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Summary of Curvature Cosmology



 
 
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Old April 11th 07, 04:46 AM posted to sci.astro
David Crawford
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Default Summary of Curvature Cosmology

INTRODUCTION
This is a summary of the major aspects of curvature cosmology (book:
Curvature Cosmology BrownWalker Press). For brevity most of the arguments
and references are omitted. Figure references are to the book and they are
also available on my web site. http://www.davidcrawford.bigpondhosting.com
For historic reasons many redshifts are expressed in velocity units.
Curvature cosmology (CC) describes a new cosmological theory that is an
alternative to the current Big-Bang cosmology. It rests on two hypotheses:
curvature-redshift and curvature-pressure and is fully compatible with
General Relativity and quantum mechanics.

CURVATURE REDSHIFT
In space with a positive curvature a bundle of geodesics will decrease in
cross-sectional area just like lines of longitude get closer as they go from
the equator to the poles. This decrease is applicable to all wave motion and
if we consider a photon to be a localised wave packet its cross-sectional
dimensions will also decrease as it propagates. The implication is that its
angular momentum should also decrease which contrary to quantum mechanics.
The hypothesis of curvature redshift is that this impasse is overcome by the
emission of two very low energy secondary photons. In effect there is a
gravitational interaction with curved space time. Because the photon
interacts with a very large effective mass and because of symmetries there
is no angular scattering and the usual argument against tired-light
redshifts is not applicable. The ‘focussing theorem’ shows that the rate of
loss of energy is proportional to the product square root of the local gas
(plasma) density and the photon energy. There is not curvature redshift for
a photon passing a large mass like the sun. Since the process is applicable
to any wave a similar interaction occurs for electrons and other particles.
Because the basic interaction is one of a slow build up any other
interaction that occurs before the interaction takes place can inhibit
curvature redshift. Refractive index is a very important inhibiting
interaction. It makes it very difficult to see the effect in a laboratory.
Nevertheless a possible laboratory test is suggested. It is similar to the
famous Pond and Snyder Harvard tower experiment.

CURVATURE PRESSURE
Consider a point at the bottom of the ocean. It is clear that the large
pressure is due to the opposition by the elastic forces of the ocean floor
opposing the gravitation acceleration of the water above it. There is no
pressure if the water was in free fall. Hence the simple principle that
follows is that if gravitational accelerations are partly or fully opposed
by some other forces a pressure will be produced. The hypothesis of
curvature pressure is that in plasma that is producing the local curvature
of space the non-geodesic motion of electrons and nuclei due to
electromagnetic forces will produce a pressure that reacts back upon the
plasma. In this case it is a self interacting pressure that will act against
changes in density. Since the curvature depends on density an increase in
density will produce an increase in curvature and hence an increase in
pressure that will act to try and decrease the density. Although the
curvature pressure is negligible in most circumstances it is very important
in cosmology and may be important in solar neutrino production.

THE COSMOLOGICAL MODEL
The simplest cosmological model is for a universe that consists only of
uniform plasma. In the Friedmann equations the curvature pressure replaces
the cosmologic constant. Except for this modification there is no change
needed in the equations for general relativity. The result is a set of
equations that are easily solved to get a static cosmology. Of most
importance is that the model is
stable and thus it obeys the perfect cosmological principle. There is only
one free parameter, the plasma density. The Hubble constant and the radius
of the universe are directly determined by the density. What is interesting
is that this model predicts that the temperature of the plasma is
independent of the density and is 2.56E9 K. The real universe clearly has
large density variations. Unfortunately these variations are not in
equilibrium and it is difficult to determined appropriate equations of
state. While they may not greatly change the broad picture they will make
second order corrections to many predictions.

OLBER’S PARADOX
There is no problem with Olber’s paradox in this model. Any radiation will
be redshifted until all of its energy is lost. This energy goes into heating
the cosmic plasma. In turn galaxies and stars are being continuously created
from the cosmic plasma so that in a statistical sense the universe is the
same everywhere and for all time.

CREATION OF THE ELEMENTS
A major problem in any cosmology is the creation of deuterium and helium
from hydrogen. In this model the cosmic plasma is hot enough to sustain
nuclear interactions. Furthermore the major interactions will be the
destruction of heavier nuclei that were produced in stars and supernovae.

