arXiv subjects

Stephen F. King

Publications and source records attributed to Stephen F. King.

At least 19 recordsLinked to original sources

arXiv2026

Chaotic Inflation RIDES Again

Following the recent Atacama Cosmology Telescope (ACT) results, we revisit chaotic inflation based on a single complex scalar field with mass term $M^2 |Φ|^2$, which usually predicts a spectra index $n_s\approx 0.96$ but a too-large tensor to scalar ratio $r\approx 0.16$. With radiative corrections, the potential $M^2 |Φ|^2 \ln \left( |Φ|^2/Λ^2 \right)$ induces spontaneous symmetry breaking near the scale $Λ$, yielding a Pseudo Nambu-Goldstone boson which can play the role of a quintessence field, hence radiative inflation and dark energy (RIDE). Including a non-minimal coupling to gravity $ξ|Φ|^2 R^2$ reduces $r$, allowing a good fit of the RIDE model to Planck data. Allowing a small additional quartic coupling correction $λ|Φ|^4$ increases both $n_s$ and $r$, with a good fit to ACT data sets achieved for $ξ\approx 1$.

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arXiv2026

Domain Walls in $A_4$ Flavour Models

The spontaneous breaking of an $A_4$ flavour symmetry, often used to predict leptonic mixing, can lead to the formation of domain walls which can annihilate and generate a stochastic gravitational wave background. We study this phenomenon in three scenarios where the nature of the scalar field responsible for breaking the $A_4$ symmetry spontaneously differs: real, complex, and supersymmetric. For the real scalar, a biased potential produces metastable walls that decay into oscillating two-wall systems with important consequences for gravitational wave signals. In the complex scalar case, we discuss the interplay between domain walls and global strings and classify the types of domain walls that form in terms of the $A_4$ group symmetries. We investigate the properties of supersymmetric $A_4$ domain walls, and highlight the BPS walls. Through a detailed analysis of these models with non-Abelian symmetries, we discover new kinds of domain walls, which we denote as ``oreo''-type composite domain walls, CP-violating domain walls and SUSY non-Abelian domain walls. Finally we show how these results may be achieved in leptonic $A_4$ flavour models, with and without supersymmetry, and discuss their distinctive gravitational wave signatures.

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arXiv2026

Two Flavon Froggatt-Nielsen Models with Genetic Algorithms

We present the first systematic and comprehensive scan of two-flavon Froggatt-Nielsen (FN) models, employing artificial intelligence techniques to explore the high-dimensional, mixed discrete-continuous parameter space. Extending the standard single-flavon FN framework to a two-flavon setup in which separate flavon fields couple independently to the up- and down-type sectors, we demonstrate that the relative phase between their vacuum expectation values (vevs) provides a natural and generic source of CP violation absent in single-flavon models. To explore this enlarged model space, we cast the search for phenomenologically viable models as a multi-objective optimisation problem, formulating each experimental constraint as a separate objective, and employ the Non-dominated Sorting Genetic Algorithm III to simultaneously fit all 18 FN charges, 45 Wilson coefficients, and flavon parameters to both the quark and lepton sectors. Our approach requires no separate training phase and identifies phenomenologically viable models orders of magnitude faster than prior reinforcement learning methods. Imposing experimental constraints on CKM and PMNS mixing angles and CP phases, charged fermion masses, and neutrino squared-mass differences, we discover over $100\,000$ unique viable models with a remarkably low duplication rate, indicating that the space of valid two-flavon FN realisations has not been exhausted. Both Normal and Inverted neutrino mass squared orderings are realised, with the relative hierarchy between the flavon vevs producing qualitatively distinct predictions for the effective neutrinoless double beta decay mass $m_{ee}$. We further demonstrate the existence of minimal FN realisations with maximal flavon exponent as small as three, and of models reproducing charged fermion masses to within $6\%$ without any dedicated continuous parameter optimisation.

