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Kai Schmitz

Publications and source records attributed to Kai Schmitz.

At least 19 recordsLinked to original sources
arXiv2026

Baryon number freeze-out in the Standard Model, precisely

Weak sphaleron transitions turn a lepton asymmetry of the Standard Model plasma in the early Universe into a baryon asymmetry, conserving baryon-minus-lepton number $B-L$ and its individual flavored charges. A baryon asymmetry can thus also arise from flavored lepton asymmetries with vanishing $B-L$. Standard equilibrium calculations in the symmetric and broken phases are performed at constant temperature and hence neglect the fact that both the Higgs expectation value and the sphaleron rate vary as functions of temperature across the electroweak crossover. We derive a Boltzmann equation for the baryon number evolution across the crossover and calculate the freeze-out abundance including higher-order corrections to both the grand canonical partition function and the perturbative Higgs expectation value. This yields two sphaleron conversion factors: $C_\text{sph} = 0.3328(5)$ for $B-L$ and $\mathcal{F}_\text{sph} = 0.0279(19)$ for the flavored charges weighted by the charged-lepton Yukawa couplings.

hep-ph↗
arXiv2026

Pulsar Timing Array Sensitivity to Anisotropy: Empirical Sensitivity Curves, Scaling Relations, and the Multi-Resolution Pixel Basis

We quantify pulsar timing array (PTA) sensitivity to anisotropy in the gravitational wave background using the cross-correlation based Fisher information matrix in the pixel and spherical harmonic bases. We use a set of simulations to empirically determine scaling relations of a PTA's sensitivity to anisotropy with the number of pulsars $N_\mathrm{psr}$ in the array, the error $δt$ on the times of arrival, the frequency $f_\mathrm{GW}$ of the gravitational waves, and the angular scale $ΔΩ$ of the anisotropy. The sensitivity scales approximately as $N_\mathrm{psr}^{0.8}$, $δt^{-0.08}$, and $ΔΩ^{1.6}-ΔΩ^{2.1}$ (depending on the ranges of $\ell$ and $m$ under consideration). In addition, we use realistic simulations to project the NANOGrav PTA sensitivity to a 30-year baseline and quantify the growth in sensitivity at several timeslices. Except at the lowest frequencies, we find negligible effect on sensitivity through increasing the observation duration only. Finally, we introduce a multi-resolution pixel basis motivated by the large dependence of the sensitivity on sky location, and demonstrate the operation of the basis through a set of injections and recoveries.

astro-ph.IM↗
arXiv2026

Axion-driven spontaneous leptogenesis, precisely

We revisit a minimal scenario for spontaneous leptogenesis where the asymmetry generation is driven by a heavy axion-like field evolving via standard misalignment. We focus on the simplest framework in which lepton number violation originates from the dimension-five Weinberg operator and contributions from standard thermal leptogenesis become negligible. The asymmetry is computed by solving a set of transport equations, which incorporate fully flavor-dependent interaction rates for the Weinberg operator that are presented here for the first time. We also derive a simple algebraic master formula for the generated $B\!-\!L$ asymmetry, valid for arbitrary axion velocities and classically shift-symmetric couplings to the Standard Model, that reproduces the $B\!-\!L$-production dynamics of the full set of transport equations in controlled parameter regions. Along the way, we quantify the importance of low-scale neutrino masses and the two mass orderings on the final prediction for the generated asymmetry. Finally, we assess the cosmological viability of different axion couplings by accounting for entropy dilution from late-time axion decays and imposing constraints from baryonic isocurvature perturbations. We demonstrate that explaining the baryon asymmetry via standard Majoron misalignment is under severe tension due to dilution from late-time decays. In contrast, axions coupled to strong or weak sphalerons can successfully produce the observed asymmetry for decay constants near the energy scale of grand unification and axion oscillation temperatures $T_{\text{osc}} \gtrsim 10^{11\cdots12}$ GeV, provided a cosmological history featuring high-scale inflation and efficient reheating.

