arXiv subjects

William J. Wolf

Publications and source records attributed to William J. Wolf.

At least 19 recordsLinked to original sources

arXiv2026

Consistency between cosmological and standard siren observations in evolving dark energy

A scalar field non-minimally coupled to gravity can be the driver of cosmic acceleration. Such a non-minimal coupling (NMC) can produce a non-zero gravitational-wave (GW) friction function $α_M(z)$, which modifies the luminosity distance inferred from GW sources relative to its electromagnetic counterpart. We use a particular NMC scalar-tensor model, that explains time-varying dark energy in good alignment with DESI, to predict $α_M(z)$ and the expected GW/EM luminosity-distance ratio $D_L^{\rm GW}/D_L^{\rm EM}$, and map it onto two common parametrizations---the $c_M$ and the $(Ξ_0,n)$ models. We find $c_M = -0.5\pm 0.2$ and $Ξ_0 = 0.88\pm 0.05$, $n=3.2\pm 0.3$, both consistent with GWTC-5 constraints at the $\lesssim 1σ$ level. This consistency is mostly driven by current large uncertainties in GW data, which lead to measurements consistent with both $Λ$CDM and the NMC model. By contrast, the dark energy constraints derived from analyzing cosmological data, under the common parametric scalar-tensor model using $α_M(z)=c_MΩ_Λ(z)/Ω_{Λ0}$ and the CPL parametrized equation of state $w_0w_a$, are in $2.2σ$ ($3.6σ$) tension with the NMC predictions for the $c_M$ ($w_0w_a$) parameter. We confirm that, in order to avoid cosmological instabilities, this parametrized model imposes strong implicit priors that are incompatible with physically-motivated scalar-tensor models when dark energy is dynamical.

astro-ph.CO↗

arXiv2026

The Status of Single Scalar Field Dark Energy

We present an assessment of the current observational status of single scalar field models of dark energy. Motivated by recent cosmological measurements -- including baryon acoustic oscillations, Type Ia supernovae, and CMB data -- we examine whether a dynamical scalar field offers a viable explanation for the accelerated expansion of the Universe. Working within an effective field theory (EFT) framework, we argue that cosmological observations are fundamentally limited and can at most constrain a small number of parameters that govern scalar field dynamics. We show that quintessence remains only marginally distinguishable from a cosmological constant, $Λ$, and that more general EFT extensions exhibit modest statistical preference, though such evidence is sensitive to data set selection and prior assumptions. These extended models generically predict fifth forces and modifications to the growth of structure, raising challenges from astrophysical constraints. We compare their predictions with current growth rate measurements, Integrated Sachs-Wolfe (ISW) effect and Solar System constraints. We emphasize that viable screening mechanisms remain theoretically non-trivial and observationally testable. On the other hand, we find that current ISW and growth data remain largely in agreement. Looking ahead to Stage IV surveys we forecast improvements in constraints on the dark energy behaviour; although there will be some tightening of bounds, we argue that the problem of underdetermination will persist. We conclude that while single scalar field dark energy remains a natural and flexible framework, its ultimate viability will hinge on improved low-redshift growth measurements and a clearer understanding of gravitational screening.

astro-ph.CO↗

arXiv2026

Cosmological constraints on Galileon dark energy with broken shift symmetry

Current cosmological data seem to show that dark energy is evolving in time and that it possibly crossed the phantom divide in the past. So far the only theories that lead to such a behavior involve a non-trivial coupling between dark energy, in the form of a scalar field, and the gravitational or matter sector. We show that there is another possibility involving both a non-trivial kinetic sector in a cubic Galileon theory and a scalar field potential that breaks the Galileon shift symmetry, which can lead to a similar phenomenology on large scales. We perform a full Bayesian analysis using the latest cosmological data, including DESI DR2 BAO measurements, type Ia SNe measurements from DESY5, Union3, and Pantheon+, and CMB data from Planck and ACT. We find that it is statistically strongly favored over a Universe dominated by a cosmological constant (with a Bayes factor of $\log B\simeq 6.5$). Yet, as with other non-minimally coupled theories, it has severe ancillary gravitational effects. These can be mitigated to some extent, but as with other viable theories, the penalty is ever more elaborate scalar field models of dark energy.