BLACK HOLES
The collapse of a body to something smaller than a neutron star will be
invariably accompanied by the production of energy so that such an object
will be very hot. In such an object there will be curvature pressure due to
the strong nuclear forces preventing the particles from following geodesics.
It is argued that this will prevent the final collapse to a black hole.
Moreover if the body is rotating the combination of curvature pressure and
instabilities may provide a mechanism for the production of two jets of
material. Could this explain the occurrence of astrophysics jets on both
stellar and galactic dimensions? The result is an object smaller than a
neutron star with all the external characteristics of a black hole.

COSMOLOGICAL TESTS
Because it has very few free parameters CC is easily refutable. Probably it
most important prediction that can be tested is that there is no evolution.
To be more precise if it is shown that there is any characteristic of any
object that can be shown to change with time this would be a major blow to
CC. The tests to be discussed have two objectives. The first is to show that
they have strong support for the model and the second is to critically
examine the evidence for evolution.

BACKGROUND X-RAY OBSERVATIONS
These are very important in that they can provide an estimate of the cosmic
plasma density and an estimate of its temperature. Although the energy range
below about 10 kev and that above about 300 kev are well explained by the
presence of discrete sources; the explanation for the intermediate range is
uncertain. Although in big bang (BB) cosmology the explanation of X-rays
being due to bremsstrahlung provides a good fit the large plasma densities
required are ruled out by the Sunyaev-Zel’dovitch effect. In CC the required
densities are lower and Figs. 4 & 5 show an excellent fit. For the plasma
composition of hydrogen with 8.5% helium the density is 1.34 H atoms/cubic
metre. The fitted temperature is (2.62 +/- 0.04)E9 K to be compared with the
predicted temperature of 2.56E9 K. The temperature agreement is excellent.

COSMIC MICROWAVE BACKGROUND RADIATION
The prediction and black body spectrum of the CMBR is claimed as a major
victory for BB cosmology. First we note that a black body spectrum is the
maximum entropy distribution for photons with a fixed energy density
provided that all energy levels are available and there is a mechanism for
transferring photons between levels. Thus the black body spectrum is a
default spectrum. Without belittling the claim I would be more impressed if
BB cosmology had predicted a non-black body spectrum which was then found.
Note that in BB cosmology the prediction of an exact temperature is
difficult and the best a priori prediction was a lower limit of 5K. In CC
the CMBR arises from the secondary photons of electrons undergoing the
curvature redshift interaction. What we observe is the
local production of the CMBR photons (say z1). They are continuously
produced and redshifted in a two stage process that will populate all levels
and therefore a black body spectrum is predicted. We can estimate the
temperature of the CMBR by requiring that the energy loss rate by the
electrons must equal the energy loss rate by the CMBR photons. That is we
ignore other radiation such as the background X-ray radiation. This gives a
temperature of 3.48 K to be compared with the observation of 2.729 K. Note
that the prediction is sensitive to the second order effects of density
variations.

SUNYAEV-ZEL’DOVICH EFFECT
The major criticism of tired-light redshifts is that we do not observe the
Sunyaev-Zel’dovich effect in the CMBR. In this model the mean free path for
a density of 1.34 is 435 Gpc whereas the production distance is less than
4.9 Gpc (z=1) which means that only about 1% of the photons have a Compton
interaction. Thus the effect is negligible.

TYPE 1A SUPERNOVAE
The observations of these supernovae are critical since they appear to show
a well defined time-dilation of their light curves which is contrary to CC.
Fig. 6 shows the light curve widths relative to a template of supernovae
from the Supernovae Cosmology Project. The straight line shows the fitted
straight line which shows a power law slope of 0.956+/- 0.022 which is in
full agreement with BB cosmology. The only worry is that the Chi^2 fit has a
value of 509.4 for 48 (DoF). The width uncertainties are accurate so why is
the Chi^2 a factor of about 10 too large. In CC this width verses z
dependence is explained as a selection effect. Fig. 7 shows the absolute
magnitudes verses width factor and shows that the power law between
luminosity and width has a value of -1.07+/-0.18 which is opposite in sign
to that suggested by Phillips (1993) & Hamuy et al(1996). My analysis of
their data (local supernovae in Fig. 8) gave an exponent of 1.16+/-0.47.
Using BB cosmology there is no variation of absolute magnitude with width.
The particular choice of BB parameters used produces a luminosity-distance
equation that differs from the CC one by a factor close to (1+z). Thus in BB
cosmology the luminosity-width relation is hidden by the BB
luminosity-distance equation.