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arXiv2026

Whispers of Supergravity in Gravitational Wave Backgrounds: Determining the Gravitino Mass from Cosmic Thermal History

Gravitino masses above the electroweak scale provide the simplest solution to the gravitino problem, but such large mass scales lie far beyond the reach of collider experiments. We show that the stochastic gravitational wave background offers a direct probe of this otherwise inaccessible regime. Despite decaying before Big-Bang Nucleosynthesis (BBN), these gravitinos naturally generate a period of early matter domination in the early universe. This non-standard epoch leaves a characteristic imprint on any primordial gravitational wave background, characterised by two frequencies corresponding to the onset and end of this phase. We demonstrate that these features can be used to directly infer both the gravitino mass and its initial abundance in a direct mapping. Future gravitational wave observatories span a vast frequency range, enabling sensitivity to gravitino masses from the BBN bound of $\mathcal{O}(100)\,\text{TeV}$ all the way up to $\mathcal{O}(10^{10})\,\text{TeV}$, with recent signal by NANOGrav already probing masses in the range $500$-$10^4$ TeV. Gravitational wave observables therefore probe an enormous region of parameter space, far beyond the reach of collider experiments. We are entering an era in which supergravity can be probed through gravitational wave backgrounds alongside collider experiments.

astro-ph.CO↗

arXiv2026

Curvaton-assisted hilltop inflation

Following the recent Atacama Cosmology Telescope (ACT) results, we consider hilltop inflation where the inflaton is coupled to a curvaton, simultaneously addressing two main challenges faced by conventional hilltop inflation models: the initial-value problem; and their viability for sub-Planckian field values. In standard single-field hilltop inflation, the inflaton must start extremely close to the maximum of the potential, raising concerns about the naturalness of the initial conditions. We demonstrate that the curvaton field not only significantly relaxes the initial-value tuning required for hilltop inflation, but also opens up parameter space through modifying the curvature perturbation power spectrum, reviving the quartic hilltop inflation model in the sub-Planckian regime. We find viable parameter space consistent with the recent cosmological observations.

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arXiv2026

Coupled Dark Energy and Dark Matter for DESI: An Effective Guide to the Phantom Divide

Motivated by the recent Dark Energy Spectroscopic Instrument (DESI) DR2 preference for dynamical dark energy, we study interacting dark energy models in which a canonical quintessence field couples to cold dark matter through a field-dependent mass $m(ϕ)$. In such scenarios, the effective equation of state inferred under the assumption of non-interacting dark sectors, $w_{\rm eff}(z)$, can differ from the intrinsic scalar-field equation of state $w_ϕ(z)$, making an apparent phantom crossing $w_{\rm eff}<-1$ possible without introducing a phantom scalar. We show that a viable realization of this mechanism requires the scalar field to originate from a frozen phase deep in the radiation era, in order for the effective coupling to remain sufficiently suppressed before recombination to evade cosmic microwave background constraints, and for the late-time evolution to become strong enough to reproduce the apparent behavior of $w_{\rm eff}(z)$ preferred by DESI. We identify the general conditions that allow these requirements to be satisfied simultaneously, and present an illustrative phenomenological realization in which $w_{\rm eff}(z)$ evolves from $w_{\rm eff}\approx -1.2$ at $z \approx 1.0$ to $w_{\rm eff}\approx -0.9$ at $z\approx 0.4$. These conditions and requirements serve as a guide for designing future models of this kind which can safely navigate the phantom divide at $w=-1$ in an effective way without phantom fields.

astro-ph.CO↗

arXiv2026

Natural neutrino mass hierarchy in a theory of gauge flavour deconstruction

We show how a natural neutrino mass hierarchy with large lepton mixing angles may be achieved in a theory of gauge flavour deconstruction. Hitherto it has been shown that neutrino anarchy may result from such theories, but here we show that this need not necessarily be the case. In particular we consider the minimal tri-hypercharge theory, and show that the decomposition of the family hypercharges into the corresponding $B-L$ gauge groups, together with the charged lepton mass hierarchy, implies the sequential dominance conditions for a neutrino mass hierarchy, where lepton mixing originates from both the neutrino and charged lepton sectors. We present novel and model-independent sequential dominance results applicable to this case, but also useful more generally. We also show how natural quark mass and mixing are included in such a framework.

