This is the user manual for CosmoLattice, a modern package for lattice simulations of the dynamics of interacting scalar and gauge fields in an expanding universe. CosmoLattice incorporates a series of features that makes it very versatile and powerful: i) it is written in C++ fully exploiting the object oriented programming paradigm, with a modular structure and a clear separation between the physics and the technical details, ii) it is MPI-based and uses a discrete Fourier transform parallelized in multiple spatial dimensions, which makes it specially appropriate for probing scenarios with well-separated scales, running very high resolution simulations, or simply very long ones, iii) it introduces its own symbolic language, defining field variables and operations over them, so that one can introduce differential equations and operators in a manner as close as possible to the continuum, iv) it includes a library of numerical algorithms, ranging from O(δ t^2) to O(δ t^10) methods, suitable for simulating global and gauge theories in an expanding grid, including the case of `self-consistent' expansion sourced by the fields themselves. Relevant observables are provided for each algorithm (e.g. energy densities, field spectra, lattice snapshots) and we note that remarkably all our algorithms for gauge theories always respect the Gauss constraint to machine precision. In this manual we explain how to obtain and run CosmoLattice in a computer (let it be your laptop, desktop or a cluster). We introduce the general structure of the code and describe in detail the basic files that any user needs to handle. We explain how to implement any model characterized by a scalar potential and a set of scalar fields, either singlets or interacting with U(1) and/or SU(2) gauge fields. CosmoLattice is publicly available at www.cosmolattice.net.

Millions of medical consultations are conducted each year in Burkina Faso using the Electronic Register of Consultations (REC). Based on the consultation data collected, we present a method to quantify the quality of individual and ensembles of consultations conducted by frontline healthcare workers (FHWs). We focus on anthropometric measurements and vital signs (age, weight, height, mid-upper arm circumference and temperature) of children aged between six months and five years old. We compare individual and ensemble of consultations to a multivariate probability distribution defined by an external population-specific, gold standard consultation dataset. By comparing the distributions of consultations to the reference probability distribution, we define a score to rate the quality of measurements and data entry of FHWs. The defined scores allow us to detect which measurements are most problematic. They also allow us to detect potential biases in the consultation and treatment of different patient groups. No systematic gender-bias was found among FHWs. Height measurements were the most challenging; consultations with the lowest scores were associated with underestimated heights in children. Among these consultations, height was found to be even more underestimated among boys than girls. Our findings enable us to support capacity building of frontline healthcare workers. Based on our work, we present how the REC can be enriched with real-time alert on specific errors, and individual FHW can be proposed targeted trainings. We also propose dynamic dashboards that can support district managers to navigate the entire population of FHWs, understand FHWs' main challenges and prioritise their interventions in primary healthcare centres.

Accurately forecasting the case rate of malaria would enable key decision makers to intervene months before the onset of any outbreak, potentially saving lives. Until now, methods that forecast malaria have involved complicated numerical simulations that model transmission through a community. Here we present the first data-driven malaria epidemic early warning system that can predict the 13-week case rate in a primary health facility in Burkina Faso. Using the extraordinarily high-fidelity data of infant consultations taken from the Integrated e-Diagnostic Approach (IeDA) system that has been rolled out throughout Burkina Faso, we train a combination of Gaussian Processes and Random Forest Regressors to estimate the weekly number of malaria cases over a 13 week period. We test our algorithm on historical epidemics and find that for our lowest threshold for an epidemic alert, our algorithm has 30% precision with > 99% recall at raising an alert. This rises to > 99% precision and 5% recall for the high alert threshold. Our two-tailed predictions have an average 1σ and 2σ precision of 5 cases and 30 cases respectively.

