Among the most consequential topics at the meeting was the so-called Hubble tension, the statistically significant discrepancy between independent measurements of the present-day expansion rate of the universe. Distance-ladder determinations anchored by Type Ia supernovae calibrated with Cepheid variables yield values of the Hubble constant that differ substantially from those inferred from the temperature anisotropies of the Cosmic Microwave Background within the standard Lambda-CDM framework. The tension now stands at roughly five sigma, and its resolution may reflect uncharacterized systematics in one or both measurement chains, or a genuine breakdown of the standard cosmological model. Michael S. Turner delivered a critical status report on Lambda-CDM, framed as a sequel to his talk at the inaugural 2017 Lemaître meeting, focusing on the DESI Collaboration’s evidence from its first two data releases for a time-evolving dark-energy equation of state in the w0–wa parametrization. The most provocative feature of that evidence is a dark-energy density sharply peaked around redshift z of roughly 0.5, rather than the constant value predicted by a cosmological constant. Joseph Silk, meanwhile, opened from the observation that modern cosmology effectively began with Georges Lemaître in 1927, and proposed a strikingly concrete response to the field’s observational limits: a sustained scientific presence on the lunar far side, whose radio silence, seismic quietness and lack of atmosphere make it uniquely suited to several genuinely guaranteed measurements. Participants also emphasized how data from the James Webb Space Telescope have already tested the robustness of Lambda-CDM at high redshift.

Inflationary cosmology, the leading account of the early universe’s homogeneity, isotropy, flatness and the origin of the primordial density fluctuations that seeded cosmic structure, received a thorough technical audit. Michele Cicoli presented recent progress on inflation and dark energy within type IIB string compactifications, centering on the Loop Blow-up Inflation scenario, in which a blow-up Kähler modulus with an approximate shift symmetry drives slow-roll inflation through a potential generated by string-loop corrections. The model yields sharp, falsifiable predictions: a scalar spectral index in the narrow range between about 0.9757 and 0.9765, and a tensor-to-scalar ratio of roughly two times ten to the minus five, in excellent agreement with current CMB and baryon-acoustic-oscillation data. On dark energy, Cicoli surveyed the difficulty of realizing quintessence in a UV-complete setting, presenting a two-axion hilltop model exploiting poly-instanton suppression as the most promising route to a phenomenologically viable, string-derived dynamical dark energy. Renata Kallosh and Andrei Linde reviewed inflation from the perspective of supergravity, highlighting the predictive successes of attractor models while stressing the open challenge of embedding inflation in a UV-complete framework.

The Swampland programme, which seeks to identify which effective low-energy theories can be consistently completed into quantum gravity, featured prominently. Hirosi Ooguri reviewed Swampland-type constraints in asymptotically anti-de Sitter spacetimes, where they can be rigorously tested via the AdS/CFT correspondence. He summarized, in particular, a proof with Daniel Harlow that any exact global symmetry in a bulk gravitational theory is incompatible with the consistency of the dual boundary conformal field theory, and a further result establishing universal bounds on the exponential decay rate governing the Distance Conjecture in two-dimensional CFTs dual to AdS3 gravity. Cumrun Vafa combined the Distance Conjecture, the associated species scale, the de Sitter Conjecture and the TransPlanckian Censorship Conjecture to derive increasingly sharp bounds on inflationary potentials. Imposing the TCC, he argued, renders standard slow-roll inflation viable only in a strongly fine-tuned corner of parameter space with an essentially unobservable tensor-to-scalar ratio. Applied to the present epoch, the same reasoning implies that our universe, if presently in a metastable de Sitter phase, cannot remain so for much longer than of order two trillion years, a bound Vafa frames as string theory’s answer to the question posed by the very title of Lemaître’s 1927 paper, now viewed from the vantage of the universe’s future rather than its origin.

