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Due to the large dynamic ranges involved with separating the cosmological 21-cm signal from the Cosmic Dawn from galactic foregrounds, a well-calibrated instrument is essential to avoid biases from instrumental systematics. In this paper we present three methods for calibrating a global 21-cm cosmology experiment using the noise wave parameter formalisation to characterise a low noise amplifier including a careful consideration of how calibrator temperature noise and singularities will bias the result. The first method presented in this paper builds upon the existing conjugate priors method by weighting the calibrators by a physically motivated factor, thereby avoiding singularities and normalising the noise. The second method fits polynomials to the noise wave parameters by marginalising over the polynomial coefficients and sampling the polynomial orders as parameters. The third method introduces a physically motivated noise model to the marginalised polynomial method. Running these methods on a suite of simulated datasets based on the REACH receiver design and a lab dataset, we found that our methods produced a calibration solution which is equally as or more accurate than the existing conjugate priors method when compared with an analytic estimate of the calibrator's noise. We find in the case of the measured lab dataset the conjugate priors method is biased heavily by the large noise on the shorted load calibrator, resulting in incorrect noise wave parameter fits. This is mitigated by the methods introduced in this paper which calibrate the validation source spectra to within 5% of the noise floor., Comment: 9 pages, 5 figures

When fits of the same physical model to two different datasets disagree, we call this tension. Several apparent tensions in cosmology have occupied researchers in recent years, and a number of different metrics have been proposed to quantify tension. Many of these metrics suffer from limiting assumptions, and correctly calibrating these is essential if we want to successfully determine whether discrepancies are significant. A commonly used metric of tension is the evidence ratio R. The statistic has been widely adopted by the community as a Bayesian way of quantifying tensions, however, it has a non-trivial dependence on the prior that is not always accounted for properly. We show that this can be calibrated out effectively with Neural Ratio Estimation. We demonstrate our proposed calibration technique with an analytic example, a toy example inspired by 21-cm cosmology, and with observations of the Baryon Acoustic Oscillations from the Dark Energy Spectroscopic Instrument~(DESI) and the Sloan Digital Sky Survey~(SDSS). We find no significant tension between DESI and SDSS.

The first billion years of cosmic history remains largely unobserved. We demonstrate, using a novel machine learning technique, how combining upper limits on the spatial fluctuations in the 21-cm signal with observations of the sky-averaged 21-cm signal from neutral hydrogen can improve our understanding of this epoch. By jointly analysing data from SARAS3 (redshift $z\approx15-25$) and limits from HERA ($z\approx8$ and $10$), we show that such a synergetic analysis provides tighter constraints on the astrophysics of galaxies 200 million years after the Big Bang than can be achieved with the individual data sets. Although our constraints are weak, this is the first time data from a sky-averaged 21-cm experiment and power spectrum experiment have been analysed together. In synergy, the two experiments leave only $64.9^{+0.3}_{-0.1}$% of the explored broad theoretical parameter space to be consistent with the joint data set, in comparison to $92.3^{+0.3}_{-0.1}$% for SARAS3 and $79.0^{+0.5}_{-0.2}$% for HERA alone. We use the joint analysis to constrain star formation efficiency, minimum halo mass for star formation, X-ray luminosity of early emitters and the radio luminosity of early galaxies. The joint analysis disfavours at 68% confidence a combination of galaxies with X-ray emission that is $\lesssim 33$ and radio emission that is $\gtrsim 32$ times as efficient as present day galaxies. We disfavour at $95$% confidence scenarios in which power spectra are $\geq126$ mK$^{2}$ at $z=25$ and the sky-averaged signals are $\leq-277$ mK., Comment: Accepted for MNRAS

We present a method for improving the performance of nested sampling as well as its accuracy. Building on previous work by Chen et al., we show that posterior repartitioning may be used to reduce the amount of time nested sampling spends in compressing from prior to posterior if a suitable ``proposal'' distribution is supplied. We showcase this on a cosmological example with a Gaussian posterior, and release the code as an LGPL licensed, extensible Python package https://gitlab.com/a-p-petrosyan/sspr.

Bayesian analysis has become an indispensable tool across many different cosmological fields including the study of gravitational waves, the Cosmic Microwave Background and the 21-cm signal from the Cosmic Dawn among other phenomena. The method provides a way to fit complex models to data describing key cosmological and astrophysical signals and a whole host of contaminating signals and instrumental effects modelled with `nuisance parameters'. In this paper, we summarise a method that uses Masked Autoregressive Flows and Kernel Density Estimators to learn marginal posterior densities corresponding to core science parameters. We find that the marginal or 'nuisance-free' posteriors and the associated likelihoods have an abundance of applications including; the calculation of previously intractable marginal Kullback-Leibler divergences and marginal Bayesian Model Dimensionalities, likelihood emulation and prior emulation. We demonstrate each application using toy examples, examples from the field of 21-cm cosmology and samples from the Dark Energy Survey. We discuss how marginal summary statistics like the Kullback-Leibler divergences and Bayesian Model Dimensionalities can be used to examine the constraining power of different experiments and how we can perform efficient joint analysis by taking advantage of marginal prior and likelihood emulators. We package our multipurpose code up in the pip-installable code margarine for use in the wider scientific community., Comment: Accepted for MNRAS

A stress-energy tensor for linear gravity adapted to the harmonic gauge was recently proposed by Butcher, Hobson and Lasenby. By removing gauge constraints and imposing full metrical GR, we find a natural generalisation to the pseudotensor of Einstein. M{\o}ller's pseudotensor is an alternative to that of Einstein formulated using tetrads. We obtain the pseudotensor of M{\o}ller for gauge theory gravity (GTG) using a variational approach, identifying a potentially interesting recipe for constructing conserved currents in that theory. We show that in static, spherical spacetimes with a central gravitational mass M{\o}ller's pseudotensor describes gravitational stress-energy as if the gravitational potential were a scalar (i.e. Klein-Gordon) field coupled to a gravitational mass density on the Minkowski background. The old Newtonian formula successfully describes the potential of even strong fields in this picture. The Newtonian limit of this effect was previously observed in the tensor of Butcher; we recover a local virial theorem in this limit. We demonstrate using the `Schwarzschild star' solution for an incompressible perfect fluid ball., Comment: Replaced with published version. 19 pages, 2 figures