The interesting physics is that a slope of -1.07 shows that the total energy
output of a type 1a supernova is constant, that is in full agreement with
the Chandrasekar limit. The BB result shows that the total energy varies
with width exponent of 2.31! Thus the CC result shows that the supernovae
maximum luminosity is inversely proportional to the width of its light
curve. Now Richardson et al (2002) have shown that for local supernovae the
standard deviation of their absolute magnitudes is 0.56 mag. Thus if there
is a selection effect there is sufficient variation in magnitudes and hence
widths to cover the observed distribution. However this is not sufficient
since we still must explain why there is a strong dependence of width on z
and not a scatter plot. The process getting these supernovae results is a
two stage process. The first stage is to monitor a large number of galaxies
to wait for possible supernovae. The second stage is to make repeated
observations of it to determine its parameters. Now this second stage is
very expensive and as a result there is considerable pressure to eliminate
supernovae of other types as soon as possible. After all the major objective
was to get magnitudes and the width verses redshift relationship was deemed
to be well understood. Using the BB cosmological model the rms value for the
absolute magnitudes was 0.22 mag which is a surprising small value (c.f.0.56
mag cited above). Thus a simple selection model is that after initial
observations any candidate that had an absolute magnitude (BB) greater than
a chosen value was rejected. Then because of the absolute magnitude verses
width relationship a curve (dashed line in Fig. 6) is expected. Given the
absolute magnitude and width for a type 1a supernova we can use the width to
correct the absolute magnitude to a “standard candle”. This is shown for SCP
data in Fig. 9 and for data from Riess et al (2004) in Fig. 10. This latter
set goes to a larger redshift than the SCP data. A minor
problem is that in CC the redshift is a good measure of distance for distant
objects but it is distorted by galactic halos and gas clouds for nearby
objects. In Fig 10 the fitted straight line for all the supernova with z0.1
has an exponent of -0.061+\-0.088 with Chi^2=57.0 (62 DoF) which is
consistent with no variation of magnitude with distance. Thus there is no
indication of any dark energy. The simple CC equation to convert from
apparent to absolute magnitudes has very strong support from the supernovae
data provided the magnitudes are corrected for width.

QUASAR VARIABILITY WITH TIME
Hawkins (2001,2003) has measured the variability of quasars over an eighteen
year period and has found no dependence on redshift. Exactly what is
predicted by CC.

LINEAR SIZE OF RADIO SOURCES
Gurvits, Kellerman & Frey (1999) have measured the angular size of extended
radio sources from the central peak to the most distant part that had a
brightness of at least 2% of the peak brightness. Fig. 11 shows a plot of
the linear size of there sources out to a redshift of about 3.9. The sources
were placed in bins and the median value was taken for each bin. The
straight line fitted to the medians has a slope of 47.3+/-10.9 kpc/z.
Because of the omission of large nearby sources and distant small objects
(lack of resolution) we would expect a small positive slope. Therefore the
data is consistent with no change in linear size with redshift. Buchalter et
al (19980) have looked at 103 double-lobed sources from the VLA First
survey. These sources are about one order of magnitude large than the
previous ones. The result was a slope of 0.39+/-0.15 Mpc/z, which is not
significant. Both these data sets show good support for the geometry of CC.