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arXiv2026

Minimal complete tri-hypercharge theories of flavour

The tri-hypercharge proposal introduces a separate gauged weak hypercharge assigned to each fermion family as the origin of flavour. This is arguably one of the simplest setups for building "gauge non-universal theories of flavour" or "flavour deconstructed theories". In this paper we propose and study two minimal but ultraviolet complete and renormalisable tri-hypercharge models. We show that both models, which differ only by the heavy messengers that complete the effective theory, are able to explain the observed patterns of fermion masses and mixings (including neutrinos) with all fundamental coefficients being of $\mathcal{O}(1)$. In fact, both models translate the complicated flavour structure of the Standard Model into three simple physical scales above electroweak symmetry breaking, completely correlated with each other, that carry meaningful phenomenology. In particular, the heavy messenger sector determines the origin and size of fermion mixing, which controls the size and nature of the flavour-violating currents mediated by the two heavy $Z'$ gauge bosons of the theory. The phenomenological implications of the two minimal models are compared. In both models the lightest $Z'$ remains discoverable in dilepton searches at the LHC Run 3.

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arXiv2026

Tri-hypercharge: a separate gauged weak hypercharge for each fermion family as the origin of flavour

We propose a tri-hypercharge (TH) embedding of the Standard Model (SM) in which a separate gauged weak hypercharge is associated with each fermion family. In this way, every quark and lepton multiplet carries unique gauge quantum numbers under the extended gauge group, providing the starting point for a theory of flavour. If the Higgs doublets only carry third family hypercharge, then only third family renormalisable Yukawa couplings are allowed. However, non-renormalisable Yukawa couplings may be induced by the high scale Higgs fields (hyperons) which break the three hypercharges down to the SM hypercharge, providing an explanation for fermion mass hierarchies and the smallness of CKM quark mixing. Following a similar methodology, we study the origin of neutrino masses and mixing in this model. Due to the TH gauge symmetry, the implementation of a seesaw mechanism naturally leads to a low scale seesaw, where the right-handed neutrinos in the model may be as light as the TeV scale. We present simple examples of hyperon fields which can reproduce all quark and lepton (including neutrino) masses and mixing. After a preliminary phenomenological study, we conclude that one of the massive $Z'$ bosons can be as light as a few TeV, with implications for flavour-violating observables, LHC physics and electroweak precision observables.

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arXiv2026

New modular fixed point models and their phenomenological implications for JUNO, T2HK and DUNE

We perform a general analysis of minimal modular fixed point models based on two right-handed neutrinos (2RHNs) and three modular fixed points, and find that the only viable possibilities are based on modular $S_4'$ and $A_5$ symmetry. Such models are highly predictive, with neutrino masses and the lepton mixing mixing matrix being fixed by three real parameters, as in the Littlest Seesaw Models. We perform an exhaustive scan over all possible models in this class and find many viable fixed points and modular form alignments, after confronting them with the latest neutrino oscillation global fits. The resulting models have the new feature that the two Dirac columns take more general forms than traditional Littlest Seesaw models, resulting in new sum rule relations between the solar and reactor angles, beyond those associated with TM1 (where the first column of the tri-bimaximal mixing matrix is preserved), which are compared to present and future projected JUNO results. We also compare the predictions of these models for the atmospheric angle and CP violating phase to current global fits and future T2HK and DUNE sensitivities.

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arXiv2026

Modular $S_4$ and $A_4$ Symmetries and Their Fixed Points: New Predictive Examples of Lepton Mixing