astro-ph.CO↗

arXiv2026

Inflationary attractors and radiative corrections in light of ACT data

In light of the recent results from the Atacama Cosmology Telescope (ACT), which have provided a notable shift in the constraints on $(n_s, r)$ and placed several otherwise viable models of inflation in tension with the latest data, we investigate the possible effects that radiative corrections can have on $ξ$-attractor and $α$-attractor models of inflation. These models, which share much in common with Starobinsky inflation, have likewise been put under pressure by these results. We find that percent (and even sub-percent) level radiative corrections can easily shift both of these classes of inflation models comfortably into the regions of parameter space favoured by the most recent constraints. However, the flexibility under such corrections calls into question to what extent it is possible to precisely pin down model-specific predictions for important cosmological observables.

astro-ph.CO↗

arXiv2026

Navigating permanent underdetermination in dark energy and inflationary cosmology

We identify troubling cases of so-called `permanent underdetermination' in both dark energy and inflationary cosmology. We bring to bear (a) a taxonomy of possible responses to underdetermination, and (b) an understanding of both dark energy and inflationary cosmology from an effective field theory point of view. We argue that, under certain conditions, there are viable responses which can arguably alleviate at least some of the concerns about underdetermination in the dark energy and inflationary sectors. However, the epistemic threat of permanent underdetermination remains a significant challenge.

physics.hist-ph↗

arXiv2025

Assessing cosmological evidence for non-minimal coupling

The recent observational evidence of deviations from the $Λ$-Cold Dark Matter ($Λ$CDM) model points towards the presence of evolving dark energy. The simplest possibility consists of a cosmological scalar field $φ$, dubbed quintessence, driving the accelerated expansion. We assess the evidence for the existence of such a scalar field. We find that, if the accelerated expansion is driven by quintessence, the data favour a potential energy $V(φ)$ that is concave, i.e., $m^2=d^2V/dφ^2<0$. Furthermore, and more significantly, the data strongly favour a scalar field that is non-minimally coupled to gravity (Bayes factor $\log(B) = 7.34 \pm 0.6$), leading to time variations in the gravitational constant on cosmological scales, and the existence of fifth forces on smaller scales. The fact that we do not observe such fifth forces implies that either new physics must come into play on non-cosmological scales or that quintessence is an unlikely explanation for the observed cosmic acceleration.

astro-ph.CO↗

arXiv2025

The Spectre of Underdetermination in Modern Cosmology

The scientific status of physical cosmology has been the subject of philosophical debate ever since detailed mathematical models of the Universe emerged from Einstein's general theory of relativity. Such debates have revolved around whether and to what extent cosmology meets established demarcation criteria for a discipline to be scientific, as well as determining how to best characterize cosmology as a science, given the unique challenges and limitations faced by a discipline which aims to study the origin, composition, and fate of the Universe itself. The present article revisits, in light of the dramatic progress in cosmology in recent decades, an earlier debate held in the 1950s between Herman Bondi and Gerald Whitrow regarding the scientific status of cosmology. We analyse cosmology's transition from an emerging science to a cornerstone of modern physics, highlighting its empirical successes in establishing the $Λ$-Cold Dark Matter ($Λ$CDM) model and in its delivery of various successful novel predictions. Despite this remarkable scientific success and progress, we argue that modern cosmology faces a further profound challenge: the permanent underdetermination of the microphysical nature of its exotic energy components: inflation, dark matter, and dark energy. Drawing historical parallels with the role of spectroscopy in revealing the microphysical nature of atomic physics, we argue that the epistemic barriers obstructing us from ascertaining the microphysical nature of these exotic energy components are significant, in turn casting doubt upon whether cosmology can ever transcend these particular epistemic challenges. We conclude by reflecting on the prospects for future breakthroughs and/or non-empirical arguments which could decide this issue conclusively.

physics.hist-ph↗

arXiv2025

Robustness of dark energy phenomenology across different parameterizations

The recent evidence for dynamical dark energy from DESI, in combination with other cosmological data, has generated significant interest in understanding the nature of dark energy and its underlying microphysics. However, interpreting these results critically depends on how dark energy is parameterized. This paper examines the robustness of conclusions about the viability of particular kinds of dynamical dark energy models to the choice of parameterization, focusing on four popular two-parameter models: the Chevallier-Polarski-Linder (CPL), Jassal-Bagla-Padmanabhan (JBP), Barboza-Alcaniz (BA), and exponential (EXP) parameterizations. We find that conclusions regarding the viability of minimally and non-minimally coupled quintessence models are independent of the parameterization adopted. We demonstrate this both by mapping these dark energy models into the $(w_0, w_a)$ parameter space defined by these various parameterizations and by showing that all of these parameterizations can equivalently account for the phenomenology predicted by these dark energy models to a high degree of accuracy.

