## Theory

#### Skewness consistency relation in large-scale structure and test of gravity theory

We investigate the skewness of galaxy number density fluctuations as a possible probe to test gravity theories. We find that the specific linear combination of the skewness parameters corresponds to the coefficients of the second-order kernels of the density contrast, which can be regarded as the consistency relation and used as a test of general relativity and modified gravity theories. We also extend the analysis of the skewness parameters from real space to redshift space and derive the redshift-space skewness consistency relation.

**†The uncertain interstellar medium of high-redshift quiescent galaxies: Impact of methodology**

How much gas and dust is contained in high-redshift quiescent galaxies (QGs) is currently an open question with relatively few and contradictory answers, as well as important implications for our understanding of the nature of star formation quenching processes at cosmic noon. Here we revisit far-infrared (FIR) observations of the REQUIEM-ALMA sample of six z = 1.6 - 3.2 QGs strongly lensed by intermediate-redshift galaxy clusters. We measured their continuum emission using priors obtained from high resolution near-infrared (NIR) imaging, as opposed to focusing on point-source extraction, converted it into dust masses using a FIR dust emission model derived from statistical samples of QGs, and compared the results to those of the reference work. We find that, while at least the most massive sample galaxy is indeed dust-poor, the picture is much more nuanced than previously reported. In particular, these more conservative constraints remain consistent with high dust fractions in early QGs. We find that these measurements are very sensitive to the adopted extraction method and conversion factors: the use of an extended light model to fit the FIR emission increases the flux of detections by up to 50% and the upper limit by up to a factor 6. Adding the FIR-to-dust conversion, this amounts to an order of magnitude difference in dust fraction, casting doubts on the power of these data to discriminate between star formation quenching scenarios. Unless these are identified by other means, mapping the dust and gas in high-redshift QGs will continue to require somewhat costly observations.

**Approach**

**†COVMOS: a new Monte Carlo approach for galaxy clustering analysis**

We validate the COVMOS method introduced in Baratta et al. (2019) allowing for the fast simulation of catalogues of different cosmological field tracers (e.g. dark matter particles, halos, galaxies, etc.). The power spectrum and one-point probability distribution function of the underlying tracer density field are set as inputs of the method and are arbitrarily chosen by the user. In order to evaluate the validity domain of COVMOS at the level of the produced two-point statistics covariance matrix, we choose to target these two input statistical quantities from realistic *N*-body simulation outputs. In particular, we perform this cloning procedure in a ΛCDM and in a massive neutrino cosmologies, for five redshifts in the range *z*∈[0,2]. First, we validate the output real-space two-point statistics (both in configuration and Fourier space) estimated over 5,000 COVMOS realisations per redshift and per cosmology, with a volume of 1 [Gpc/*h*]3 and 108 particles each. Such a validation is performed against the corresponding *N*-body measurements, estimated from 50 simulations. We find the method to be valid up to *k*∼0.2*h*/Mpc for the power spectrum and down to *r* ∼20 Mpc/*h* for the correlation function. Then, we extend the method by proposing a new modelling of the peculiar velocity distribution, aiming at reproducing the redshift-space distortions both in the linear and mildly non-linear regimes. After validating this prescription, we finally compare and validate the produced redshift-space two-point statistics covariance matrices in the same range of scales. We release on a public repository the Python code associated with this method, allowing the production of tens of thousands of realisations in record time. COVMOS is intended for any user involved in large galaxy-survey science requiring a large number of mock realisations.

**†Inference of cosmological models with principal component analysis**

In this paper, we combine the Principal Component Analysis (PCA) and Markov Chain Monte Carlo (MCMC) method to infer the parameters of cosmological models. We use No U Turn Sampler (NUTS) to run the MCMC chains in the model parameter space. After testing our methodology with simulated data, we apply the same in the observed data-set. We assume a polynomial expansion as the parametrization of the dark energy equation of state. We show that this method is effective in constraining cosmological parameters from data, including sparse data-sets.