We present a comprehensive discussion on lattice techniques for the simulation of scalar and gauge field dynamics in an expanding universe. After reviewing the continuum formulation of scalar and gauge field interactions in Minkowski and FLRW backgrounds, we introduce the basic tools for the discretization of field theories, including lattice gauge invariant techniques. Following, we discuss and classify numerical algorithms, ranging from methods of 𝒪(δ t 2 ) accuracy like staggered leapfrog and Verlet integration , to Runge-Kutta methods up to 𝒪(δ t 4 ) accuracy, and the Yoshida and Gauss-Legendre higher-order integrators, accurate up to 𝒪(δ t 10 ). We adapt these methods for their use in classical lattice simulations of the non-linear dynamics of scalar and gauge fields in an expanding grid in 3+1 dimensions, including the case of `self-consistent' expansion sourced by the volume average of the fields' energy and pressure densities. We present lattice formulations of canonical cases of: i) Interacting scalar fields , ii) Abelian (1) gauge theories , and iii) Non-Abelian (2) gauge theories . In all three cases we provide symplectic integrators, with accuracy ranging from 𝒪(δ t 2 ) up to 𝒪(δ t 10 ). For each algorithm we provide the form of relevant observables, such as energy density components, field spectra and the Hubble constraint. We note that all our algorithms for gauge theories always respect the Gauss constraint to machine precision, including when `self-consistent' expansion is considered. As a numerical example we analyze the post-inflationary dynamics of an oscillating inflaton charged under (2)×(1). We note that the present manuscript is meant to be part of the theoretical basis for the code 𝒞osmoℒattice, a multi-purpose MPI-based package for simulating the non-linear evolution of field theories in an expanding universe, publicly available at http://www.cosmolattice.net .

We present a comprehensive discussion on lattice techniques for the simulation of scalar and gauge field dynamics in an expanding universe. After reviewing the continuum formulation of scalar and gauge field interactions in Minkowski and FLRW backgrounds, we introduce basic tools for the discretization of field theories, including lattice gauge invariant techniques. Following, we discuss and classify numerical algorithms, ranging from methods of O(dt^2) accuracy like staggered leapfrog and Verlet integration, to Runge-Kutta methods up to O(dt^4) accuracy, and the Yoshida and Gauss-Legendre higher-order integrators, accurate up to O(dt^10). We adapt these methods for their use in classical lattice simulations of the non-linear dynamics of scalar and gauge fields in an expanding grid in 3+1 dimensions, including the case of `self-consistent' expansion sourced by the volume average of the fields' energy and pressure densities. We present lattice formulations of canonical cases of: i) Interacting scalar fields, ii) Abelian U(1) gauge theories, and iii) Non-Abelian SU(2) gauge theories. In all three cases we provide symplectic integrators, with accuracy ranging from O(dt^2) up to O(dt^10). For each algorithm we provide the form of relevant observables, such as energy density components, field spectra and the Hubble constraint. Remarkably, all our algorithms for gauge theories respect the Gauss constraint to machine precision, including when `self-consistent' expansion is considered. As a numerical example we analyze the post-inflationary dynamics of an oscillating inflaton charged under SU(2)× U(1). The present manuscript is meant as part of the theoretical basis for CosmoLattice, a modern C++ MPI-based package for simulating the non-linear dynamics of scalar-gauge field theories in an expanding universe, publicly available at www.cosmolattice.net

Flux ratio anomalies in strong gravitationally lensed quasars constitute a unique way to probe the abundance of non-luminous dark matter haloes, and hence the nature of dark matter. In this paper we identify double imaged quasars as a statistically efficient probe of dark matter, since they are 20 times more abundant than quadruply imaged quasars. Using N-body simulations that include realistic baryonic feedback, we measure the full distribution of flux ratios in doubly imaged quasars for cold (CDM) and warm dark matter (WDM) cosmologies. Through this method, we fold in two key systematics - quasar variability and line-of-sight structures. We find that WDM cosmologies predict a 6 per cent difference in the cumulative distribution functions of flux ratios relative to CDM, with CDM predicting many more small ratios. Finally, we estimate that 600 doubly imaged quasars will need to be observed in order to be able to unambiguously discern between CDM and the two WDM models studied here. Such sample sizes will be easily within reach of future large scale surveys such as Euclid. In preparation for this survey data we require discerning the scale of the uncertainties in modelling lens galaxies and their substructure in simulations, plus a strong understanding of the selection function of observed lensed quasars.

