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Observational Evidence Favors a Static Universe

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1 Observational evidence favors a static universe David F. Crawford Sydney Institute for Astronomy, School of Physics, University of Sydney. Correspondence: 44 Market St, Naremburn, 2065, NSW, Australia email: [email protected] Abstract The common attribute of all Big Bang cosmologies is that they are based on the assumption that the universe is expanding. However exam- ination of the evidence for this expansion clearly favors a static universe. The major topics considered are: Tolman surface brightness, angular size, type 1a supernovae, gamma ray bursts, galaxy distributions, quasar dis- tributions, X-ray background radiation, cosmic microwave background ra- diation, radio source counts, quasar variability and the Butcher{Oemler effect. An analysis of the best raw data for these topics shows that they are consistent with expansion only if there is evolution that cancels the effects of expansion. An alternate cosmology, curvature cosmology, is a tired-light cosmology that predicts a well defined static and stable uni- verse and is fully described. It not only predicts accurate values for the Hubble constant and the temperature of cosmic microwave background radiation but shows good agreement with most of the topics considered. Curvature cosmology also predicts the deficiency in solar neutrino pro- duction rate and can explain the anomalous acceleration of Pioneer 10. Note: The editor of the Journal of Cosmology required this paper to be divided into three parts. Except for the abstracts, introductions and conclusions the text of the three papers is identical to this version. For convenience a table of contents is included in this version. The correspondence between the sections in this version and those in the Journal of Cosmology are: Part I sections2,3,4 72pp 2011, JCos, 13, 3875-3946 Part II section5 53pp 2011, JCos, 13, 3947-3999 Part III sections6&7 58pp 2001, JCos, 13, 4000-4057 cosmology: observations, large-scale structure of universe, theory arXiv:1009.0953v5 [physics.gen-ph] 9 Jul 2014 CONTENTS 2 Contents 1 Introduction3 2 Cosmographic Parameters7 2.1 Big Bang cosmology (BB) . .8 2.2 Curvature cosmology (CC) . .8 2.3 Numerical comparison of BB and CC . 10 3 Theoretical 11 4 Expansion and Evolution 12 4.1 Tolman surface brightness . 12 4.1.1 Surface brightness in BB . 12 4.1.2 Surface brightness in CC . 15 4.1.3 Conclusion for surface brightness . 16 4.2 Angular size . 16 4.3 Type 1a supernovae . 17 4.3.1 Supernovae in BB . 19 4.3.2 Supernovae in CC . 20 4.3.3 Supernova conclusion . 24 4.4 Gamma ray bursts (GRB) . 25 4.5 Galaxy distribution . 25 4.6 Quasar distribution . 27 4.7 Radio Source Counts . 28 4.8 Quasar variability in time . 32 4.9 The Butcher{Oemler effect . 33 5 Non-expansion Observations 34 5.1 The Hubble redshift . 34 5.2 X-ray background radiation . 34 5.2.1 X-rays in BB . 34 5.2.2 X-rays in CC . 35 5.3 Cosmic microwave background radiation . 39 5.3.1 CMBR in BB . 40 5.3.2 CMBR in CC . 40 5.3.3 CMBR conclusions . 43 5.4 CMBR at large redshifts . 43 5.5 Fluctuations in the CMBR . 44 5.6 Dark matter . 44 5.7 The Sunyaev{Zel'dovich effect . 46 5.8 Gravitational lensing . 47 5.9 Lyman alpha forest . 48 5.10 The Gunn{Peterson trough in high redshift quasars . 49 5.11 Nuclear abundances . 51 5.12 Galactic rotation curves . 51 5.13 Redshifts in our Galaxy . 52 5.14 Anomalous redshifts . 53 5.15 Voids . 54 1 INTRODUCTION 3 6 Curvature Cosmology Theory 55 6.1 Derivation of curvature redshift . 56 6.1.1 Photons in Curved Spacetime . 57 6.1.2 Curvature redshift secondary photons . 60 6.1.3 Inhibition of curvature redshift . 61 6.1.4 Possible laboratory tests . 62 6.1.5 Interactions for other particles . 65 6.2 Derivation of curvature pressure . 66 6.2.1 Gravitation is not a force . 66 6.2.2 A Newtonian model . 67 6.2.3 General relativistic model . 68 6.2.4 Local curvature pressure . 69 6.3 The curvature cosmological model . 71 6.3.1 The Friedmann equations . 71 6.3.2 Temperature of the cosmic plasma . 72 6.3.3 Hubble constant: theory . 73 6.3.4 Geometry of CC . 73 6.3.5 Luminosities and magnitudes . 74 7 Application of Curvature Cosmology 75 7.1 Entropy . 75 7.2 Olber's Paradox . 76 7.3 Black holes and Jets . 77 7.4 Large number coincidences . 77 7.5 Solar neutrino production . 78 7.6 Heating of the solar corona . 80 7.7 Pioneer 10 acceleration . 80 8 Conclusion 83 A Analytic methods 84 1 Introduction The common attribute of all Big Bang cosmologies (BB) is that they are based on the assumption that the universe is expanding (Peebles, 1993). An early al- ternative was the steady-state theory of Hoyle, Bondi and Gold (described with later extensions by Hoyle et al.