astro-ph.CO↗

arXiv2025

Promising Stabs in the Dark: Theory Virtues and Pursuit-Worthiness in the Dark Energy Problem

This paper argues that we ought to conceive of the Dark Energy problem -- the question of how to account for observational data, naturally interpreted as accelerated expansion of the universe -- as a crisis of underdetermined pursuit-worthiness. Not only are the various approaches to the Dark Energy problem evidentially underdetermined; at present, no compelling reasons single out any of them as more likely to be true than the other. More vexingly for working scientists, none of the approaches stands out as uncontroversially preferable over its rivals in terms of its rationally warranted promise, i.e.~the reasons to further work on, explore, and develop it. We demonstrate this claim by applying a Peircean economic model of pursuit-worthiness in terms of a cognitive cost/benefit estimate -- with the instantiation of theory virtues as key indicators of cognitive gains -- to the four main Dark Energy proposals (the cosmological constant approach, modified gravity, quintessence, and inhomogeneous cosmologies). According to our analysis, these approaches do not admit of an unambiguous, or uncontroversial, ranking with respect to which ansatz deserves distinguished attention and research efforts. The overall methodological counsel that our analysis underwrites recommends a pragmatic double research strategy forward: to encourage and foster theory pluralism and the search for tests -- with the goal of enhancing the testability of the $Λ$CDM model and ``testing it to destruction".

physics.hist-ph↗

arXiv2025

Matching current observational constraints with nonminimally coupled dark energy

We show that a Universe with a nonminimally coupled scalar field can fit current measurements of the expansion rate of the Universe better than the standard $Λ$-Cold Dark Matter ($Λ$CDM) model or other minimally coupled dark energy models. In particular, the nonminimal coupling in this model allows for the dark energy model to exhibit stable phantom crossing behavior, which seems to be suggested by the constraints on the dark energy equation of state coming from the most recent data. While we find a clear improvement in the goodness of fit for this dark energy model with respect to others that have been considered in the recent literature, using information theoretic criteria, we show that the evidence for it is still inconclusive.

astro-ph.CO↗

arXiv2025

Scant evidence for thawing quintessence

New constraints on the expansion rate of the Universe seem to favor evolving dark energy in the form of thawing quintessence models, i.e., models for which a canonical, minimally coupled scalar field has, at late times, begun to evolve away from potential energy domination. We scrutinize the evidence for thawing quintessence by exploring what it predicts for the equation of state. We show that, in terms of the usual Chevalier-Polarski-Linder parameters, ($w_0$, $w_a$), thawing quintessence is, in fact, only marginally consistent with a compilation of the current data. Despite this, we embrace the possibility that thawing quintessence is dark energy and find constraints on the microphysics of this scenario. We do so in terms of the effective mass $m^2$ and energy scale $V_0$ of the scalar field potential. We are particularly careful to enforce un-informative, flat priors on these parameters so as to minimize their effect on the final posteriors. While the current data favors a large and negative value of $m^2$, when we compare these models to the standard $Λ$CDM model we find that there is scant evidence for thawing quintessence.

astro-ph.CO↗

arXiv2024

Minimizing the tensor-to-scalar ratio in single-field inflation models

We revisit a class of simple single-field inflation models and demonstrate that they can readily produce a negligible tensor/scalar ratio $r$. Motivated by recent work suggesting the need to introduce higher order operators to stabilise unregulated potentials, as well as by work indicating that such terms can have significant effects on observable predictions, we explicitly construct corrected versions of the quadratic hilltop potential that are motivated by an effective field theory expansion. We employ Markov Chain Monte Carlo (MCMC) methods and optimization techniques to sample viable models and minimize $r$. We find that such potentials can readily lower $r$ values below projected CMB-S4 sensitivity, while still remaining within observable constraints on $n_s$. Furthermore, we find that the minimum $r$ reached for each order of the expansion considered is well-described by a power law $r_{min}(q) \propto q^{-B}$ before asymptoting to a value of $r_{min} \sim 10^{-11}$, where $q$ is the order to which the expansion of $V(ϕ)$ is carried out.

