The research, carried out by B. Yildirim and A. A. Coley of the Department of Mathematics and Statistics at Dalhousie University in Halifax, Canada, approaches the problem through the mathematics of scalar-tensor gravity. This class of theories extends Einstein’s general relativity by adding a scalar field that dynamically couples to the curvature of spacetime. Scalar-tensor gravity has long attracted attention in cosmology because it provides a natural mathematical setting in which nonsingular bouncing universes can be realized. In such models, the scalar field’s evolution can drive a contraction to a halt and trigger a rebound, replacing the dreaded big bang singularity with a smooth, finite transition. But while bouncing cosmologies have been studied extensively in homogeneous settings, the inclusion of localized objects such as black holes makes the field equations dramatically harder to solve.

To make progress, the authors adopted a perturbative strategy, treating the black hole as a small deviation from an otherwise perfectly uniform cosmos. At leading order in their perturbative scheme, controlled by a small parameter epsilon, the solution is a spatially flat Friedmann-Lemaître-Robertson-Walker, or FLRW, spacetime undergoing a bounce, sourced by a perfect fluid of radiation. This background captures the essence of a bouncing cosmology in the simplest possible form: the universe contracts, reaches a minimum size at a moment identified with a conformal time coordinate eta equal to zero, and then re-expands. This leading-order solution respects what the authors call the parabolic structure of the bounce, a smoothness condition on how the scale factor behaves at the turning point.

At the next order in the expansion, the team embedded a central inhomogeneity into the bouncing background using a generalized McVittie geometry. The original McVittie solution, constructed in 1933, is a celebrated exact solution of general relativity that describes a mass concentrated at the center of an expanding universe, providing a mathematically tractable bridge between black hole physics and cosmology. By generalizing this construction to the scalar-tensor setting and treating it perturbatively, Yildirim and Coley encoded the gravitational imprint of a localized compact object within the contracting and rebounding cosmos. The perturbations appear as first-order corrections to the metric and to the scalar field, and the coupled field equations were solved as a series expansion carried up to fourth order in the parameter eta near the bounce.

A central technical challenge arose from the nature of the matter content near the inhomogeneity. In the vicinity of a concentrated mass, the stress-energy generically becomes anisotropic, meaning that pressure differs along the radial direction compared with the tangential directions. The authors therefore first allowed an anisotropic fluid with separate radial and tangential pressures, whose diagonal components suffice to solve the diagonal components of the field equations. They then imposed the physically motivated condition that the stress-energy reduce to a perfect fluid, one with a single isotropic pressure, far from the center. The resulting perfect fluid solution contains three arbitrary functions, which are constrained by demanding that the spacetime smoothly asymptote to the homogeneous FLRW background as the radial coordinate tends to infinity, ensuring that the black hole’s influence fades with distance as it must.

With suitable initial conditions chosen to preserve the parabolic structure of the bounce, a remarkable simplification emerged. The solution’s integration constants consolidate into a single quantity, denoted d0, which the authors identify as the true perturbative parameter of the problem. When d0 is set to zero, every perturbation vanishes and the spacetime reverts exactly to the homogeneous bouncing FLRW universe. When d0 is small but nonzero, a localized inhomogeneity, and with it a small evolving horizon, appears in the geometry. This clean parametrization means the entire structure of the black hole embedding is controlled by one number, allowing the authors to track precisely how the compact object’s gravitational field responds to the cosmic contraction and rebound.

The key result of the analysis concerns the fate of that horizon. Yildirim and Coley find a small evolving horizon whose radius scales linearly with the perturbative parameter, roughly as d0, and which they interpret as the horizon of the central inhomogeneity. Crucially, this horizon persists through the bounce at eta equals zero, supporting the interpretation that a black hole present before the cosmological transition survives it and continues to exist in the expanding universe on the other side. Intriguingly, the evolution is not symmetric about the bounce: the horizon’s behavior on the contracting side differs from its behavior on the expanding side, suggesting that the cosmic reversal leaves a subtle imprint on the object even as it survives. In a cosmological context, such findings resonate with long-standing speculations about black holes from a previous cosmic epoch, sometimes discussed in connection with ideas about the origin of supermassive black holes and the possible relics of a pre-bounce universe.

The authors are careful about what their construction does and does not establish. The small horizon they track is a future outer trapping horizon, a locally defined surface characterized by the convergence properties of outgoing and ingoing light rays, and it behaves as such in a two-sided neighborhood of the bounce. Because the entire construction is local and perturbative, it does not demonstrate the existence of a global event horizon, the teleological boundary beyond which nothing can escape to infinity. The distinction matters in a dynamical spacetime, where global horizons are notoriously difficult to define and can depend on the entire future evolution of the cosmos. Still, the persistence of a local trapping horizon through a nonsingular bounce is a nontrivial and suggestive result, indicating that the mechanisms of black hole formation and survival may be more robust under extreme cosmological conditions than simpler arguments had implied.

