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Small-scale biogas systems can play a pivotal role in sustainable energy provision, particularly in developing countries. However, their dependence on livestock manure as the only feedstock poses challenges to their adoption and long-term viability. This often leads to insufficient biogas production and plant abandonment. This study proposes co-digestion of livestock manure with other farm residues to enhance the technical sustainability of small-scale biogas systems by ensuring adequate and consistent biogas production throughout the plant’s lifespan, minimizing the risks associated with reliance on a single feedstock. A novel feedstock selection approach is developed using the Analytic Hierarchy Process (AHP), a multicriteria decision-making method, to prioritize feedstocks based on adequacy, supply consistency, and logistical ease. AHP is chosen due to its capability to handle both quantitative and qualitative evaluation criteria. This approach is applied to the Fès-Meknès region of Morocco, which offers abundant livestock and crop residues alongside product utilization pathways. The prioritization and ranking of the potential feedstocks identified in the region reveals cattle manure as the top-ranked feedstock due to its consistent supply and ease of collection, followed by straw, valued for its storability and nutrient stability. Sheep, horse, and chicken manure ranked third, fourth, and fifth, respectively, while household food waste and fruit and vegetable residues, limited by seasonality and perishability, were ranked lower. Based on these findings, co-digestion of cattle manure and straw is proposed as a sustainable strategy for small-scale biogas plants in Fès-Meknès, addressing feedstock shortages, enhancing biogas production, and reducing plant abandonment. This approach strengthens technical sustainability and promotes the broader adoption of biogas technologies in developing countries.

General relativity stacks up Modern cosmology relies on the assumption that general relativity is a valid theory of gravity at cosmological scales, though until now no test of the proposition has been possible. One such test was recently proposed, though, based on a determination of a quantity E G that combines measures of large-scale gravitational lensing, galaxy clustering, and the growth rate of structure as predicted by the standard model. Reyes et al . report a measurement of E G = 0.39±0.06 based on data from a sample of more than 70,000 distant galaxies, which is consistent with the value of 0.4 predicted by general relativity. Although general relativity underlies modern cosmology, its applicability on cosmological length scales has yet to be stringently tested. Now, at a length scale of tens of megaparsecs, the quantity E G , which combines measures of large-scale gravitational lensing, galaxy clustering, and the growth rate of structure, has been measured to be 0.39±0.06, in agreement with the general relativistic prediction of about 0.4. Although general relativity underlies modern cosmology, its applicability on cosmological length scales has yet to be stringently tested. Such a test has recently been proposed 1 , using a quantity, E G , that combines measures of large-scale gravitational lensing, galaxy clustering and structure growth rate. The combination is insensitive to ‘galaxy bias’ (the difference between the clustering of visible galaxies and invisible dark matter) and is thus robust to the uncertainty in this parameter. Modified theories of gravity generally predict values of E G different from the general relativistic prediction because, in these theories, the ‘gravitational slip’ (the difference between the two potentials that describe perturbations in the gravitational metric) is non-zero, which leads to changes in the growth of structure 2 and the strength of the gravitational lensing effect 3 . Here we report that E G = 0.39 ± 0.06 on length scales of tens of megaparsecs, in agreement with the general relativistic prediction of E G  ≈ 0.4. The measured value excludes a model 1 within the tensor–vector–scalar gravity theory 4 , 5 , which modifies both Newtonian and Einstein gravity. However, the relatively large uncertainty still permits models within f ( ) theory 6 , which is an extension of general relativity. A fivefold decrease in uncertainty is needed to rule out these models.

Small-scale biogas plants in developing countries present a viable alternative to traditional polluting energy sources, particularly in rural and underserved communities. These systems typically rely on locally sourced livestock manure; however, inconsistent supply often results in underfeeding, reduced biogas production, and, in many cases, system abandonment. Co-digestion with crop residues presents a promising strategy to enhance feedstock availability and system resilience. However, the recalcitrant nature of lignocellulosic biomass and limited access to suitable pretreatment technologies have constrained its adoption. This paper evaluates feasible pretreatment methods for integrating crop residues, especially straw, into small-scale biogas systems. Using the Analytic Hierarchy Process (AHP), pretreatment methods are assessed based on five criteria: (i) technology simplicity, (ii) energy requirements, (iii) capital and operational costs, (iv) effectiveness, and (v) environmental impact. The analysis identifies microbial pretreatment using the liquid fraction of digestate, combined with mechanical size reduction, as the most suitable approach for small-scale implementation, utilizing low-cost, simplified mechanical devices adaptable to various crop residues with minimal energy input. A conceptual design of a demonstration plant is proposed to validate this integrated pretreatment approach and assess its impact on biogas yield, system performance, and technology adoption. The design incorporates an on-site digestate separation unit to supply microbial inoculum and emphasizes simplicity and cost-effectiveness in material handling and energy use. Pilot trials are proposed to evaluate key performance indicators, including specific methane yield (LCH4/gVS added), volatile solids reduction (%), and methane content increase (%), ensuring evidence-based adoption and practical applicability of the design.

