Demographic studies of cosmic populations must contend with measurement errors and selection effects. We survey some of the key ideas astronomers have developed to deal with these complications, in the context of galaxy surveys and the literature on
corrections for Malmquist and Eddington bias. From the perspective of modern statistics, such corrections arise naturally in the context of multilevel models, particularly in Bayesian treatments of such models: hierarchical Bayesian models. We survey some key lessons from hierarchical Bayesian modeling, including shrinkage estimation, which is closely related to traditional corrections devised by astronomers. We describe a framework for hierarchical Bayesian modeling of cosmic populations, tailored to features of astronomical surveys that are not typical of surveys in other disciplines. This thinned latent marked point process framework accounts for the tie between selection (detection) and measurement in astronomical surveys, treating selection and measurement error effects in a self-consistent manner.
Current observational evidence does not yet exclude the possibility that dark energy could be in the form of phantom energy. A universe consisting of a phantom constituent will be driven toward a drastic end known as the `Big Rip singularity where al
l the matter in the universe will be destroyed. Motivated by this possibility, other evolutionary scenarios have been explored by Barrow, including the phenomena which he called Sudden Future Singularities (SFS). In such a model it is possible to have a blow up of the pressure occurring at sometime in the future evolution of the universe while the energy density would remain unaffected. The particular evolution of the scale factor of the universe in this model that results in a singular behaviour of the pressure also admits acceleration in the current era. In this paper we will present the results of our confrontation of one example class of SFS models with the available cosmological data from high redshift supernovae, baryon acoustic oscillations (BAO) and the cosmic microwave background (CMB). We then discuss the viability of the model in question as an alternative to dark energy.
We open the discussion into how the Laser Interferometer Space Antenna (LISA) observations of supermassive black-hole (SMBH) mergers (in the mass range ~10^6-10^8 Msun) may be complementary to pulsar timing-based gravitational wave searches. We consi
der the toy model of determining pulsar distances by exploiting the fact that LISA SMBH inspiral observations can place tight parameter constraints on the signal present in pulsar timing observations. We also suggest, as a future path of research, the use of LISA ring-down observations from the most massive (>~ a few 10^7 Msun) black-hole mergers, for which the inspiral stage will lie outside the LISA band, as both a trigger and constraint on searches within pulsar timing data for the inspiral stage of the merger.
We discuss the constraints coming from current observations of type Ia supernovae on cosmological models which allow sudden future singularities of pressure (with the scale factor and the energy density regular). We show that such a sudden singularit
y may happen in the very near future (e.g. within ten million years) and its prediction at the present moment of cosmic evolution cannot be distinguished, with current observational data, from the prediction given by the standard quintessence scenario of future evolution. Fortunately, sudden future singularities are characterized by a momentary peak of infinite tidal forces only; there is no geodesic incompletness which means that the evolution of the universe may eventually be continued throughout until another ``more serious singularity such as Big-Crunch or Big-Rip.
This note is concerned with potentially misleading concepts in the treatment of cosmological magnetic fields by magnetohydrodynamical (MHD) modelling. It is not a criticism of MHD itself but rather a cautionary comment on the validity of its use in c
osmology. Now that cosmological data are greatly improved compared with a few decades ago, and even better data are imminent, it makes sense to revisit original modelling assumptions and examine critically their shortcomings in respect of modern science. Specifically this article argues that ideal MHD is a poor approximation around recombination, since it inherently restricts evolutionary timescales, and is often misapplied in the existing literature.
The desire to extend the Hubble Diagram to higher redshifts than the range of current Type Ia Supernovae observations has prompted investigation into spectral correlations in Gamma Ray Bursts, in the hope that standard candle-like properties can be i
dentified. In this paper we discuss the potential of these new `cosmic rulers and highlight their limitations by investigating the constraints that current data can place on an alternative Cosmological model in the form of Conformal Gravity. By fitting current Type 1a Supernovae and Gamma Ray Burst (GRB) data to the predicted luminosity distance redshift relation of both the standard Concordance Model and Conformal Gravity, we show that currently emph{neither} model is strongly favoured at high redshift. The scatter in the current GRB data testifies to the further work required if GRBs are to cement their place as effective probes of the cosmological distance scale.
We present a new method for fitting peculiar velocity models to complete flux limited magnitude-redshifts catalogues, using the luminosity function of the sources as a distance indicator.The method is characterised by its robustness. In particular, n
o assumptions are made concerning the spatial distribution of sources and their luminosity function. Moreover, selection effects in redshift are allowed. Furthermore the inclusion of additional observables correlated with the absolute magnitude -- such as for example rotation velocity information as described by the Tully-Fisher relation -- is straightforward. As an illustration of the method, the predicted IRAS peculiar velocity model characterised by the density parameter beta is tested on two samples. The application of our method to the Tully-Fisher MarkIII MAT sample leads to a value of beta=0.6 pm 0.125, fully consistent with the results obtained previously by the VELMOD and ITF methods on similar datasets. Unlike these methods however, we make a very conservative use of the Tully-Fisher information. Specifically, we require to assume neither the linearity of the Tully-Fisher relation nor a gaussian distribution of its residuals. Moreover, the robustness of the method implies that no Malmquist corrections are required. A second application is carried out, using the fluxes of the IRAS 1.2 Jy sample as the distance indicator. In this case the effective depth of the volume in which the velocity model is compared to the data is almost twice the effective depth of the MarkIII MAT sample. The results suggest that the predicted IRAS velocity model, while successful in reproducing locally the cosmic flow, fails to describe the kinematics on larger scales.
In this paper, we derive a physical argument for the existence of Period-luminosity and period-luminosity-colour relations at maximum light. We examine in detail a sample of Cepheids in the Large Magellanic Cloud, and compare the variance of some PL
and PLC type distance indicators based on mean and maximum light. We show that a PLC relation based on maximum light leads to a distance estimator with a dispersion about $10 %$ smaller than its counterpart using mean light. We also show that a PLC type relation constructed using observations at both maximum and mean light has a significantly $( > 50 %)$ smaller dispersion than a PLC relation using either maximum or mean light alone. A comparable $( > 30 %)$ reduction in the dispersion of the corresponding distance estimator, however, in this case requires the relation be applied to a large $( n > 30)$ group of equidistant Cepheids in, e.g., a distant galaxy. Recent HST observations of IC4182, M81 and M100 already provide suitable candidate data sets for this relation.