In the modular symmetry approach to neutrino models, the flavour symmetry emerges as a finite subgroup $Γ_N$ of the modular symmetry, broken by the vacuum expectation value (VEV) of a modulus field $τ$. If the VEV of the modulus $τ$ takes some special value, a residual subgroup of $Γ_N$ would be preserved. We derive the fixed points $τ_S=i$, $τ_{ST}=(-1+i\sqrt{3})/2$, $τ_{TS}=(1+i\sqrt{3})/2$, $τ_T=i\infty$ in the fundamental domain which are invariant under the modular transformations indicated. We then generalise these fixed points to $τ_f=γτ_S$, $γτ_{ST}$, $γτ_{TS}$ and $γτ_{T}$ in the upper half complex plane, and show that it is sufficient to consider $γ\inΓ_{N}$. Focussing on level $N=4$, corresponding to the flavour group $S_4$, we consider all the resulting triplet modular forms at these fixed points up to weight 6. We then apply the results to lepton mixing, with different residual subgroups in the charged lepton sector and each of the right-handed neutrinos sectors. In the minimal case of two right-handed neutrinos, we find three phenomenologically viable cases in which the light neutrino mass matrix only depends on three free parameters, and the lepton mixing takes the trimaximal TM1 pattern for two examples. One of these cases corresponds to a new Littlest Modular Seesaw based on CSD$(n)$ with $n=1+\sqrt{6}\approx 3.45$, intermediate between CSD$(3)$ and CSD$(4)$. Finally, we generalize the results to examples with three right-handed neutrinos, also considering the level $N=3$ case, corresponding to $A_4$ flavour symmetry.

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arXiv2025

Cosmological Consequences of Domain Walls Biased by Quantum Gravity

One of the simplest standard model extensions leading to a domain wall network is a real scalar $S$ with a $Z_2$ symmetry spontaneously broken during universe evolution. Motivated by the swampland program, we explore the possibility that quantum gravity effects are responsible for violation of the discrete symmetry, triggering the annihilation of the domain wall network. We explore the resulting cosmological implications in terms of dark radiation, dark matter, gravitational waves, primordial black holes, and wormholes connected to baby universes.

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arXiv2025

Minimal Multi-Majoron Model

In order to provide a natural framework for hierarchical right-handed neutrinos, we propose a realistic ultraviolet complete minimal multi-Majoron model (MMMM). We consider two right-handed neutrinos for simplicity, although the model is readily extendable to more. The minimal model introduces two complex scalar Majoron fields $ϕ_1$ and $ϕ_2$, whose couplings to the two respective right-handed neutrinos are controlled by an extra global $U(1)_N$ symmetry. We show that a flavon field is required to facilitate the effective Yukawa couplings, in order to implement the type I seesaw mechanism. We analyse the resulting phenomenology related to neutrino masses, flavour mixing and cosmological predictions concerning the formation and decay of topological defects like the global cosmic strings and the domain walls when the $U(1)_N\times U(1)_{B-L}$ symmetry is broken. The resulting gravitational wave spectrum is a distinctive combination of the spectrum from the global cosmic string and strong first-order phase transitions when the symmetries are broken, the strength of the latter being enhanced by the second Majoron field. The resulting characteristic spectrum determines the two right-handed neutrino mass scales within the considered framework.

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arXiv2025

Modular domain walls and gravitational waves

We discuss modular domain walls and gravitational waves in a class of supersymmetric models where quark and lepton flavour symmetry emerges from modular symmetry. In such models a single modulus field $τ$ is often assumed to be stabilised at or near certain fixed point values such as $τ= {\rm i}$ and $τ= ω$ (the cube root of unity), in its fundamental domain. We show that, in the global supersymmetry limit of certain classes of potentials, the vacua at these fixed points may be degenerate, leading to the formation of modular domain walls in the early Universe. Taking supergravity effects into account, in the background of a fixed dilaton field $S$, the degeneracy may be lifted, leading to a bias term in the potential allowing the domain walls to collapse. We study the resulting gravitational wave spectra arising from the dynamics of such modular domain walls, and assess their observability by current and future experiments, as a window into modular flavour symmetry.

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arXiv2025

Modular Symmetry with Weighton

We systematically develop the weighton mechanism for natural quark and charged lepton mass hierarchies in the framework of modular symmetry with a single modulus field $τ$. The weighton $ϕ$ is defined as a complete singlet with unit modular weight, leading to fermion mass suppression by powers of $\tildeϕ$, which is the vacuum expectation value of the field scaled by a flavour cut-off. Further mass and mixing angle suppression comes from powers of the small parameter, $q\equiv e^{i2πτ}$. Assuming some fields transform as triplets under the finite modular symmetry, with general assignments for the other fields, we perform a complete analysis for the levels $N=3, 4, 5$, expressing fermion masses and mixings in terms of powers of the small parameters $\tildeϕ$ and $q$. We present two examples in detail, based on the modular group $T'$, close to the CP boundary of $τ$, which can address both fermion mass and mixing hierarchies using a weighton field.