The Large-Scale Structure (LSS) of the universe has the potential to provide decisive answers to the remaining open questions in cosmology. Early attempts at modelling it analytically focused on using perturbation theory. However, small-scale effects introduced by gravitational collapse cannot be described perturbatively and this failure of perturbation theory is reflected even on the largest scales. The Effective Field Theory of Large Scale Structure (EFTofLSS) has emerged as a consistent method for describing LSS on large scales by introducing counterterms that account for the effects of small-scale dynamics. So far studies of the EFT have mostly focused on the two and three point functions with little attention devoted to the four point function or trispectrum. The trispectrum probes cubic interactions arising from non-linear clustering, biasing, and primordial non-Gaussianities, and constitutes a key element of the covariance matrix of the power spectrum. In this paper, we present explicit calibrations of the EFT counterterms for the one-loop trispectrum. Specifically, we find clear evidence for non-zero EFT corrections. We define two one-parameter ans\"atze for the counterterm of the one-loop propagator and show that they provide a good correction to the residual at scales below k~0.07 h/Mpc. We then take the amplitudes of the linear and quadratic counterkernels calculated in our previous paper on the bispectrum and use them in the remaining counterterms, establishing consistency of the counterterms in the two, three and four point function. We also show that the commonly used EdS approximation for the growth of the density fields leads to errors that are of the same magnitude as loop corrections to the trispectrum on large scales.

The bispectrum is the leading non-Gaussian statistic in Large-Scale Structure (LSS) clustering and encodes the interactions in the underlying field. It is thus an important diagnostic for primordial non-Gaussianity and higher order galaxy biasing. In this paper we present a detailed test and calibration of the matter bispectrum counterterms in the Effective Field Theory of LSS against a suite of \\(N\\)-body simulations. We are going beyond previous studies in employing realisation based perturbation theory that allows for a significant reduction in cosmic variance error bars. This enables the measurement of the low-energy constants on large scales before two-loop corrections become relevant, around \\(k<0.09 hMpc^-1\\) at \\(z=0\\). We also go beyond previous work in using bispectrum propagator terms, i.e. correlators with linear and second order fields, to quantify the two new counterterms in isolation and to establish consistency with the power spectrum counterterm. By investigating the fully non-linear bispectrum, \\(B_nnn\\), as well as the terms \\(B_n11\\) and \\(B_n21\\), we find evidence for the new counterterms deviating from the shape suggested by the UV-limit of the relevant bispectrum contributions. We also show that the commonly used Einstein-de Sitter approximation for the time dependence of the tree-level bispectrum is insufficient for precise studies of the one-loop bispectrum and that it is necessary to use \\(\\)CDM growth factors in order to obtain meaningful one-loop counterterm constraints. Finally, we also find evidence for small deviations in the growth factors that arise from time integration inaccuracies in the \\(N\\)-body simulations.

Motivated by recent developments in perturbative calculations of the nonlinear evolution of large-scale structure, we present an iterative algorithm to reconstruct the initial conditions in a given volume starting from the dark matter distribution in real space. In our algorithm, objects are first moved back iteratively along estimated potential gradients, with a progressively reduced smoothing scale, until a nearly uniform catalog is obtained. The linear initial density is then estimated as the divergence of the cumulative displacement, with an optional second-order correction. This algorithm should undo nonlinear effects up to one-loop order, including the higher-order infrared resummation piece. We test the method using dark matter simulations in real space. At redshift \\(z=0\\), we find that after eight iterations the reconstructed density is more than \\(95\\%\\) correlated with the initial density at \\(k 0.35\\; hMpc^-1\\). The reconstruction also reduces the power in the difference between reconstructed and initial fields by more than 2 orders of magnitude at \\(k 0.2\\; hMpc^-1\\), and it extends the range of scales where the full broadband shape of the power spectrum matches linear theory by a factor of 2-3. As a specific application, we consider measurements of the baryonic acoustic oscillation (BAO) scale that can be improved by reducing the degradation effects of large-scale flows. In our idealized dark matter simulations, the method improves the BAO signal-to-noise ratio by a factor of 2.7 at \\(z=0\\) and by a factor of 2.5 at \\(z=0.6\\), improving standard BAO reconstruction by \\(70\\%\\) at \\(z=0\\) and \\(30\\%\\) at \\(z=0.6\\), and matching the optimal BAO signal and signal-to-noise ratio of the linear density in the same volume. For BAO, the iterative nature of the reconstruction is the most important aspect.

