

The estimated local surface brightness for the EST model, arrived at by adjusting
the observations by the factor (1+z)^{2}, taking into account the difference
in radial distance, agrees with the local baseline, but there is significant disagreement
with the SCM estimates. Lubin and Sandage IV found this discrepancy to be a factor
*(1+z) ^{n}*, with

Carroll S.M., Press W.H., Turner E.L., 1992: The Cosmological Constant, *Annu. Rev.
Astron. Astroph. 30, 499-542*

Lubin L. and Sandage A. I, 2001, *astro-ph/0102213*

Lubin L. and Sandage A. II, 2001, *astro-ph/0102214*

Lubin L. and Sandage A. III, 2001, *astro-ph/0106563*

Lubin L. and Sandage A. IV, 2001, *astro-ph/0106566*

Masreliez C. J., 1999, The Scale Expanding Cosmos Theory, *Astroph. & Space Science,
266, Issue 3, p. 399-447*

Mattig W.,1958, *Astr. Nachr.* 284, 109

Tegmark et. al., 2003*, astro-ph/0310723*

Tolman R. C., 1930, *Proc. Nat. Acad. Sci., 16, 511*