hep-ph↗
arXiv2026

Signal-to-Noise Ratio Contours for LISA

The Laser Interferometer Space Antenna (LISA) will search for a stochastic gravitational-wave (GW) background at millihertz frequencies, from both astrophysical and cosmological sources, and thereby open a new chapter in GW astronomy. In the literature, LISA's sensitivity to prospective GW background (GWB) signals is often quantified in terms of an expected signal-to-noise ratio (SNR) assuming perfect knowledge of the detector noise. The commonly employed expression for the SNR is, however, valid only in the limit of a weak GWB signal, which renders a large number of SNR values reported in the literature inaccurate. In this paper, we address this issue by deriving for the first time an expression for the expected optimal SNR of a LISA auto-correlation measurement that is valid at arbitrary signal strength. Based on our generalized expression, we conclude that LISA data worth an observing time of T_obs across the frequency band from f_min to f_max will never yield an SNR in excess of SNR_max = sqrt(T_obs(f_max-f_min)), which evaluates to SNR_max <~ 10^4 for typical mission parameters. We illustrate our findings in terms of generalized power-law-integrated (PLI) sensitivity curves at different SNR levels, i.e., LISA SNR contour lines in plots of the GW energy-density power spectrum. In contrast to earlier work on PLI sensitivity curves, we notably find that the LISA SNR contours are bounded from above, approximately by the LISA strain noise curve multiplied by a factor of Euler's number e. For GWB signals not much weaker than this range, the expected SNR for a LISA auto-correlation measurement needs to be evaluated based on our new expression. Our numerical results for the LISA SNR contours are available on Zenodo [https://doi.org/10.5281/zenodo.21275527].

gr-qc↗
arXiv2026

The NANOGrav 15 yr Data Set: Impacts of Customized Chromatic Noise Models on Gravitational Wave Analyses

We report updated nHz gravitational wave (GW) significance, characterization, and interpretations using the customized chromatic-noise models (CNMs) developed in Larsen, Baier et al. (2026). for the NANOGrav 15-year data set. We find increased evidence for the Hellings-Downs (HD) correlation signature of the stochastic gravitational wave background (GWB), with a Bayes factor of $1571\pm14$ for HD-correlations over a common uncorrelated red-noise process using a power-law model with $14$ Fourier modes. We find this $\sim8\times$ increase in Bayes factor from Agazie et al. (2023a) is a result of improved noise mitigation. Assuming an analytic null distribution for the frequentist interpulsar correlation statistic, this corresponds to a slightly more significant measurement from $3.16σ$ to $3.32σ$ against the no-correlation scenario. Spectral inference with CNMs brings the power-law GWB amplitude down to $A_{\rm GWB} = 2.1^{+0.6}_{-0.5}\times10^{-15}$ at fixed $γ_{\rm GWB} = 13/3$. In a varied-$γ$ analysis, the spectral index increases to $γ_{\rm GWB}=3.5^{+0.7}_{-0.6}$. We report updates on an all-sky continuous gravitational wave (CW) search as well as select targeted searches and calculate a $3.2\times$ larger detection volume for the NANOGrav detector. With CNMs, we find reduced evidence for a non-Einsteinian, scalar-transverse mode of gravity. Finally, we reinterpret the GWB first with the assumption of an astrophysical background sourced by SMBHBs and then assuming the more exotic origins of cosmic inflation, a first-order cosmological phase transition, and stable cosmic strings. Under both the SMBHB hypothesis and the cosmological hypotheses, we see only marginal shifts in model parameter posteriors which are consistent with the slightly quieter and steeper power-law GWB spectrum.

astro-ph.CO↗
arXiv2026

Gravitational Wave Measurement of the $M_\mathrm{BH}$-$M_\mathrm{bulge}$ Intrinsic Scatter at High Redshift