Thomas Hertog returned most directly to Lemaître’s own 1931 Nature letter on the primeval atom, reading it as an early and remarkably prescient statement that the origin of the universe should be a proper object of physical, rather than merely metaphysical, inquiry. Tracing a conceptual line from Lemaître’s primeval quantum through the Hartle–Hawking no-boundary wave function to the modern “top-down” reformulation of quantum cosmology, Hertog confronted a long-standing embarrassment of the no-boundary proposal: taken at face value, it overwhelmingly favors nearly empty histories incompatible with the existence of observers. He showed that once an observer is treated as a genuine quantum subsystem within the theory, modeled concretely via the information content of a CMB temperature map, the resulting conditional probability distribution can undergo a Page-like transition, in which the dominant saddle point shifts abruptly from a low-inflation history to one beginning deep in the eternal-inflation regime for sufficiently detailed observational situations. The past, on this view, is contingent on the question being asked of the wave function, a striking modern echo of Lemaître’s insistence at the 1958 Solvay Council that any information on the state of matter must be inferred from the condition that the actual universe has been able to evolve from it.

The nature of spacetime singularities, whether at the Big Bang or in the deep interior of black holes, remains one of the most profound unresolved problems in theoretical physics, and two contributions took Lemaître’s own 1933 dust model as their explicit point of departure. Claus Kiefer and Hamid Mohaddes asked what happens to the classical singularity of Lemaître’s model under canonical quantization. Working first with a thin null dust shell and then with the full Lemaître–Tolman–Bondi cloud, reduced shell by shell to a self-adjoint Hamiltonian for the outermost layer, they constructed exact, normalizable wave-packet solutions whose unitary evolution forces the collapsing packet to bounce at a minimal radius and re-expand rather than terminate. This picture persists in the homogeneous Oppenheimer–Snyder limit under affine coherent-state quantization, though the authors remain open about whether the bounce timescale is compatible with observation and whether the method extends beyond spherical symmetry. Alexander Kamenshchik revisited the problem of singularity crossing, showing that a Big Bang–Big Crunch singularity in the Jordan frame can correspond to a perfectly regular geometry in the Einstein conformal frame, allowing the crossing to be described unambiguously. The idea, first worked out for isotropic Friedmann–Lemaître universes, has since been extended to anisotropic Bianchi-I and Kantowski–Sachs cosmologies, and in the quantum cosmology of soft future singularities such as the “Big Brake,” the wave function can vanish at the singularity while the correctly normalized probability density does not.

Gabriele Veneziano presented progress on the central open problem of the Pre-Big-Bang scenario he proposed with Maurizio Gasperini over three decades ago: whether the singularity separating the inflationary pre-bang branch from the decelerating post-bang branch can be tamed by higher-order alpha-prime corrections consistent with the O(d,d) duality symmetry of classical string cosmology. Building on the all-order reformulation by Hohm and Zwiebach, a Hamiltonian approach reduces the existence of regular bouncing solutions to a simple analytic criterion, yielding explicit bounces and, with a non-perturbative dilaton potential, late-time attractors of Minkowski, metastable-vacuum or de Sitter type. Roberto Casadio questioned the common assumption that quantum gravity is relevant only at the Planck length, arguing that this conflates the Compton length governing scattering with the very different scales governing bound states. Proposing that quantum effects become important for any self-gravitating system whose compactness approaches unity, he built a many-body ground state for a dust ball from a hierarchy of quantized shells obeying hydrogen-atom-like radial equations, finding a core radius of order the gravitational radius, with the ground-state occupation number reproducing the Bekenstein area scaling. The resulting interior has finite tidal forces and no inner Cauchy horizon, replacing the point singularity with what Casadio calls an integrable singularity. Misao Sasaki reviewed the formation of primordial black holes from rare, large-amplitude curvature perturbations, with non-minimally coupled curvaton models capable of producing primordial black hole dark matter in the asteroid-mass window of roughly 10^18 to 10^22 grams together with a scalar-induced gravitational-wave background within reach of forthcoming detectors such as LISA. Gia Dvali proposed a microscopic, string-theoretic account of de Sitter horizon entropy via open–closed string duality, showing that at a critical coupling the species entropy of open-string degrees of freedom in a D9–anti-D9 brane construction exactly reproduces the closed-string Gibbons–Hawking entropy.

