Observational Evidence Favors a Static Universe - Journal of ...

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The next step is to estimate the exponential parameter βk. A small com- plication is that the apparent magnitudes have a measurement uncertainty so that assuming a Gaussian error distribution the expected distribution is the convolution of a Gaussian with the exponential distribution to get p(m) dm = β exp(−β( m − m) + 1 2 β2 σ 2 ) dm where σ is the standard deviation of the magnitude uncertainty. Note that the second term shows that there is an excess of quasars moved from fainter magnitudes compared to those moved to fainter magnitudes. The maximum likelihood estimate for β is the solution to the quadratic equation β 2 σ 2 − ( m − m)β + 1 where m is the mean magnitude and its variance is var(β) = β 2 N(1 − β 2 σ 2 ) This analysis has been done for the SDSS data (Richards et al., 2007) and the results are shown in Fig. 4 where filled circles (red) are for CC volumes and the filled diamonds (blue) are for BB volumes. Both sets of points have been normalized to be the same for z = 0.9. The selection probability for each quasar is allowed for by including only those quasars that have a selection probability greater than 0.3 and by dividing each quasars contribution to the distribution by the selection probability. As expected the different volumes between the cosmologies have only a small effect. The full (blue) line shows the BB distance modulus and the dashed (red) line is for the CC modulus. The uncertainties were estimated from the deviations from a smooth curve: in this case µ CC(z). The plotted lines are the theoretical distance moduli normalized in the same way as the data. The apparently lower values for observations near z=2.8 are probably due to confusion between the spectra of stars and that for quasars in 45
this region which not only produces lower selection probabilities but also makes their estimates more uncertain. The very clear result is that the quasars are consistent with CC but they are not consistent with BB without evolution. Figure 4: The distance modulus of SDSS quasars as a function of redshift. The diamonds (blue) are for BB and the circles (red) are for CC. The full (blue) line is the theoretical distance modulus for BB and the dotted (red) line is for CC. All have been normalized to be the same at z = 0.9. The conclusion is that CC clearly fits the data whereas BB would require evolution that cancels the expansion term in its distance modulus. 4.7 Radio Source Counts The count of the number of radio sources as a function of their flux density is one of the earliest cosmological tests that arose from the development of radio astronomy after World War II. Indeed, this test played a pivotal role 46
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Page 5 and 6: premise that the most constant char
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Page 9 and 10: cosmic gas (i.e. inter-galactic gas
Page 11 and 12: For this geometry the area of a thr
Page 13 and 14: 3 Theoretical Table 2: Comparison o
Page 15 and 16: characteristics would constitute se
Page 17 and 18: Table 3: Galactic properties for Pe
Page 19 and 20: Table 4: Fitted exponents for dista
Page 21 and 22: Table 5: Radii and fitted exponents
Page 23 and 24: used 393 galaxies with redshift ran
Page 25 and 26: likelihood estimate of ˆ S is ˆSe
Page 27 and 28: can be compared with β = 2.28 give
Page 29 and 30: Figure 1: Width of supernovae type
Page 31 and 32: 4.3.2 Supernovae in CC Since the re
Page 33 and 34: Figure 2: Absolute magnitudes, M CC
Page 35 and 36: the peak luminosity will be proport
Page 37 and 38: that is M0, is −19.070 ± 0.042.
Page 39 and 40: evidence for strong luminosity sele
Page 41 and 42: Table 8: M ∗ CC for SED Type 1 ga
Page 43: volume and ρ is the quasar density
Page 47 and 48: S would be constant. It has the fur
Page 49 and 50: Table 9: Origin of radio source-cou
Page 51 and 52: Clearly, the model satisfies the ba
Page 53 and 54: e more precise fB is the fraction t
Page 55 and 56: where σi is the uncertainty in yi,
Page 57 and 58: Buchalter, A., Helfand, D.J., Becke
Page 59 and 60: Djorgovski, S.G. & Spinrad H., (198
Page 61 and 62: Hogg D.W., (1999). Distance measure
Page 63 and 64: Liddle, A.E. & Lyth, D.H., 2000, Co
Page 65 and 66: Peacock, J.A., (1999), Cosmological
Page 67 and 68: Sloan Digital Sky Survey Quasar Sur
Page 69 and 70: Schneider, D. P., Hall, P. B., Rich
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