TOLMAN SURFACE BRIGHTNESS
This well known test is often quoted to show that tired-light redshifts are
invalid. I have used the data from Sandage & Lubin (in four papers in 2001)
of the surface brightness of elliptical and S0 galaxies. I have followed
their analysis except that I have used CC geometry. Results are shown in
Figs. 13 & 14. Of interest is that the surface brightness as a function of
the logarithm of linear radius Has a slope of -0.401+/-0.053 which shows
that the surface luminosity is proportional to the radius. At the end of the
analysis what we have is the surface brightness for a large number of nearby
galaxies and that for three distant clusters of galaxies. Now the expected
dependence is a power law with a slope of -1 for tired-light redshifts and a
slope of -4 for an expansion cosmology. Fig 15 shows a plot of the corrected
surface brightness verses redshift. The fitted slope was -1.81+/-0.11 which
is inconsistent with both models. However a critical point is that all the
nearby galaxies were the brightest members of their clusters! If we fit to
all the nearby galaxies and only the three brightest members of each of the
three distant clusters the slope is -0.58+/-0.24. Although it is not
conclusive we could argue that it rules out BB cosmology.

CLUSTERS OF GALAXIES
One of the major reasons for introducing dark matter was to explain the
apparent fact that the virial theorem when applied to the velocities of
galaxies in a cluster gave one or more orders of magnitude mass for the
cluster than that obtained from luminosities. The Coma cluster is fairly
symmetric and has
a gas cloud in its centre. Curvature redshift predicts that galaxies seen
through this gas cloud will have increased redshifts. For 583 galaxies the
rms velocity is 893 km/s. Unfortunately we do not know the Z distance of
each galaxy. However if we assume that our position is not privileged we can
use a Monte Carlo method and give each galaxy a Z position that is the same
as an X or Y position for another arbitrary galaxy. This was done many times
and using the gas density and distribution obtained from X-ray observations
the average rms was estimated to be 554 km/s. Although this differs from the
observed value it must be emphasised that there were no free parameters, it
is very sensitive to the distance to the Coma cluster and it should be noted
that both the galaxy and the gas cloud density distributions are quite
complex.

Although the Virgo cluster is fairly irregular a plot (Fig. 16) of the
redshifts of inner galaxies verses their (non Hubble) distance shows a
strong dependence and a straight line has a slope of 436+/-152 km/s/Mpc
which is consistent with the Coma results.

An important consequence of redshift due to cluster gas is that galaxies
within the cluster and those seen though it will have increased redshifts.
For the Coma cluster the average increase is about 1200 km/s. This is
evidence for this from Karaji et al (1976). Furthermore there is a well
known void in front of the Coma cluster with a width of about 3000 km/s.
Although the numerical agreement is not perfect there is no doubt that many
of the voids and structure in the redshift distribution of galaxies could be
due to the presence of gas clouds.

THE HUBBLE CONSTANT
The basic theory says that the Hubble constant (parameter?) is given by
H=42.21sqrt(N) km/s/Mpc, and with N=1.34 we get H=48.9 km/s/Mpc. For the
Coma cluster with an average velocity of 6926 km/s and a distance of 87.1
Mpc we get H=(6926-1205)/87.1=65.7 km/s/Mpc. The supernovae 1a results
provide a value of 69 km/s/Mpc. Given the unknown corrections needed for
inhomogeneous cosmic plasma in the theoretical value and uncertainties in
the observational values the agreement is reasonable.

LYMAN-ALPHA FOREST
The obvious cosmological test is to determine the density of Lyman-alpha
absorption lines as a function of redshift. There are two big problems in
that each quasar only provides a narrow range of redshifts and the number of
lines is critically dependent on measuring the correct base levels. It is
now thought that the problem of resolution is now largely overcome. The
result is that there does not appear to be a consistent set of observations
that can be used for definitive cosmological tests. In addition the
occurrence of curvature redshift in an absorbing cloud will broaden any
spectral line. This may explain the occurrence of lines with very large
widths.