astro-ph.CO↗

arXiv2024

Underdetermination of dark energy

There is compelling evidence that the Universe is undergoing a late phase of accelerated expansion. One of the simplest explanations for this behaviour is the presence of dark energy. A plethora of microphysical models for dark energy have been proposed. The hope is that, with the ever increasing precision of cosmological surveys, it will be possible to precisely pin down the model. We show that this is unlikely and that, at best, we will have a phenomenological description for the microphysics of dark energy. Furthermore, we argue that the current phenomenological prescriptions are ill-equipped for shedding light on the fundamental theory of dark energy.

astro-ph.CO↗

arXiv2024

The Non-Relativistic Geometric Trinity of Gravity

The geometric trinity of gravity comprises three distinct formulations of general relativity: (i) the standard formulation describing gravity in terms of spacetime curvature, (ii) the teleparallel equivalent of general relativity describing gravity in terms of spacetime torsion, and (iii) the symmetric teleparallel equivalent of general relativity (STEGR) describing gravity in terms of spacetime non-metricity. In this article, we complete a geometric trinity of non-relativistic gravity, by (a) taking the non-relativistic limit of STEGR to determine its non-relativistic analogue, and (b) demonstrating that this non-metric theory is equivalent to the Newton--Cartan theory and its teleparallel equivalent, i.e., the curvature and the torsion based non-relativistic theories that are both geometrised versions of classical Newtonian gravity.

gr-qc↗

arXiv2024

On the geometric trinity of gravity, non-relativistic limits, and Maxwell gravitation

We show that the dynamical common core of the recently-discovered non-relativistic geometric trinity of gravity is Maxwell gravitation. Moreover, we explain why no analogous distinct dynamical common core exists in the case of the better-known relativistic geometric trinity of gravity.

physics.hist-ph↗

arXiv2024

Respecting Boundaries: Theoretical Equivalence and Structure Beyond Dynamics

A standard line in the contemporary philosophical literature has it that physical theories are equivalent only when they agree on their empirical content, where this empirical content is often understood as being encoded in the equations of motion of those theories. In this article, we question whether it is indeed the case that the empirical content of a theory is exhausted by its equations of motion, showing that (for example) considerations of boundary conditions play a key role in the empirical equivalence (or otherwise) of theories. Having argued for this, we show that philosophical claims made by Knox (2011) that general relativity is equivalent to teleparallel gravity, and by Weatherall (2016) that electromagnetism in the Faraday tensor formalism is equivalent to electromagnetism in the vector potential formalism, can both be called into question. We then show that properly considering the role of boundary conditions in theory structure can potentially restore these claims of equivalence and close with some remarks on the pragmatics of adjudications on theory identity.

physics.hist-ph↗

arXiv2024

Underdetermination in Classic and Modern Tests of General Relativity

Canonically, `classic' tests of general relativity (GR) include perihelion precession, the bending of light around stars, and gravitational redshift; `modern' tests have to do with, inter alia, relativistic time delay, equivalence principle tests, gravitational lensing, strong field gravity, and gravitational waves. The orthodoxy is that both classic and modern tests of GR afford experimental confirmation of that theory in particular. In this article, we question this orthodoxy, by showing there are classes of both relativistic theories (with spatiotemporal geometrical properties different from those of GR) and non-relativistic theories (in which the lightcones of a relativistic spacetime are `widened') which would also pass such tests. Thus, (a) issues of underdetermination in the context of GR loom much larger than one might have thought, and (b) given this, one has to think more carefully about what exactly such tests in fact are testing.

physics.hist-ph↗

arXiv2024

The Virtues of Pursuit-Worthy Speculation: The Promises of Cosmic Inflation

The paper investigates the historical and contemporary pursuit-worthiness of cosmic inflation-the rationale for working on it (rather than necessarily the evidential support for claims to its approximate truth): what reasons existed, and exist, that warrant inflation's status as the mainstream paradigm studied, explored, and further developed by the majority of the cosmology community? We'll show that inflation exemplifies various salient theory virtues: explanatory depth, unifying/integrative power, fertility and positive heuristics, the promotion of understanding, and the prospect (and passing) of novel benchmark tests. This, we'll argue, constitutes inflation's auspicious promise. It marks inflation as preferable over both the inflation-less Hot Big Bang Model, as well as rivals to inflation: inflation, we maintain, rightly deserved, and continues to deserve, the concerted research efforts it has enjoyed.

physics.hist-ph↗