We introduce a new, non-parametric method to infer deprojected 3D mass profiles M(r) of galaxy clusters from weak gravitational lensing observations. The method assumes spherical symmetry and a moderately small convergence, κ≲1. The assumption of spherical symmetry is an important restriction, which is, however, quite common in practice, for example in methods that fit lensing data to an NFW profile. Moreover, with a mild assumption on the probability distributions of the source redshifts, our method relies on spherical symmetry only at radii larger than the radius r at which the mass M is inferred. That is, the method may be useful even for clusters with a non-symmetric inner region, since it correctly estimates the enclosed mass beyond the radius where spherical symmetry is restored. We discuss how to correct, statistically and approximately, for miscentering given that the probability distribution of miscentering offsets is known. We provide an efficient implementation in Julia code that runs in a few milliseconds per galaxy cluster. We explicitly demonstrate the method by using data from KiDS DR4 to infer mass profiles for two example clusters, Abell 1835 and Abell 2744, finding results consistent with existing literature.

The Aether-Scalar-Tensor (AeST) theory is an extension of General Relativity (GR) which can support Modified Newtonian Dynamics (MOND) behaviour in its static weak-field limit, and cosmological evolution resembling ΛCDM. We consider static spherically symmetric weak-field solutions in this theory and show that the resulting equations can be reduced to a single equation for the gravitational potential. The reduced equation has apparent isolated singularities at the zeros of the derivative of the potential and we show how these are removed by evolving, instead, the canonical momentum of the corresponding Hamiltonian system that we find. We construct solutions in three cases: (i) in vacuum outside a bounded spherical object, (ii) within an extended prescribed source, and (iii) for an isothermal gas in hydrostatic equilibrium, serving as a simplified model for galaxy clusters. We show that the oscillatory regime that follows the Newtonian and MOND regimes, obtained in previous works in the vacuum case, also persists for isothermal spheres, and we show that the gas density profiles in AeST can become more compressed than their Newtonian or MOND counterparts. We construct the Radial Acceleration Relation (RAR) in AeST for isothermal spheres and find that it can display a peak, an enhancement with respect to the MOND RAR, at an acceleration range determined by the value of the AeST weak-field mass parameter, the mass of the system and the boundary value of the gravitational potential. For lower accelerations, the AeST RAR drops below the MOND expectation, as if there is a negative mass density. Similar observational features of the galaxy cluster RAR have been reported. This illustrates the potential of AeST to address the shortcomings of MOND in galaxy clusters, but a full quantitative comparison with observations will require going beyond the isothermal case.

Reconstructions of the primordial power spectrum (PPS) of curvature perturbations from cosmic microwave background anisotropies and large-scale structure data suggest that the usually assumed power-law PPS has localised features (up to \sim 10\%∼10% in amplitude), although of only marginal significance in the framework of \LambdaΛCDM cosmology. On the other hand if the cosmology is taken to be Einstein-de Sitter, larger features in the PPS (up to \sim 20\%∼20% in amplitude) are required to accurately fit the observed acoustic peaks. Within the context of single clock inflation, we show that any given reconstruction of the PPS can be mapped on to functional parameters of the underlying effective theory of the adiabatic mode within a 2nd-order formalism, provided the best fit fractional change of the PPS, \Delta{P}_{R}/{P}_{R}ΔPR/PR is such that (\Delta{P}_{R}/{P}_{R})^3(ΔPR/PR)3 falls within the 1\,\sigma1σ confidence interval of the reconstruction for features induced by variations of either the sound speed c_\mathrm{s}cs or the slow-roll parameter \epsilonϵ. Although there is a degeneracy amongst these functional parameters (and the models that project onto them), we can identify simple representative inflationary models that yield such features in the PPS. Thus we provide a dictionary (more accurately, a thesaurus) to go from observational data, via the reconstructed PPS, to models that reproduce them to per cent level precision.