Edward Witten presented progress toward a background-independent algebraic formulation of quantum gravity, constructing an algebra of observables, fields gravitationally dressed to the worldline of an observer with bounded-below energy, defined without reference to any particular background spacetime and becoming background-dependent only once a Hilbert-space representation is chosen. Specialized to a geodesic observer in empty de Sitter space, the algebra acquires a genuine trace, and the thermal Bunch–Davies state of maximum entropy reproduces, via its vanishing relative entropy, Bousso’s intuition that the late-time empty static patch is the entropically preferred state. Raphael Bousso and Sami Kaya extended the notion of a generalized entanglement wedge from AdS/CFT boundary regions to arbitrary gravitating regions, yielding a full complementarity theorem for holograms and showing that any spacetime containing a Big Bang or Big Crunch is trivially reconstructible, an information-theoretic counterpart to Lemaître’s intuition that a genuine cosmological beginning renders any pre-existence of the universe causally inaccessible. Batoul Banihashemi and Ted Jacobson argued that the Gibbons–Hawking derivation of the Bekenstein–Hawking entropy A/4G from the Euclidean gravitational path integral rests on shaky foundations, since the Euclidean Einstein–Hilbert action is unbounded below and the correct integration contour is unknown, and showed how a Lorentzian version of the Gauss–Bonnet theorem combined with a Regge-calculus treatment of the horizon’s deficit angle can reproduce the Bekenstein–Hawking result. On the foundational side, Rosa-Laura Lechuga-Solis and Daniel Sudarsky examined the routine identification of quantum uncertainties with genuine stochastic fluctuations in inflationary cosmology, deriving modified power spectra with a substantially suppressed tensor-to-scalar signal using spontaneous collapse dynamics, while Lajos Diósi formulated a stochastic semiclassical dynamics based on spontaneous quantum monitoring that reduces in the Newtonian limit to a modified Schrödinger–Newton equation free of Born-rule violations.

The collection was completed by Dominique Lambert’s historical and epistemological reconstruction of the genesis of Lemaître’s 1931 primeval-atom hypothesis, tracing its roots to Lemaître’s engagement with cosmic-ray physics, his 1930–1931 work on quantum theory, and his response to Eddington’s philosophical rejection of a cosmic beginning, while carefully distinguishing the shifting ontological status the hypothesis held across his career and his explicit theological separation of a physical “natural beginning” from metaphysical creation. The conference, co-sponsored by the Vatican Observatory and the Istituto Nazionale di Fisica Nucleare, achieved its principal goal of fostering productive interaction between theory and observation. As the editors note, progress on the Hubble tension will require improved observational precision and theoretical creativity in exploring extensions of and alternatives to Lambda-CDM; the resolution of spacetime singularities awaits a formulation of a quantum theory of gravity; and the relationship between quantum mechanics, measurement and gravity remains one of the deepest open problems in theoretical physics. The enduring example of Georges Lemaître, a scientist who combined mathematical rigor, physical intuition, philosophical sophistication and intellectual courage, serves as an inspiration for all of these endeavors.

Subject of Research: A topical collection from the Lemaître Conference 2024 presenting research on black holes, gravitational waves, spacetime singularities, cosmology and quantum gravity.

Article Title: Black holes, gravitational waves and space-time singularities (Lemaître Conference 2024)

Article References: Bianchi, M., Cacciatori, S. L., Galaverni, M., Gionti S.J., G., & Scardigli, F. (2026). Black holes, gravitational waves and space-time singularities (Lemaître Conference 2024). General Relativity and Gravitation, 58(9), Article 108. https://doi.org/10.1007/s10714-026-03608-0

Image Credits: AI Generated

DOI: 10.1007/s10714-026-03608-0

Keywords: black holes, gravitational waves, spacetime singularities, Hubble tension, Lambda-CDM, inflation, quantum gravity, string theory, primordial black holes, horizon thermodynamics, Georges Lemaître, cosmology