Cosmology with photometric redshift surveys

We explore the utility of future photometric redshift imaging surveys for delineating the large-scale structure of the Universe, and assess the resulting constraints on the cosmological model. We perform the following two complementary types of analysis. (i) We quantify the statistical confidence and the accuracy with which such surveys will be able to detect and measure characteristic features in the clustering power spectrum such as the acoustic oscillations and the turnover, in a 'model-independent' fashion. We show for example that a 10 000-deg2 imaging survey with depth r= 22.5 and photometric redshift accuracy δz/(1 +z) = 0.03 will detect the acoustic oscillations with 99.9 per cent confidence, measuring the associated preferred cosmological scale with 2 per cent precision. Such a survey will also detect the turnover with 95 per cent confidence, determining the corresponding scale with 20 per cent accuracy. (ii) By assuming a Λ cold dark matter (ΛCDM) model power spectrum we calculate the confidence with which a non-zero baryon fraction can be deduced from such future galaxy surveys. We quantify 'wiggle detection' by calculating the number of standard deviations by which the baryon fraction is measured, after marginalizing over the shape parameter. This is typically a factor of 4 more significant (in terms of number of standard deviations) than the above 'model-independent' result. For both analyses, we quantify the variation of the results with magnitude depth and photometric redshift precision, and discuss the prospects for obtaining the required performance with realistic future surveys. We conclude that the precision with which the clustering pattern may be inferred from future photometric redshift surveys will be competitive with contemporaneous spectroscopic redshift surveys, assuming that systematic effects can be controlled. We find that for equivalent wiggle detection power, a photometric redshift survey requires an area approximately 12[δz/(1 +z)]/0.03 times larger than a spectroscopic survey, for a given magnitude limit. We also note that an analysis of luminous red galaxies in the Sloan Digital Sky Survey may yield a marginal detection of acoustic oscillations in the imaging survey, in addition to that recently reported for the spectroscopic component

Cosmological parameters from CMB and other data: a Monte-Carlo approach

We present a fast Markov Chain Monte-Carlo exploration of cosmological parameter space. We perform a joint analysis of results from recent CMB experiments and provide parameter constraints, including sigma_8, from the CMB independent of other data. We next combine data from the CMB, HST Key Project, 2dF galaxy redshift survey, supernovae Ia and big-bang nucleosynthesis. The Monte Carlo method allows the rapid investigation of a large number of parameters, and we present results from 6 and 9 parameter analyses of flat models, and an 11 parameter analysis of non-flat models. Our results include constraints on the neutrino mass (m_nu < 0.3eV), equation of state of the dark energy, and the tensor amplitude, as well as demonstrating the effect of additional parameters on the base parameter constraints. In a series of appendices we describe the many uses of importance sampling, including computing results from new data and accuracy correction of results generated from an approximate method. We also discuss the different ways of converting parameter samples to parameter constraints, the effect of the prior, assess the goodness of fit and consistency, and describe the use of analytic marginalization over normalization parameters

Combining Supernovae and LSS Information with the CMB

Observations of the Cosmic Microwave Background (CMB), large scale structure (LSS) and standard candles such as Type 1a Supernovae (SN) each place different constraints on the values of cosmological parameters. We assume an inflationary Cold Dark Matter model with a cosmological constant, in which the initial density perturbations in the universe are adiabatic. We discuss the parameter degeneracies inherent in interpreting CMB or SN data, and derive their orthogonal nature. We then present our preliminary results of combining CMB and SN likelihood functions. The results of combining the CMB and IRAS 1.2 Jy survey information are given, with marginalised confidence regions in the H_0, Omega_m, b_IRAS and Q_rms-ps directions assuming n=1, Omega_Lambda+Omega_m=1 and Omega_b h^2=0.024. Finally we combine all three likelihood functions and find that the three data sets are consistent and suitably orthogonal, leading to tight constraints on H_0, Omega_m, b_IRAS and Q_rms-ps, given our assumptions.Comment: 7 pages, 4 figures, submitted to ``The CMB and the Planck Mission'', proceedings of the workshop held in Santander, Spain, June 199

Combining cosmological datasets: hyperparameters and Bayesian evidence

A method is presented for performing joint analyses of cosmological datasets, in which the weight assigned to each dataset is determined directly by it own statistical properties. The weights are considered in a Bayesian context as a set of hyperparameters, which are then marginalised over in order to recover the posterior distribution as a function only of the cosmological parameters of interest. In the case of a Gaussian likelihood function, this marginalisation may be performed analytically. Calculation of the Bayesian evidence for the data, with and without the introduction of hyperparameters, enables a direct determination of whether the data warrant the introduction of weights into the analysis; this generalises the standard likelihood ratio approach to model comparison. The method is illustrated by application to the classic toy problem of fitting a straight line to a set of data. A cosmological illustration of the technique is also presented, in which the latest measurements of the cosmic microwave background power spectrum are used to infer constraints on cosmological parameters.Comment: 12 pages, 6 figures, submitted to MNRA