The observed GWB spectrum is higher in amplitude than model predictions by a factor of 2-3. Using a semi-analytic model, we evaluate the effect of a high-scatter supermassive black hole (SMBH) scaling relation ($M_\mathrm{BH}$-$M_\mathrm{bulge}$) on models of the nanohertz gravitational wave background (GWB). By implementing an intrinsic scatter of the $M_\mathrm{BH}$-$M_\mathrm{bulge}$ relation, which is larger at higher redshift, but matches local observations, we find that the amplitude of GWB models increases to be consistent with the low-frequency end of the GWB spectrum. This amplitude increase is not uniform across frequencies, a strongly evolving scatter preferentially increases the number density of the most massive SMBHs which, in the GWB spectrum, minimizes the strength of the low-frequency turnover. Our models with positively evolving intrinsic scatter can reproduce the electromagnetically observed overmassive SMBHs at $4 < z < 6$ without changing the $M_\mathrm{BH}$-$M_\mathrm{bulge}$ normalization though we find that including moderate normalization evolution marginally improves fits to the GWB data. We conclude that the $M_\mathrm{BH}$-$M_\mathrm{bulge}$ relation which best describes the available GWB and electromagnetic data sets has intrinsic scatter that evolves as $\varepsilon(z) = \varepsilon_0 + (0.56 \pm 0.4) \log_{10}(1 + z)$ and normalization that evolves as $α(z) = α_0 (1 + z)^{0.84 \pm 0.35}$. The results of this work imply that the $M_\mathrm{BH}$-$M_\mathrm{bulge}$ relation we see today is not universal throughout cosmic time and that a diversity of seeding models and growth mechanisms may be at play in the early stages of SMBH-galaxy evolution.

astro-ph.HE↗
arXiv2026

New gravitational-wave templates for metastable cosmic strings: Loop breaking versus network collapse

Metastable cosmic strings are a common prediction of grand unified theories and act as a source of a gravitational-wave background (GWB) that can explain the 2023 pulsar timing array (PTA) signal. In this paper, we revisit the GWB signal from metastable strings, emphasizing the need to carefully distinguish between two different time scales: (i) t_LB, the time scale of loop breaking because of spontaneous monopole nucleation on closed string loops, and (ii) t_NC, the time scale of network collapse when string segments attached to monopoles begin to enter the Hubble horizon. We discuss under which conditions these two time scales are similar or far apart from each other and illustrate the resulting consequences for the GWB signal. In doing so, we generalize the description of the GWB signal from metastable strings to a three-parameter model in terms of the string tension Gμand the time scales t_LB and t_NC, which allows us to unify the modeling of standard metastable strings with what is known as quasi-stable strings. In the limit of a large t_LB/t_NC ratio, we, moreover, derive a compact analytical expression for the predicted GWB spectrum in excellent agreement with numerical results in the literature. We thus conclude that our new templates for the GWB spectrum from metastable strings can be readily used in the analysis of future PTA data sets.

hep-ph↗
arXiv2026

Gravitational waves from axion inflation in the gradient expansion formalism. Part I. Pure axion inflation

Axion inflation is a well-motivated model of cosmic inflation with a rich phenomenology. The abundant production of gauge fields during axion inflation notably sources a stochastic gravitational-wave (GW) background signal, which nourishes the hope that future GW searches might have a chance to probe the model. In this paper, we scrutinize GW production during axion inflation in the gradient expansion formalism (GEF), a powerful numerical technique that captures the nonlinear dynamics of the system in the limit of vanishing axion gradients. We focus on {single-field} axion inflation coupled to a pure Abelian gauge sector, i.e., pure axion inflation (PAI), and perform the first-ever {detailed} parameter scan of GW production in the Abelian PAI model close to the onset of strong backreaction. {We approximate the axion potential around its minimum by a quadratic mass term and study the tensor modes that exit the Hubble horizon as the axion rolls down this potential.} Remarkably enough, we find that GW signals within the reach of future GW interferometers can only be realized in parameter regions that also lead to strong backreaction and that are in conflict with the upper limit on $ΔN_{\rm eff}$, i.e., the allowed energy density of dark radiation. This observation defines a clear target for future lattice studies of axion inflation that may confirm or improve the predictions of our GEF benchmark.

astro-ph.CO↗
arXiv2026

Gravitational waves from axion inflation in the gradient expansion formalism. Part II. Fermionic axion inflation