**Sparse Bayesian mass-mapping using trans-dimensional MCMC**

Uncertainty quantification is a crucial step of cosmological mass-mapping that is often ignored. Suggested methods are typically only approximate or make strong assumptions of Gaussianity of the shear field. Probabilistic sampling methods, such as Markov chain Monte Carlo (MCMC), draw samples form a probability distribution, allowing for full and flexible uncertainty quantification, however these methods are notoriously slow and struggle in the high-dimensional parameter spaces of imaging problems. In this work we use, for the first time, a trans-dimensional MCMC sampler for mass-mapping, promoting sparsity in a wavelet basis. This sampler gradually grows the parameter space as required by the data, exploiting the extremely sparse nature of mass maps in wavelet space. The wavelet coefficients are arranged in a tree-like structure, which adds finer scale detail as the parameter space grows. We demonstrate the trans-dimensional sampler on galaxy cluster-scale images where the planar modelling approximation is valid. In high-resolution experiments, this method produces naturally parsimonious solutions, requiring less than 1% of the potential maximum number of wavelet coefficients and still producing a good fit to the observed data. In the presence of noisy data, trans-dimensional MCMC produces a better reconstruction of mass-maps than the standard smoothed Kaiser-Squires method, with the addition that uncertainties are fully quantified. This opens up the possibility for new mass maps and inferences about the nature of dark matter using the new high-resolution data from upcoming weak lensing surveys such as Euclid.

## interest

**The basics of primordial black hole formation and abundance estimation**

This paper is a biased review of the primordial black hole (PBH) formation and abundance estimation. We first review the three-zone model for PBH formation to help an intuitive understanding of the PBH formation process. Then, for more accurate analyses, we introduce necessary tools such as cosmological long-wavelength solutions, the definition of the mass and compaction function in a spherically symmetric spacetime and peak theory. Combining all these tools, we calculate the PBH mass spectrum for the case of the monochromatic curvature power spectrum as a demonstration.

**Why and When to Expect Gaussian Error Distributions in Epoch of Reionization 21-cm Power Spectrum Measurements**

We explore error distributions in Epoch of Reionization 21-cm power spectrum estimators using a combination of mathematical analysis and numerical simulations. We provide closed form solutions for the error distributions of individual bins in 3d-power spectra for two estimators currently in use in the field, which we designate as “straight-square” and “cross-multiply” estimators. We then demonstrate when the corresponding spherically binned power spectra should (and should not) have Gaussian error distributions, which requires appealing to nonstandard statements of the central limit theorem. This has important implications for how upper limits are reported, as well as how cosmological inferences are performed based on power spectrum measurements. Specifically, assuming a Gaussian error distribution can over or underestimate the upper limit depending on the type of estimator, and produces overly compact likelihood functions for the power spectrum.

**Evidence for non-merger co-evolution of galaxies and their supermassive black holes**

**Recent observational and theoretical studies have suggested that supermassive black holes (SMBHs) grow mostly through non-merger (`secular’) processes.** Since galaxy mergers lead to dynamical bulge growth, the only way to observationally isolate non-merger growth is to study galaxies with low bulge-to-total mass ratio (e.g. B/T < 10%). However, bulge growth can also occur due to secular processes, such as disk instabilities, making disk-dominated selections a somewhat incomplete way to select merger-free systems. Here we use the Horizon-AGN simulation to select simulated galaxies which have not undergone a merger since z = 2, regardless of bulge mass, and investigate their location on typical black hole-galaxy scaling relations in comparison to galaxies with merger dominated histories. While the existence of these correlations has long been interpreted as co-evolution of galaxies and their SMBHs driven by galaxy mergers, we show here that they persist even in the absence of mergers.**We find that the correlations between SMBH mass and both total mass and stellar velocity dispersion are independent of B/T ratio for both merger-free and merger-dominated galaxies. In addition, the bulge mass and SMBH mass correlation is still apparent for merger-free galaxies, the intercept for which is dependent on B/T. Galaxy mergers reduce the scatter around the scaling relations, with merger-free systems showing broader scatter. We show that for merger-free galaxies, the co-evolution is dominated by radio-mode feedback, and suggest that the long periods of time between galaxy mergers make an important contribution to the co-evolution between galaxies and SMBHs in all galaxies.**