By 1917, V.M. Slipher had singlehandedly established a tendency for spiral nebulae to be redshifted (21 out of 25 cases). From a modern perspective, it could seem surprising that the expansion of the universe was not announced at this point. Examinat
ion of Sliphers papers shows that he reached a more subtle conclusion: the identification of cosmological peculiar velocities, including the bulk motion of the Milky Way, leading to a beautiful argument in favour of nebulae as distant stellar systems. Nevertheless, Sliphers data actually contain evidence at >8sigma for a positive mean velocity, even after subtracting the dipole owing to the motion of the observer. In 1929, Hubble estimated distances for a sample of no greater depth, using redshifts due almost entirely to Slipher. Hubbles distances were flawed in two distinct ways: in addition to an incorrect absolute calibration, the largest distances were systematically under-estimated. Nevertheless, he claimed the detection of a linear distance-redshift relation. Statistically, the evidence for such a correlation is less strong than the simple evidence for a positive mean velocity in Hubbles sample. Comparison with modern data shows that a sample of more than twice Hubbles depth would generally be required in order to reveal clearly the global linear expansion in the face of the noise from peculiar velocities. When the theoretical context of the time is examined, the role of the de Sitter model and its prediction of a linear distance-redshift relation looms large. A number of searches for this relation were performed prior to Hubble over the period 1924-1928, with a similar degree of success. All were based on the velocities measured by Slipher, whose work from a Century ago stands out both for the precision of his measurements and for the subtle clarity of the arguments he employed to draw correct conclusions from them.
We discuss the use of the Bayesian evidence ratio, or Bayes factor, for model selection in astronomy. We treat the evidence ratio as a statistic and investigate its distribution over an ensemble of experiments, considering both simple analytical exam
ples and some more realistic cases, which require numerical simulation. We find that the evidence ratio is a noisy statistic, and thus it may not be sensible to decide to accept or reject a model based solely on whether the evidence ratio reaches some threshold value. The odds suggested by the evidence ratio bear no obvious relationship to the power or Type I error rate of a test based on the evidence ratio. The general performance of such tests is strongly affected by the signal to noise ratio in the data, the assumed priors, and the threshold in the evidence ratio that is taken as `decisive. The comprehensiveness of the model suite under consideration is also very important. The usefulness of the evidence ratio approach in a given problem can be assessed in advance of the experiment, using simple models and numerical approximations. In many cases, this approach can be as informative as a much more costly full-scale Bayesian analysis of a complex problem.
In a flat universe dominated by dark energy, the Integrated Sachs-Wolfe (ISW) effect can be detected as a large-angle cross-correlation between the CMB and a tracer of large scale structure. We investigate whether the inconclusive ISW signal derived
from 2MASS galaxy maps can be improved upon by including photometric redshifts for the 2MASS galaxies. These redshifts are derived by matching the 2MASS data with optical catalogues generated from SuperCOSMOS scans of major photographic sky surveys. We find no significant ISW signal in this analysis; an ISW effect of the form expected in a LambdaCDM universe is only weakly preferred over no correlation, with a likelihood ratio of 1.5:1. We consider ISW detection prospects for future large scale structure surveys with fainter magnitude limits and greater survey depth; even with the best possible data, the ISW cross-correlation signal would be expected to evade detection in >~ 10% of cases.
We estimate the local density field in redshift shells to a maximum redshift of z=0.3, using photometric redshifts for the 2MASS galaxy catalogue, matched to optical data from the SuperCOSMOS galaxy catalogue. This density-field map is used to predic
t the Integrated Sachs-Wolfe (ISW) CMB anisotropies that originate within the volume at z<0.3. We investigate the impact of this estimated ISW foreground signal on large-scale anomalies in the WMAP CMB data. We find that removal of the foreground ISW signal from WMAP data reduces the significance of a number of reported large-scale anomalies in the CMB, including the low quadrupole power and the apparent alignment between the CMB quadrupole and octopole.
Some comments are made on the usefulness or otherwise of the concept of `expanding space in cosmology. These notes are an expanded version of material first published in 2001 but not previously available online except at www.roe.ac.uk/japwww. Since t
hat personal webpage has been referred to in published work, it seems sensible to give these notes a more permanent home.
It has been claimed that the observed magnitude of the vacuum energy density is consistent with the distribution predicted in anthropic models, in which an ensemble of universes is assumed. This calculation is revisited, without making the assumption
that the CMB temperature is known, and considering in detail the possibility of a recollapsing universe. New accurate approximations for the growth of perturbations and the mass function of dark haloes are presented. Structure forms readily in the recollapsing phase of a model with negative Lambda, so collapse fraction alone cannot forbid Lambda from being large and negative. A negative Lambda is disfavoured only if we assume that formation of observers can be neglected once the recollapsing universe has heated to T > 8 K. For the case of positive Lambda, however, the current universe does occupy a extremely typical position compared to the predicted distribution on the Lambda-T plane. Contrasting conclusions can be reached if anthropic arguments are applied to the curvature of the universe, and we discuss the falsifiability of this mode of anthropic reasoning.