Axion inflation represents an intriguing source of gravitational waves (GWs) from the early Universe. In a companion paper, arXiv:2508.00798, we previously leveraged the gradient expansion formalism (GEF) to investigate pure axion inflation (PAI), i.e., axion inflaton coupled to a pure gauge sector. In this paper, we extend our analysis to fermionic axion inflation (FAI), i.e., we allow for the presence of fermions in the gauge sector. PAI predicts a strongly blue-tilted GW spectrum; in our GEF benchmark study, all parameter regions leading to observable GWs turned out to violate the upper limit on the number of extra relativistic degrees of freedom, $ΔN_{\rm eff}$. As we demonstrate in this paper, the situation is different for FAI: Schwinger pair creation of the charged fermions results in a damping of gauge-field production, which attenuates the GW signal. As a result, the GW signal from FAI can fall into the sensitivity reach of LISA and ET without violating the upper limit on $ΔN_{\rm eff}$. This result notably applies to the arguably most realistic variant of Abelian axion inflation, in which the axion couples to the hypercharge sector of the Standard Model. Besides, we discuss GW emission from the fermion gas, which may further enhance the total GW signal but which also requires a more quantitative investigation in future work. Additionally, we identify a new backreaction regime in which fermion production moderates the axion--vector dynamics. In this regime, the axion velocity and all energy-density components exhibit oscillations analogous to the strong backreaction in PAI, but here, the oscillations occur around the slow-roll trajectory and are damped by the presence of charged fermions. These observations define again an interesting GEF benchmark for future lattice studies.

astro-ph.CO↗
arXiv2026

Nonlinear physics of axion inflation

An axion-like field coupled to an Abelian gauge field provides one of the simplest inflationary models that is free from the eta problem and possesses an efficient reheating mechanism. For sufficiently large coupling, this system enters a regime of strong gauge-field backreaction, exhibiting rich and intricate dynamics. In this work, we employ a semi-analytical method, the gradient-expansion formalism, to perform a comprehensive parameter scan and determine the precise conditions under which backreaction sets in. Previous studies have shown that the Anber-Sorbo solution, in which the potential-gradient force acting on the axion is balanced by Hubble friction and gauge-field backreaction, is unstable. Here, we broaden the parameter space and identify a new region in which the Anber-Sorbo solution remains stable despite strong backreaction. Although our analysis is restricted to a homogeneous axion field and to perturbations that depend only on time, we expect that this stability property can be extrapolated to generic time- and space-dependent perturbations. This newly identified region therefore represents a distinct type of backreaction - stable backreaction - which may not be accompanied by the rapid growth of perturbations. We further investigate the nonlinear behavior of solutions in the backreaction regime in a toy model (de Sitter, constant potential slope, no axion gradients), identifying a supercritical Hopf bifurcation at the onset of instability, a nontrivial limit cycle in the unstable regime, and burst-like oscillatory dynamics. Finally, we present a more stringent criterion for the onset of (unstable) backreaction, based on crossing the instability threshold, and apply this criterion to two benchmark inflationary models.

hep-ph↗
arXiv2026

Gravitational waves from cosmic strings for pedestrians

Cosmic strings represent an attractive source of gravitational waves (GWs) from the early Universe. However, numerical computation of the GW signal from cosmic strings requires the evaluation of complicated integral and sum expressions, which can become computationally costly in large parameter scans. This motivates us to rederive the GW signal from a network of local stable cosmic strings in the Nambu-Goto approximation and based on the velocity-dependent one-scale model from a ``pedestrian'' perspective. That is, we derive purely analytical expressions for the total GW spectrum, which remain exact wherever possible and whose error can be tracked and reduced in a controlled way in crucial situations in which we are forced to introduce approximations. In this way, we obtain powerful formulas that, unlike existing results in the literature, are valid across the entire frequency spectrum and across the entire conceivable range of cosmic-string tensions. We provide an in-depth discussion of the GW spectra thus obtained, including their characteristic break frequencies and approximate power-law behaviors, comment on the effect of changes in the effective number of degrees of freedom during radiation domination, and conclude with a concise summary of our main formulas that can readily be used in future studies.