Observations of the redshifted 21-cm signal (in absorption or emission) allow us to peek into the epoch of "dark ages" and the onset of reionization. These data can provide a novel way to learn about the nature of dark matter, in particular about the formation of small size dark matter halos. However, the connection between the formation of structures and 21-cm signal requires knowledge of stellar to total mass relation, escape fraction of UV photons, and other parameters that describe star formation and radiation at early times. This baryonic physics depends on the properties of dark matter and in particular in warm-dark-matter (WDM) models, star formation may follow a completely different scenario, as compared to the cold-dark-matter case. We use the recent measurements by the EDGES [J. D. Bowman, A. E. E. Rogers, R. A. Monsalve, T. J. Mozdzen, and N. Mahesh, An absorption profile centred at 78 megahertz in thesky-averaged spectrum,Nature (London) 555, 67 (2018).] to demonstrate that when taking the above considerations into account, the robust WDM bounds are in fact weaker than those given by the Lyman-$\alpha$ forest method and other structure formation bounds. In particular, we show that resonantly produced 7 keV sterile neutrino dark matter model is consistent with these data. However, a holistic approach to modelling of the WDM universe holds great potential and may in the future make 21-cm data our main tool to learn about dark matter clustering properties.

We quantify the error in the results of mixed baryon-dark-matter hydrodynamic simulations, stemming from outdated approximations for the generation of initial conditions. The error at redshift 0 in contemporary large simulations is of the order of few to 10 per cent in the power spectra of baryons and dark matter, and their combined total-matter power spectrum. After describing how to properly assign initial displacements and peculiar velocities to multiple species, we review several approximations: (1) using the total-matter power spectrum to compute displacements and peculiar velocities of both fluids, (2) scaling the linear redshift-zero power spectrum back to the initial power spectrum using the Newtonian growth factor ignoring homogeneous radiation, (3) using a mix of general-relativistic gauges so as to approximate Newtonian gravity, namely longitudinal-gauge velocities with synchronous-gauge densities and (4) ignoring the phase-difference in the Fourier modes for the offset baryon grid, relative to the dark-matter grid. Three of these approximations do not take into account that dark matter and baryons experience a scale-dependent growth after photon decoupling, which results in directions of velocity that are not the same as their direction of displacement. We compare the outcome of hydrodynamic simulations with these four approximations to our reference simulation, all setup with the same random seed and simulated using GADGET-III.

We measure the weak gravitational lensing shear power spectra and their cross-power in two photometric redshift bins from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). The measurements are performed directly in multipole space in terms of adjustable band powers. For the extraction of the band powers from the data we have implemented and extended a quadratic estimator, a maximum likelihood method that allows us to readily take into account irregular survey geometries, masks, and varying sampling densities. We find the 68 per cent credible intervals in the sigma(8)-Omega(m) plane to be marginally consistent with results from Planck for a simple five-parameter Lambda cold dark matter (Lambda CDM) model. For the projected parameter S-8 equivalent to sigma(8)(Omega m/0.3)(0.5) we obtain a best-fitting value of S-8 = 0.768(-0.039)(+0.045). This constraint is consistent with results from other CFHTLenS studies as well as the Dark Energy Survey. Our most conservative model, including modifications to the power spectrum due to baryon feedback and marginalization over photometric redshift errors, yields an upper limit on the total mass of three degenerate massive neutrinos of Sigma(m nu) < 4.53 eV at 95 per cent credibility, while a Bayesian model comparison does not favour any model extension beyond a simple five-parameter Lambda CDM model. Combining the shear likelihood with Planck breaks the sigma 8-Omega(m) degeneracy and yields sigma(8) = 0.818 +/- 0.013 and Omega(m) = 0.300 +/- 0.011 which is fully consistent with results from Planck alone.