Cosmography: Cosmology without the Einstein equations

How much of modern cosmology is really cosmography? How much of modern cosmology is independent of the Einstein equations? (Independent of the Friedmann equations?) These questions are becoming increasingly germane -- as the models cosmologists use for the stress-energy content of the universe become increasingly baroque, it behoves us to step back a little and carefully disentangle cosmological kinematics from cosmological dynamics. The use of basic symmetry principles (such as the cosmological principle) permits us to do a considerable amount, without ever having to address the vexatious issues of just how much "dark energy", "dark matter", "quintessence", and/or "phantom matter" is needed in order to satisfy the Einstein equations. This is the sub-sector of cosmology that Weinberg refers to as "cosmography", and in this article I will explore the extent to which cosmography is sufficient for analyzing the Hubble law and so describing many of the features of the universe around us.Comment: 7 pages; uses iopart.cls setstack.sty. Based on a talk presented at ACRGR4, the 4th Australasian Conference on General Relativity and Gravitation, Monash University, Melbourne, January 2004. To appear in the proceedings, in General Relativity and Gravitatio

Homoeopathy

Homoeopathy is a system of treating patients using very low dose preparations according to the principle: "like should be cured with like". This paper summarises the research evidence presented in a recent issue of Effective Health Care on the effectiveness of homoeopathy. Increasing numbers of patients are seeking information on complementary medicines from NHS health professionals. Results of a 1998 survey of use and expenditure on complementary medicine in England suggested that 28% of respondents had either visited a complementary therapist or had purchased an over the counter herbal or homoeopathic remedy in the past year. From this survey it was estimated that there could be over 470 000 recent users of homoeopathic remedies in England

Bayesian `Hyper-Parameters' Approach to Joint Estimation: The Hubble Constant from CMB Measurements

Recently several studies have jointly analysed data from different cosmological probes with the motivation of estimating cosmological parameters. Here we generalise this procedure to take into account the relative weights of various probes. This is done by including in the joint \chi^2 function a set of `Hyper-Parameters', which are dealt with using Bayesian considerations. The resulting algorithm (in the case of uniform priors on the log of the Hyper-Parameters) is very simple: instead of minimising \sum \chi_j^2 (where \chi_j^2 is per data set j) we propose to minimise \sum N_j \ln (\chi_j^2) (where N_j is the number of data points per data set j). We illustrate the method by estimating the Hubble constant H_0 from different sets of recent CMB experiments (including Saskatoon, Python V, MSAM1, TOCO and Boomerang).Comment: submitted to MNRAS, 6 pages, Latex, with 3 figures embedde

Limitations of model fitting methods for lensing shear estimation

Gravitational lensing shear has the potential to be the most powerful tool for constraining the nature of dark energy. However, accurate measurement of galaxy shear is crucial and has been shown to be non-trivial by the Shear TEsting Programme. Here we demonstrate a fundamental limit to the accuracy achievable by model-fitting techniques, if oversimplistic models are used. We show that even if galaxies have elliptical isophotes, model-fitting methods which assume elliptical isophotes can have significant biases if they use the wrong profile. We use noise-free simulations to show that on allowing sufficient flexibility in the profile the biases can be made negligible. This is no longer the case if elliptical isophote models are used to fit galaxies made up of a bulge plus a disk, if these two components have different ellipticities. The limiting accuracy is dependent on the galaxy shape but we find the most significant biases for simple spiral-like galaxies. The implications for a given cosmic shear survey will depend on the actual distribution of galaxy morphologies in the universe, taking into account the survey selection function and the point spread function. However our results suggest that the impact on cosmic shear results from current and near future surveys may be negligible. Meanwhile, these results should encourage the development of existing approaches which are less sensitive to morphology, as well as methods which use priors on galaxy shapes learnt from deep surveys.Comment: 10 pages, 8 figure

Improving Search through A3C Reinforcement Learning based Conversational Agent

We develop a reinforcement learning based search assistant which can assist users through a set of actions and sequence of interactions to enable them realize their intent. Our approach caters to subjective search where the user is seeking digital assets such as images which is fundamentally different from the tasks which have objective and limited search modalities. Labeled conversational data is generally not available in such search tasks and training the agent through human interactions can be time consuming. We propose a stochastic virtual user which impersonates a real user and can be used to sample user behavior efficiently to train the agent which accelerates the bootstrapping of the agent. We develop A3C algorithm based context preserving architecture which enables the agent to provide contextual assistance to the user. We compare the A3C agent with Q-learning and evaluate its performance on average rewards and state values it obtains with the virtual user in validation episodes. Our experiments show that the agent learns to achieve higher rewards and better states.Comment: 17 pages, 7 figure