astro-ph.CO↗
arXiv2026

Kinematic Anisotropies in PTA Observations: Analytical Toolkit

The reported evidence for an isotropic gravitational-wave background (GWB) from pulsar timing array (PTA) collaborations has motivated searches for extrinsic and intrinsic anisotropies. Kinematic anisotropies may arise as a consequence of a boosted observer moving with respect to the frame in which the GWB appears isotropic. In this work, we present an analytical toolbox to describe the effects of kinematic anisotropies on the overlap reduction function. Our analytical results differ from previous findings at the quadrupole order and are detailed in three appendices. For the first time, we also derive the corresponding auto-correlation using two approaches, taking the pulsar distances to be infinite or finite, respectively. Our formulas can be used in forecasts or Bayesian analysis pipelines.

gr-qc↗
arXiv2026

Inference on inner galaxy structure via gravitational waves from supermassive binaries

The detection of a stochastic gravitational wave background by pulsar-timing arrays indicates the presence of a population of supermassive black hole binaries. Although the observed spectrum generally matches predictions for orbital evolution driven by gravitational-wave emission in circular orbits, there is a preference for a spectral turnover at the lowest observed frequencies, which may point to substantial hardening during a transition from early environmental influences to later stages dominated by emission. In the vicinity of these binaries, the ejection of stars or dark matter particles through gravitational three-body slingshots efficiently extracts orbital energy, leading to a low-frequency turnover in the spectrum. Here we model how the gravitational-wave spectrum depends on the initial inner galactic profile before scouring by binary ejections while accounting for a range of initial binary eccentricities. By analysing the NANOGrav 15-year data, we find that a parsec-scale galactic-centre density of around $10^6 M_{\odot} \mathrm{pc}^{-3}$ is favoured across most of the parameter space, thus shedding light on the environmental effects that shape black hole evolution and the combined matter density near galaxy centres.

astro-ph.HE↗
arXiv2026

The NANOGrav 15 yr Data Set: Piecewise Power-Law Reconstruction of the Gravitational-Wave Background

The NANOGrav 15-year (NG15) data set provides evidence for a gravitational-wave background (GWB) signal at nanohertz frequencies, which is expected to originate either from a cosmic population of inspiraling supermassive black-hole binaries or new particle physics in the early Universe. A firm identification of the source of the NG15 signal requires an accurate reconstruction of its frequency spectrum. In this paper, we provide such a spectral characterization of the NG15 signal based on a piecewise power-law (PPL) ansatz that strikes a balance between existing alternatives in the literature. Our PPL reconstruction is more flexible than the standard constant-power-law model, which describes the GWB spectrum in terms of only two parameters: an amplitude A and a spectral index gamma. Concurrently, it better approximates physically realistic GWB spectra -- especially those of cosmological origin -- than the free spectral model, since the latter allows for arbitrary variations in the GWB amplitude from one frequency bin to the next. Our PPL reconstruction of the NG15 signal relies on individual PPL models with a fixed number of internal nodes (i.e., constant power law, broken power law, doubly broken power law, etc.) that are ultimately combined in a Bayesian model average. The data products resulting from our analysis provide the basis for fast refits of spectral GWB models.

astro-ph.HE↗
arXiv2026

The NANOGrav 15 yr Data Set: Targeted Searches for Supermassive Black Hole Binaries

We present the first targeted searches for continuous gravitational waves (CWs) from 114 active galactic nuclei (AGN) that may host supermassive black hole binaries, using the NANOGrav 15 yr data set. By incorporating electromagnetic priors on sky location, distance, redshift, and CW frequency, our strain and chirp mass upper limits are typically improved by a factor of $\sim 2$ (median 2.2) relative to all-sky limits at the same frequency. Bayesian comparisons against a model including only a Hellings-Downs correlated background disfavors a CW signal for all targets, with a mean Bayes factor of $0.73 \pm 0.32$. Two targets have Bayes factors slightly above unity, but coherence tests, random targeting experiments, and a conservative accounting of the 114-target trials factor all indicate that they are consistent with noise. We use these two candidates as worked examples to illustrate an end-to-end targeted CW search analysis and a suite of follow up tests that future promising candidates would need to pass. We find that the electromagnetic interpretations of both candidates are ambiguous, and we update the constraints on a putative binary in 3C 66B, ruling out part of its previously allowed parameter space. Ultimately, our results demonstrate the current sensitivity of targeted pulsar timing array searches for CWs and define a roadmap for future multimessenger CW detections.