(2000)) that required continuous creation of matter. However steady-state theories have serious difficulties in explaining the cosmic microwave background radiation. This left BB as the dominant cosmol- ogy but still subject to criticism. Recently Lal(2010) and Joseph(2010) have continued major earlier criticisms of Big Bang cosmologies (Ellis, 1984; Lerner, 1991; Disney, 2000; Van Flandern, 2002). Whereas most of theses criticisms have been of a theoretical nature this paper concentrates on whether observa- tional data supports BB or a static cosmological model, curvature cosmology (CC), described below. Expansion produces two distinct effects. The first effect of expansion is the increasing redshift with distance as described by Hubble's law. This could be due to either a genuine expansion or resulting from a tired-light phenomenon. 1 INTRODUCTION 4 The second effect of expansion is time dilation resulting from the slowing down of the arrival times of the photons as the source gets further away. Section4 concentrates on the evidence for expansion as shown by time dilation and shows that the evidence is only consistent with BB if there is evolution in either lu- minosity or in angular size that closely cancels the effects of time dilation. To illustrate that a static cosmology can explain the data, a particular model, cur- vature cosmology (CC), is used. Curvature cosmology is based on the hypothesis of curvature redshift and the hypothesis of curvature pressure. Curvature red- shift arises from the principle that any localized wave travelling in curved space time will follow geodesics and be subject to geodesics focussing. Since this will alter the transverse properties of the wave some of its properties such as angu- lar momentum will be altered which is contrary to quantum mechanics. For a photon the result is an interaction that results in three new photons. One with almost identical energy and momentum as the original and two extremely low energy secondary photons. In effect the photon loses energy via an interaction with curved space-time. The concept of curvature pressure arises from the idea that the density of particles produce curved space-time. Then as a function of their velocity there will be a reaction pressure that acts to decrease the local space-time curvature. It is the evaluation of evidence for this expansion that forms the major ba- sis of this paper. Consequently minor differences between different expansion cosmologies are not particularly important here; it is the broad brush approach that is relevant. Nevertheless to provide appropriate numerical quantities the evaluation is based on a particular BB cosmology, the (ΛCDM) model, which is defined in Section2 by the equations for angular size, volume and distance modulus. Since the major difference between BB and CC arises from the expan- sion in BB, the major results of the comparison are applicable to other static cosmologies and do not depend on the validity of CC. A problem in evaluating a well established cosmology like Big Bang cosmology is that all of the obser- vations have been analyzed within the BB paradigm. Thus there can be subtle effects that may lead to a possible bias. In order to avoid this bias and wherever possible comparisons are made using original observations. Section3 discusses the theoretical justification for the basic and additional hypotheses that have been incorporated into the cosmologies. For BB these includes inflation, dark matter and dark energy. For CC the hypotheses are curvature redshift and curvature pressure. The evaluation of BB and its comparison with CC using observational evi- dence is divided into four major parts. The first in Section4 concentrates on those observations that have measurements that are strongly dependent on ex- pansion. It is found that in all cases where there is direct evidence for evolution this evolution is close to what is required to cancel the expansion term in the BB equations. This is an extraordinary coincidence. The simplest conclusion is that the universe is not expanding. Section5 looks at observations that have different explanations in CC from what they have in BB. It is found that not only does CC gave better agreement with most of the observations but it does so without requiring extra ad hoc parameters or hypotheses. The next section is a description of CC and possible experimental tests of its validity. Finally Section7 examines additional important topics that are relevant to CC. The test for Tolman surface brightness in Section4 is through the expected variation of apparent surface brightness with redshift. The results strongly favor 1 INTRODUCTION 5 a static universe but could be consistent with BB provided there is luminosity evolution. The relationship between angular size and linear size in BB includes a aber- ration factor of (1 + z) that does not occur in static cosmologies.
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