The work also fits into a broader effort to understand how inhomogeneities behave in bouncing scenarios. Previous studies have explored whether structure formation is possible through a bounce, whether primordial black holes can survive ekpyrotic contractions, and how numerical simulations of nonsingular bouncing spacetimes handle black holes and their horizons. By providing an analytic, perturbative solution in scalar-tensor gravity, the Dalhousie team adds a complementary tool to this mostly numerical and heuristic literature. The mathematical framework, combining generalized McVittie geometries with a controlled expansion around a radiation-dominated bounce, offers a concrete laboratory in which questions about horizons, matter anisotropies, and scalar-field dynamics can be addressed with precision. While the analysis is idealized, assuming spherical symmetry, a radiation fluid, and a small perturbation strength, it demonstrates that black hole persistence through a bounce is a mathematically consistent possibility in a well-motivated class of gravitational theories, bringing the speculative picture of black holes bridging cosmic epochs one step closer to rigorous footing.

Subject of Research: Perturbative scalar-tensor cosmology modeling black hole survival through a nonsingular bouncing universe

Article Title: Black hole persistence in scalar-tensor theories

Article References: Yildirim, B., & Coley, A. A. (2026). Black hole persistence in scalar-tensor theories. General Relativity and Gravitation, 58(9), Article 111. https://doi.org/10.1007/s10714-026-03610-6

Image Credits: AI Generated

DOI: 10.1007/s10714-026-03610-6

Keywords: black holes, scalar-tensor gravity, bouncing cosmology, general relativity, McVittie metric, trapping horizon, FLRW spacetime, cosmic bounce, perturbation theory, theoretical cosmology, nonsingular cosmology, gravitational physics

The idea that (G) might vary is not new. It has appeared in theories inspired by Dirac’s large-number hypothesis, scalar–tensor gravity, Brans–Dicke theory, and several approaches to modified gravity. In ordinary general relativity, (G) sets the strength of the coupling between matter and spacetime curvature. If it changes, the gravitational response of the universe changes as well, potentially affecting the expansion rate, the growth of cosmic structure, stellar evolution, planetary motion, and the behavior of compact objects. The cosmological term (\Lambda), meanwhile, is usually interpreted as a constant vacuum-energy density that drives the late-time acceleration of cosmic expansion. Allowing both quantities to evolve introduces a new degree of freedom into the background dynamics and may provide a way to describe observations that do not fit perfectly within a rigid constant-(G), constant-(\Lambda) framework.

Mandal and colleagues focus on an isotropic and homogeneous universe, described by the Friedmann–Lemaître–Robertson–Walker metric. This approximation treats the cosmos on very large scales as spatially uniform and directionally equivalent, making it possible to connect theoretical equations with measurements of the Hubble expansion. The authors adopt a power-law parametrization for the gravitational constant, allowing (G) to change in a controlled mathematical form rather than introducing an entirely arbitrary function. They then solve the corresponding cosmological equations to derive the model’s expansion rate. Because a time-dependent gravitational coupling modifies the Friedmann equations and their consistency conditions, the model must be examined as a coupled system in which the evolution of (G), (\Lambda), matter, and the scale factor are not independent ingredients.

The observational engine of the study is DESI’s second data release, which provides baryon acoustic oscillation measurements across a broad range of cosmic epochs. Baryon acoustic oscillations are relics of sound waves that travelled through the hot plasma of the early universe before atoms formed. Their characteristic scale became imprinted in the distribution of galaxies, quasars, and intergalactic matter. Today, that scale functions as a cosmic ruler. By measuring its apparent size across different redshifts, astronomers can infer combinations of the expansion history, including the Hubble parameter (H(z)) and distance–redshift relations. DESI’s measurements are especially valuable because they probe the period when dark energy began to dominate the universe, precisely the era in which departures from a constant cosmological term could become visible.

To strengthen the analysis, the researchers combine DESI BAO observations with two independent classes of data. Cosmic Chronometers estimate the expansion rate directly through the differential ageing of passively evolving galaxies. Rather than relying primarily on a distance ladder, this method uses galaxies as cosmic clocks: the change in their ages over redshift provides an estimate of (dz/dt), which can be converted into (H(z)). The Pantheon+SH0ES supernova dataset contributes luminosity-distance information from Type Ia supernovae, stellar explosions whose calibrated brightness allows them to be used as standardisable candles. Together, the three datasets test the model through complementary observables—cosmic distances, direct expansion rates, and supernova brightness—reducing the risk that a preferred result is driven by a single observational technique.