astro-ph.HE↗
arXiv2025

Inferring Mbh-Mbulge Evolution from the Gravitational Wave Background

We test the impact of an evolving supermassive black hole (SMBH) mass scaling relation (Mbh-Mbulge) on the predictions for the gravitational wave background (GWB). The observed GWB amplitude is 2-3 times higher than predicted by astrophysically informed models which suggests the need to revise the assumptions in those models. We compare a semi-analytic model's ability to reproduce the observed GWB spectrum with a static versus evolving-amplitude Mbh-Mbulge relation. We additionally consider the influence of the choice of galaxy stellar mass function on the modeled GWB spectra. Our models are able to reproduce the GWB amplitude with either a large number density of massive galaxies or a positively evolving Mbh-Mbulge amplitude (i.e., the Mbh / Mbulge ratio was higher in the past). If we assume that the Mbh-Mbulge amplitude does not evolve, our models require a galaxy stellar mass function that implies an undetected population of massive galaxies (Mstellar > 10^11 Msun at z > 1). When the Mbh-Mbulge amplitude is allowed to evolve, we can model the GWB spectrum with all fiducial values and an Mbh-Mbulge amplitude that evolves as alpha(z) = alpha_0 (1 + z)^(1.04 +/- 0.5).

astro-ph.HE↗
arXiv2025

A lower bound on the right-handed neutrino mass from wash-in leptogenesis

Leptogenesis is an attractive scenario for the generation of the baryon asymmetry of the Universe that relies on the dynamics of right-handed neutrinos (RHNs) in the seesaw extension of the Standard Model. In standard thermal leptogenesis, the RHN mass scale $M_N$ is subject to the Davidson--Ibarra bound, $M_N \gtrsim 10^9\,\textrm{GeV}$, which builds on the assumption that RHN decays are responsible for the violation of both charge-parity invariance ($CP$) and baryon-minus-lepton number ($B\!-\!L$). In this paper, we relax this assumption in the context of the more flexible framework of wash-in leptogenesis, in which $CP$ violation is encoded in the initial conditions and the only remaining task of the RHN decays is to violate $B\!-\!L$. Solving the relevant set of Boltzmann equations for vanishing initial baryon and lepton numbers (i.e., $B = L_e = L_μ= L_τ= 0$ initially), we find that, in wash-in leptogenesis, the RHN mass scale can be as low as 7~TeV. Wash-in leptogenesis at such low RHN masses requires the presence of a primordial charge asymmetry between right-handed electrons and left-handed positrons. We discuss several possibilities for the origin of such an asymmetry and comment on its implications for the chiral instability of the Standard Model plasma.

hep-ph↗
arXiv2025

Gravitational waves from low-scale cosmic strings without scaling

Cosmic strings are predicted in many extensions of the Standard Model and constitute a plausible source of gravitational waves (GWs) from the early Universe. In a previous article arXiv:2405.10937v2, we pointed out that the GW spectrum from a population of string loops in the scaling regime can exhibit a sharp cutoff frequency associated with the fundamental oscillation mode of string loops. In this paper, we study the effect of particle decay due to kink-kink collisions and cusps on the GW spectrum in the nonscaling scenario introduced in Ref. arXiv:1911.12066. We find analytical conditions for the existence of a cutoff frequency in the fundamental spectrum and provide expressions for this frequency. In large regions of parameter space, our results in the nonscaling model turn out to be identical to those in the scaling model. Finally, we demonstrate how the spectrum changes when transitioning from the regime with a cutoff frequency to the regime without a cutoff frequency. Our analytical estimates are validated at qualitatively different benchmark points by comparing them with numerical spectra.

astro-ph.CO↗