EVOLUTION
There are four topics that will be covered in this section. They are the
distribution and evolution of galaxies and quasars, the Butcher-Oemler
effect and the radio source counts as a function of flux density. The
analysis of galaxies and quasars follow essentially the same procedure. The
absolute magnitude is computed for each object and then given the
characteristics of the data set the total volume in which that object could
be have been observed and still accepted into the data set is calculated.
The reciprocal of this volume is the density for that object. This is down
for each object and the densities are added into bins in absolute magnitude.
For both galaxies and quasars a distribution was observed that was very
close to a Gaussian with a narrow width. For galaxies the curves are shown
in Fig. 17 and the distribution had a peak (B magnitude of -19.14 mag and a
HWHM of 1.16 mag. The quasar results are shown in Fig.23 with a peak
of -22.82 mag and HWHM of 0.854 mag. To look for evolution it is essential
to only use those objects that can be observed at all redshifts within the
range. A suitable measure is the average absolute magnitude as a function of
redshift. For galaxies the selection criteria are shown in Fig. 18 and the
magnitude verses redshift dependence is shown in Fig. 19. For quasars the
figures are Fig. 22 and Fig. 24. In both cases the spread in magnitude as a
function of z is small and there is no consistent trend. Thus are no obvious
signs of evolution.

The Butcher-Oemler effect is the apparent increase in the fraction of blue
galaxies in a cluster as the redshift of the cluster increases. There
appears to be great difficulty in achieving consistent results over a wide
range of wavelengths. Often one cannot tell whether K-corrections (which are
essential) have been applied. Adreon et al (2004) state that “Twenty years
after the original intuition by Butcher & Oemler, we are still in the
process of ascertaining the reality of the Butcher-Oemler effect”.

I have been able to devise a simple distribution for radio sources that
shows excellent agreement with observed results. The results are shown in
Fig. 25 where the counts have been corrected to a Euclidean distribution and
the points for each frequency group have been increased by a factor of 10
from the set immediately below it. Except for the early low frequency
results the model shows all of the basic structure and a good fit to the
data. These results are meant to be a proof of concept rather than
definitive results.

In conclusion after examining four of the major sets of observations which
show strong evolution in bag bang cosmology I have shown that the
observations are consistent with CC without any sign of evolution.

MISCELLANEOUS TOPICS
One topic for which CC does not have a clear cut answer is that of galactic
rotation curves. The typical spiral galactic rotation curve shows a rapid
rise in (linear) velocity and then an almost constant value to points beyond
the visible galaxy. This is usually ascribed to the presence of a huge halo
of dark matter. In CC the magnitude of the velocity is readily achieved by
curvature redshift in the normal galactic halo. The problem is that a
symmetric halo would produce a symmetric velocity curve unlike the observed
asymmetric ones. One possibility is that the halos are in fact asymmetric
because of ram pressure due to the galaxy moving through the external
medium.

In the Milky Way galaxy the density of interstellar gas is sufficient to
inhibit curvature redshift for radio frequency photons but not for optical
photons. Consequently any object that can be seen at both frequencies should
show curvature redshift for the optical lines but not for 21 cm and other
radio frequency lines.

Although the deficiency in rate of solar neutrinos can be explained by a
non-zero neutrino mass and neutrino mixing it is interesting to investigate
the application of curvature pressure in the sun. Using the standard solar
model the presence of curvature pressure decreased the pressure at 0.1 solar
radii by 12.5% and the temperature by 4.1%. The resulting predictions for
the solar neutrino experiments a

Table 23: Predicted and observed solar neutrino production rates.
Experiment, Unit, Predicted, Observed, Chi^2
Homes SNU, 2.66±0.42, 2.56±0.23, 0.04
GALLEX+GNO, SNU, 85.6±5.4, 70.8±5.9, 3.42
SAGE, SNU, 85.6±5.4, 70.9±6.4, 3.08
Kamiokande, 10E6cm-2/s, 1.45±0.26, 2.8±0.38, 8.60
Super-Kamiokande,10E6cm-2/s, 1.45±0.26, 2.35±0.08, 10.95
SNO, 10E6cm-2/s, 1.45±0.26, 1.76±0.10, 0.25

The anomalous acceleration of Pioneer 10 can be explained by the occurrence
of curvature redshift due to the inter-planetary dust. Although the apparent
acceleration from curvature redshift is away from the sun it must be
remembered that the only navigation information comes from Doppler radar. In
solving the celestial mechanics equations the navigation program in effect
reverses the sign of the apparent acceleration. The required dust density is
about 8.8E-19 kg/m^3. Although this is higher than measurements made with a
limited range of grain sizes it is feasible.

--
David F. Crawford
(Please remove the bird)
http://www.davidcrawford.bigpondhosting.com


 




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