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arXiv2025

Leptogenesis with Majoron Dark Matter

We discuss a model of neutrino mass based on the type I seesaw mechanism embedded in a spontaneously broken global lepton number framework with a $Z_2$ symmetry. We show that the resulting Majoron is a viable freeze-in dark matter candidate. Two right-handed neutrinos are assumed to have dominant off-diagonal masses suggesting resonant leptogenesis as the origin of baryon asymmetry of the Universe. Explicit higher dimensional lepton number violating operators, are shown to play a crucial role in simultaneously controlling both the Majoron production in the early Universe and the right handed neutrino mass splitting relevant for resonant leptogenesis. We perform a combined analysis of Majoron dark matter and leptogenesis, discussing the relative importance of self energy and vertex contributions to CP asymmetry, and explore the parameter space, leading to an intricate relation between neutrino mass, dark matter and baryon asymmetry.

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arXiv2025

Non-Abelian Domain Walls and Gravitational Waves

We investigate the properties of domain walls arising from non-Abelian discrete symmetries, which we refer to as non-Abelian domain walls. We focus on $S_4$, one of the most commonly used groups in lepton flavour mixing models. The spontaneous breaking of $S_4$ leads to distinct vacua preserving a residual $Z_2$ or $Z_3$ symmetry. Five types of domain walls are found, labelled as SI, SII, TI, TII, and TIII, respectively, the former two separating $Z_2$ vacua and the latter three separating $Z_3$ vacua. We highlight that SI, TI and TIII may be unstable for some regions of the parameter space and decay to stable domain walls. Stable domain walls can collapse and release gravitational radiation for a suitable size of explicit symmetry breaking. A symmetry-breaking scale of order 100 TeV may explain the recent discovery of nanohertz gravitational waves by PTA experiments. For the first time, we investigate the properties of these domain walls, which we obtain numerically with semi-analytical formulas applied to compute the tension and thickness across a wide range of parameter space. We estimate the resulting gravitational wave spectrum and find that, thanks to their rich vacuum structure, non-Abelian domain walls manifest in a very interesting and complex phenomenology.

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arXiv2025

Primordial Black Holes and Scalar-induced Gravitational Waves in Sneutrino Hybrid Inflation

We investigate the possibility that primordial black holes (PBHs) can be formed from large curvature perturbations generated during the waterfall phase transition in a supersymmetric scenario where sneutrino is the inflaton in a hybrid inflationary framework. We obtain a spectral index ($n_s \simeq 0.966$), and a tensor-to-scalar ratio ($r\simeq 0.0056-10^{-11}$), consistent with the current Planck data satisfying PBH as dark matter (DM) and detectable Gravitational Wave (GW) signal. Our findings show that the mass of PBH and the peak in the GW spectrum is correlated with the right-handed (s)neutrino mass. We identify parameter space where PBHs can be the entire DM candidate of the universe (with mass $10^{-13}\, M_\odot$) or a fraction of it. This can be tested in future observatories, for example, with amplitude $Ω_{\rm GW}h^2$ $\sim 10^{-9}$ and peak frequency $f\sim 0.1$ Hz in LISA and $Ω_{\rm GW}h^2 \sim 10^{-11}$ and peak frequency of $\sim 10$ Hz in ET via second-order GW signals. We study two models of sneutrino inflation: Model$-1$ involves canonical sneutrino kinetic term which predicts the sub-Planckian mass parameter $M$, while the coupling between a gauge singlet and the waterfall field, $β$, needs to be quite large whereas, for the model$-2$ involving $α-$attractor canonical sneutrino kinetic term, $β$ can take a natural value. Estimating explicitly, we show that both models have mild fine-tuning. We also derive an analytical expression for the power spectrum in terms of the microphysics parameters of the model like (s)neutrino mass, etc. that fits well with the numerical results. The typical reheat temperature for both the models is around $10^{7}-10^{8}$~GeV suitable for non-thermal leptogenesis.

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