The team estimates the parameters of the varying-(G), varying-(\Lambda) framework using Markov chain Monte Carlo analysis. MCMC methods explore the multidimensional parameter space by generating chains of possible cosmological models, assigning greater statistical weight to those that provide better agreement with the data. The resulting likelihood analysis allows the authors to constrain the parameters controlling the gravitational variation and the cosmic expansion while accounting for observational uncertainties and parameter correlations. The study also compares parameter estimates obtained from different dataset combinations, an important test of robustness. If independent observations point toward compatible regions of parameter space, confidence in the model’s viability increases; if they disagree, the apparent preference for evolving physics may instead reflect statistical fluctuations or hidden systematic effects.

Beyond fitting the expansion data, the researchers reconstruct the evolution of several quantities that describe the universe’s physical behavior. The Hubble parameter (H(z)) tracks the expansion rate at different times, while the deceleration parameter (q(z)) indicates whether expansion is slowing or accelerating. A transition from positive (q) in the matter-dominated past to negative (q) in the recent universe signals the onset of accelerated expansion. The authors also examine an effective equation-of-state parameter, (w_{\rm eff}), which summarizes the pressure-to-density behavior of the total cosmic contents. In standard terminology, values near (-1) resemble a cosmological constant, while departures from that value can indicate evolving dark energy or an effective modification of gravity. In a model where (G) and (\Lambda) vary, these reconstructed parameters provide an intuitive view of how the new physics reshapes cosmic history.

A central motivation for the work is the continuing debate over whether dark energy is truly constant. Several recent analyses of large-scale structure and supernova data have reported hints that the properties of dark energy may evolve, although the statistical significance and interpretation remain under discussion. A varying cosmological term could mimic some of the observational signatures associated with dynamical dark energy, while a changing (G) could alter the inferred expansion history without behaving like a conventional dark-energy fluid. This distinction matters because cosmological parameters are not measured in isolation. Inferences about the amount and nature of dark energy depend on assumptions about gravity, the standard ruler, the calibration of supernovae, and the conservation of matter and energy. By varying (G) and (\Lambda) together, the study explores a broader theoretical landscape in which apparent tensions may arise from interactions between gravitational physics and cosmic acceleration.

The authors also test the late-time behavior of the model by examining the present-day rate of change of the gravitational constant, expressed as (\dot G/G), and by applying information criteria to compare the model with (\Lambda)CDM. The quantity (\dot G/G) is especially important because local experiments place stringent limits on any present variation in (G), using lunar laser ranging, planetary dynamics, pulsar timing, and other precision measurements. A cosmological model can fit large-scale observations yet remain physically problematic if it predicts a modern rate of change that violates these local bounds. Information criteria provide a complementary perspective: they penalize models for adding parameters, asking whether improved agreement with observations is substantial enough to justify the extra complexity. The study therefore treats a successful cosmology not simply as one capable of matching data, but as one that remains compatible with local gravitational tests and earns its additional freedom statistically.

The broader significance of the research lies in its attempt to connect two major questions in contemporary cosmology: why the universe is accelerating and whether the laws governing gravity are immutable. The analysis does not overturn general relativity or establish that (G) and (\Lambda) definitely vary. Instead, it supplies observational constraints on a specific phenomenological framework and evaluates how its predicted expansion history compares with the established cosmological model. As DESI continues mapping the universe and future supernova, galaxy, and gravitational-wave surveys expand the available data, models with evolving constants will face increasingly precise tests. If their parameters converge toward zero variation, the result will reinforce (\Lambda)CDM and place tighter limits on alternatives. If consistent evidence for evolution emerges across independent datasets, cosmology could be forced to reconsider whether the constants written into its foundational equations are truly constant—or only appear so across the limited cosmic history we have measured.

Subject of Research: Varying gravitational constant and cosmological term in observational cosmology

Article Title: Observational constraints on varying-((G,\Lambda)) cosmology with DESI DR2

Article References: Mandal, S., Singh, A. & Chaubey, R. Astrophysics and Space Science 371, 44 (2026). https://doi.org/10.1007/s10509-026-04576-2

Image Credits: AI Generated

DOI: 10.1007/s10509-026-04576-2

Keywords: Varying dark energy, gravitational constant, cosmological constant, DESI DR2, Cosmic Chronometers, Pantheon+SH0ES, cosmology, cosmic acceleration