We examine the deviation of Cold Dark Matter particle trajectories from the Newtonian result as the size of the region under study becomes comparable to or exceeds the particle horizon. To first order in the gravitational potential, the general relativistic result coincides with the Zel'dovich approximation and hence the Newtonian prediction on all scales. At second order, General Relativity predicts corrections which overtake the corresponding second order Newtonian terms above a certain scale of the order of the Hubble radius. However, since second order corrections are very much suppressed on such scales, we conclude that simulations which exceed the particle horizon but use Newtonian equations to evolve the particles, reproduce the correct trajectories very well. The dominant relativistic corrections to the power spectrum on scales close to the horizon are at most of the order of $\sim 10^{-5}$ at $z=49$ and $\sim 10^{-3}$ at $z=0$. The differences in the positions of real space features are affected at a level below $10^{-6}$ at both redshifts. Our analysis also clarifies the relation of N-body results to relativistic considerations.

We present a description for setting initial particle displacements and field values for simulations of arbitrary metric theories of gravity, for perfect and imperfect fluids with arbitrary characteristics. We extend the Zel'dovich Approximation to nontrivial theories of gravity, and show how scale dependence implies curved particle paths, even in the entirely linear regime of perturbations. For a viable choice of Effective Field Theory of Modified Gravity, initial conditions set at high redshifts are affected at the level of up to 5% at Mpc scales, which exemplifies the importance of going beyond Λ-Cold Dark Matter initial conditions for modifications of gravity outside of the quasi-static approximation. In addition, we show initial conditions for a simulation where a scalar modification of gravity is modelled in a Lagrangian particle-like description. Our description paves the way for simulations and mock galaxy catalogs under theories of gravity beyond the standard model, crucial for progress towards precision tests of gravity and cosmology.

We present a new programme for placing constraints on radial inhomogeneity in a dark-energy dominated universe. We introduce a new measure to quantify violations of the Copernican principle. Any violation of this principle would interfere with our interpretation of any dark-energy evolution. In particular, we find that current observations place reasonably tight constraints on possible late-time violations of the Copernican principle: the allowed area in the parameter space of amplitude and scale of a spherical inhomogeneity around the observer has to be reduced by a factor of three so as to confirm the Copernican principle. Then, by marginalizing over possible radial inhomogeneity we provide the first constraints on the cosmological constant which are free of the homogeneity prior prevalent in cosmology.

We discuss the relation between the output of Newtonian N-body simulations on scales that approach or exceed the particle horizon to the description of general relativity. At leading order, the Zeldovich approximation is correct on large scales, coinciding with the general relativistic result. At second order in the initial metric potential, the trajectories of particles deviate from the second order Newtonian result and hence the validity of second order Lagrangian perturbation theory initial conditions should be reassessed when used in very large simulations. We also advocate using the expression for the synchronous gauge density as a well behaved measure of density fluctuations on such scales.

We present a new analysis on how to distinguish between isotropic and anisotropic cosmological models based on tracking the angular displacements of a large number of distant quasars over an extended period of time, and then performing a multipole-vector decomposition of the resulting displacement maps. We find that while the GAIA mission operating at its nominal specifications does not have sufficient angular resolution to resolve anisotropic universes from isotropic ones using this method within a reasonable timespan of ten years, a next-generation GAIA-like survey with a resolution ten times better should be equal to the task. Distinguishing between different anisotropic models is however more demanding. Keeping the observational timespan to ten years, we find that the angular resolution of the survey will need to be of order 0.1 mu as in order for certain rotating anisotropic models to produce a detectable signature that is also unique to models of this class. However, should such a detection become possible, it would immediately allow us to rule out large local void models.