The baryon acoustic oscillation (BAO) feature provides an important distance scale for the measurement of the expansion history of the Universe. Theoretical models of the BAO in the distribution of biased tracers of the large scale structure usually rely on an initially linear BAO. With aid of N-body simulations, we demonstrate that the BAO in the initial (Lagrangian) halo 2-point function is significantly sharper than in the linear matter distribution, in agreement with peak theory. Using this approach, we delineate the scale-dependence induced by the higher-derivative and velocity bias before assessing how much of the initial BAO enhancement survives until the collapse epoch. Finally, we discuss the extent to which the velocity or gravity bias, which is also imprinted in the displacement field of halos, affects the contrast of the BAO obtained with a reconstruction.

Predictions of the next-to-leading order, i.e. one-loop, halo power spectra depend on local and non-local bias parameters up to cubic order. The linear bias parameter can be estimated from the large scale limit of the halo-matter power spectrum, and the second order bias parameters from the large scale, tree-level, bispectrum. Cubic operators would naturally be quantified using the tree-level trispectrum. As the latter is computationally expensive, we extent the quadratic field method proposed in Schmittfull et al. 2014 to cubic fields in order to estimate cubic bias parameters. We cross-correlate a basis set of cubic bias operators with the halo field and express the result in terms of the cross-spectra of these operators in order to cancel cosmic variance. We obtain significant detections of local and non-local cubic bias parameters, which are partially in tension with predictions based on local Lagrangian bias schemes. We directly measure the Lagrangian bias parameters of the protohaloes associated with our halo sample and clearly detect a non-local quadratic term in Lagrangian space. We do not find a clear detection of non-local cubic Lagrangian terms for low mass bins, but there is some mild evidence for their presence for the highest mass bin. While the method presented here focuses on cubic bias parameters, the approach could also be applied to quantifications of cubic primordial non-Gaussianity.

The bispectrum is the leading non-Gaussian statistic in large-scale structure, carrying valuable information on cosmology that is complementary to the power spectrum. To access this information, we need to model the bispectrum in the weakly non-linear regime. In this work we present the first two-loop, i.e., next-to-next-to-leading order perturbative description of the bispectrum within an effective field theory (EFT) framework. Using an analytic expansion of the perturbative kernels up to \\(F_6\\) we derive a renormalized bispectrum that is demonstrated to be independent of the UV cutoff. We show that the EFT parameters associated with the four independent second-order EFT operators known from the one-loop bispectrum are sufficient to absorb the UV sensitivity of the two-loop contributions in the double-hard region. In addition, we employ a simplified treatment of the single-hard region, introducing one extra EFT parameter at two-loop order. We compare our results to N-body simulations using the realization-based grid-PT method and find good agreement within the expected range, as well as consistent values for the EFT parameters. The two-loop terms start to become relevant at \\(k 0.07h~Mpc^-1\\). The range of wavenumbers with percent-level agreement, independently of the shape, extends from \\(0.08h~Mpc^-1\\) to \\(0.15h~Mpc^-1\\) when going from one to two loops at \\(z=0\\). In addition, we quantify the impact of using exact instead of Einstein-de-Sitter kernels for the one-loop bispectrum, and discuss in how far their impact can be absorbed into a shift of the EFT parameters.

Associating the formation sites of haloes with the maxima of the smoothed linear density field, we present non-perturbative predictions for the Lagrangian and evolved halo correlation functions that are valid at all separations. In Lagrangian space, we find significant deviations from the perturbative bias calculation at small scales, in particular, a pronounced exclusion region where \\(=-1\\) for maxima of unequal height. Our predictions are in good agreement with the Lagrangian clustering of dark matter proto-haloes reconstructed from N-body simulations. Our predictions for the mean infall and velocity dispersion of haloes, which differ from the local bias expansion, show a similar level of agreement with simulations. Finally, we displace the initial density peaks according to the Zeldovich approximation in order to predict the late-time clustering of dark matter haloes. While we are able to reproduce the early evolution of this conserved set of tracers, our approximation fails at the collapse epoch (z=0) on non-linear scales r<10Mpc/h, emphasizing the need for a non-perturbative treatment of the halo displacement field.