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We introduce the rapidly emerging field of multi-messenger gravitational lensing—the discovery and science of gravitationally lensed phenomena in the distant universe through the combination of multiple messengers. This is framed by gravitational lensing phenomenology that has grown since the first discoveries in the twentieth century, messengers that span 30 orders of magnitude in energy from high-energy neutrinos to gravitational waves, and powerful ‘survey facilities’ that are capable of continually scanning the sky for transient and variable sources. Within this context, the main focus is on discoveries and science that are feasible in the next 5–10 years with current and imminent technology including the LIGO–Virgo–KAGRA network of gravitational wave detectors, the Vera C. Rubin Observatory and contemporaneous gamma/X-ray satellites and radio surveys. The scientific impact of even one multi-messenger gravitational lensing discovery will be transformational and reach across fundamental physics, cosmology and astrophysics. We describe these scientific opportunities and the key challenges along the path to achieving them. This article therefore describes the consensus that emerged at the eponymous Theo Murphy meeting in March 2024, and also serves as an introduction to this Theo Murphy meeting issue. This article is part of the Theo Murphy meeting issue ‘Multi-messenger gravitational lensing (Part 2)’. 

Synthetic methods that utilise iron to facilitate C–H bond activation to yield new C–C and C–heteroatom bonds continue to attract significant interest. However, the development of these systems is still hampered by a limited molecular-level understanding of the key iron intermediates and reaction pathways that enable selective product formation. While recent studies have established the mechanism for iron-catalysed C–H arylation from aryl-nucleophiles, the underlying mechanistic pathway of iron-catalysed C–H activation/functionalisation systems which utilise electrophiles to establish C–C and C–heteroatom bonds has not been determined. The present study focuses on an iron-catalysed C–H allylation system, which utilises allyl chlorides as electrophiles to establish a C–allyl bond. Freeze-trapped inorganic spectroscopic methods ( 57 Fe Mössbauer, EPR, and MCD) are combined with correlated reaction studies and kinetic analyses to reveal a unique and rapid reaction pathway by which the allyl electrophile reacts with a C–H activated iron intermediate. Supporting computational analysis defines this novel reaction coordinate as an inner-sphere radical process which features a partial iron–bisphosphine dissociation. Highlighting the role of the bisphosphine in this reaction pathway, a complementary study performed on the reaction of allyl electrophile with an analogous C–H activated intermediate bearing a more rigid bisphosphine ligand exhibits stifled yield and selectivity towards allylated product. An additional spectroscopic analysis of an iron-catalysed C–H amination system, which incorporates N -chloromorpholine as the C–N bond-forming electrophile, reveals a rapid reaction of electrophile with an analogous C–H activated iron intermediate consistent with the inner-sphere radical process defined for the C–H allylation system, demonstrating the prevalence of this novel reaction coordinate in this sub-class of iron-catalysed C–H functionalisation systems. Overall, these results provide a critical mechanistic foundation for the rational design and development of improved systems that are efficient, selective, and useful across a broad range of C–H functionalisations. 

Abstract We outline the “dark siren” galaxy catalog method for cosmological inference using gravitational wave (GW) standard sirens, clarifying some common misconceptions in the implementation of this method. When a confident transient electromagnetic counterpart to a GW event is unavailable, the identification of a unique host galaxy is in general challenging. Instead, as originally proposed by Schutz, one can consult a galaxy catalog and implement a dark siren statistical approach incorporating all potential host galaxies within the localization volume. Trott & Huterer recently claimed that this approach results in a biased estimate of the Hubble constant, H 0 , when implemented on mock data, even if optimistic assumptions are made. We demonstrate explicitly that, as previously shown by multiple independent groups, the dark siren statistical method leads to an unbiased posterior when the method is applied to the data correctly. We highlight common sources of error possible to make in the generation of mock data and implementation of the statistical framework, including the mismodeling of selection effects and inconsistent implementations of the Bayesian framework, which can lead to a spurious bias. 

Abstract Since 2015 the gravitational-wave observations of LIGO and Virgo have transformed our understanding of compact-object binaries. In the years to come, ground-based gravitational-wave observatories such as LIGO, Virgo, and their successors will increase in sensitivity, discovering thousands of stellar-mass binaries. In the 2030s, the space-based LISA will provide gravitational-wave observations of massive black holes binaries. Between the $$\sim 10$$ ∼ 10 –10 3 Hz band of ground-based observatories and the $$\sim 10^{-4}$$ ∼ 1 0 − 4 –10 − 1 Hz band of LISA lies the uncharted decihertz gravitational-wave band. We propose a Decihertz Observatory to study this frequency range, and to complement observations made by other detectors. Decihertz observatories are well suited to observation of intermediate-mass ( $$\sim 10^{2}$$ ∼ 1 0 2 –10 4 M ⊙ ) black holes; they will be able to detect stellar-mass binaries days to years before they merge, providing early warning of nearby binary neutron star mergers and measurements of the eccentricity of binary black holes, and they will enable new tests of general relativity and the Standard Model of particle physics. Here we summarise how a Decihertz Observatory could provide unique insights into how black holes form and evolve across cosmic time, improve prospects for both multimessenger astronomy and multiband gravitational-wave astronomy, and enable new probes of gravity, particle physics and cosmology. 

The standard model of cosmology has provided a good phenomenological description of a wide range of observations both at astrophysical and cosmological scales for several decades. This concordance model is constructed by a universal cosmological constant and supported by a matter sector described by the standard model of particle physics and a cold dark matter contribution, as well as very early-time inflationary physics, and underpinned by gravitation through general relativity. There have always been open questions about the soundness of the foundations of the standard model. However, recent years have shown that there may also be questions from the observational sector with the emergence of differences between certain cosmological probes. In this White Paper, we identify the key objectives that need to be addressed over the coming decade together with the core science projects that aim to meet these challenges. These discordances primarily rest on the divergence in the measurement of core cosmological parameters with varying levels of statistical confidence. These possible statistical tensions may be partially accounted for by systematics in various measurements or cosmological probes but there is also a growing indication of potential new physics beyond the standard model. After reviewing the principal probes used in the measurement of cosmological parameters, as well as potential systematics, we discuss the most promising array of potential new physics that may be observable in upcoming surveys. We also discuss the growing set of novel data analysis approaches that go beyond traditional methods to test physical models. These new methods will become increasingly important in the coming years as the volume of survey data continues to increase, and as the degeneracy between predictions of different physical models grows. There are several perspectives on the divergences between the values of cosmological parameters, such as the model-independent probes in the late Universe and model-dependent measurements in the early Universe, which we cover at length. The White Paper closes with a number of recommendations for the community to focus on for the upcoming decade of observational cosmology, statistical data analysis, and fundamental physics developments 

The first direct syntheses, structural characterizations, and reactivity studies of multinuclear iron–phenyl species formed upon reaction of Fe(acac)₃and PhMgBr in THF are described. 

Abstract Homoleptic σ‐bonded uranium–alkyl complexes have been a synthetic target since the Manhattan Project. The current study describes the synthesis and characterization of several unprecedented uranium–methyl complexes. Amongst these complexes, the first example of a homoleptic uranium–alkyl dimer, [Li(THF)₄]₂[U₂(CH₃)₁₀], as well as a seven‐coordinate uranium–methyl monomer, {Li(OEt₂)Li(OEt₂)₂UMe₇Li}_nwere both crystallographically identified. The diversity of complexes reported herein provides critical insight into the structural diversity, electronic structure and bonding in uranium–alkyl chemistry.