We find that if we live at the center of an inhomogeneity with total density contrast of roughly 0.1, dark energy is not a cosmological constant at 95% confidence level. Observational constraints on the equation of state of dark energy, w, depend strongly on the local matter density around the observer. We model the local inhomogeneity with an exact spherically symmetric solution which features a pressureless matter component and a dark-energy fluid with constant equation of state and negligible sound speed, that reaches a homogeneous solution at finite radius. We fit this model to observations of the local expansion rate, distant supernovae and the cosmic microwave background. We conclude that the possible uncertainty from large-scale structure has to be taken into account if one wants to progress towards not just precision but also accurate cosmology.

We argue that there is an intrinsic noise on measurements of the equation of state parameter w = p/rho from large-scale structure around us. The presence of the large-scale structure leads to an ambiguity in the definition of the background universe and thus there is a maximal precision with which we can determine the equation of state of dark energy. To study the uncertainty due to local structure, we model density perturbations stemming from a standard inflationary power spectrum by means of the exact Lemaitre-Tolman-Bondi solution of Einstein's equation, and show that the usual distribution of matter inhomogeneities in a Lambda CDM cosmology causes a variation of w - as inferred from distance measures - of several percent. As we observe only one universe, or equivalently because of the cosmic variance, this uncertainty is systematic in nature. (C) 2014 The Authors. Published by Elsevier B.V.

A perfect irrotational fluid with the equation of state of dust, Irrotational Dark Matter (IDM), is incapable of virializing and instead forms a cosmoskeleton of filaments with supermassive black holes at the joints. This stark difference from the standard cold dark matter (CDM) scenario arises because IDM must exhibit potential flow at all times, preventing shell-crossing from occurring. This scenario is applicable to general non-oscillating scalar-field theories with a small sound speed. Our model of combined IDM and CDM components thereby provides a solution to the problem of forming the observed billion-solar-mass black holes at redshifts of six and higher. In particular, as a result of the reduced vortical flow, the growth of the black holes is expected to be more rapid at later times as compared to the standard scenario.

There is an approximately 9% discrepancy, corresponding to 2.4 σ, between two independent constraints on the expansion rate of the Universe: one indirectly arising from the cosmic microwave background and baryon acoustic oscillations and one more directly obtained from local measurements of the relation between redshifts and distances to sources. We argue that by taking into account the local gravitational potential at the position of the observer this tension--strengthened by the recent Planck results--is partially relieved and the concordance of the Standard Model of cosmology increased. We estimate that measurements of the local Hubble constant are subject to a cosmic variance of about 2.4% (limiting the local sample to redshifts z > 0.010) or 1.3% (limiting it to z > 0.023), a more significant correction than that taken into account already. Nonetheless, we show that one would need a very rare fluctuation to fully explain the offset in the Hubble rates. If this tension is further strengthened, a cosmology beyond the Standard Model may prove necessary.

We describe inhomogeneities in a Lambda CDM universe with a gradient series expansion and show that it describes the gravitational evolution far into the nonlinear regime and beyond the capacity of standard perturbation theory at any order. We compare the gradient expansion with exact inhomogeneous Lambda LTB solutions (Lemaitre-Tolman-Bondi metric with the inclusion of a cosmological constant) describing growing structure in a Lambda CDM universe and find that the expansion approximates the exact solution well, following the collapse of an over-density all the way into a singularity.

We present elliptic solutions to the background equations describing the Lemaître–Tolman–Bondi metric as well as the homogeneous Friedmann equation, in the presence of dust, curvature and a cosmological constant Λ. For none of the presented solutions any numerical integration has to be performed. All presented solutions are given for expanding and collapsing phases, preserving continuity in time and radius; both radial and angular scale functions are given. Hence, these solutions describe the complete spacetime of a collapsing spherical object in an expanding universe, as well as those of ever expanding objects. In the appendix we present for completeness a solution of the Friedmann equation in the additional presence of radiation, only valid for the Robertson–Walker metric.