arXiv subjects

K. Schmitz

Publications and source records attributed to K. Schmitz.

10 recordsLinked to original sources

arXiv2026

The Neumann problem for a multivalued p-Laplace equation of Allen-Cahn type with a multiplicative stochastic force

In this paper, we consider a parabolic problem with constraint written as a differential inclusion, driven by a multiplicative colored noise and involving a p-Laplace operator (for $p \geq 2$), nonlinear random source terms and subject to Neumann boundary conditions on a bounded Lipschitz domain of $R^d$ with $d \geq 1$. This contribution aims at proving existence and uniqueness of a solution for such a multivalued problem. On one hand, the existence result is proved by the analysis of a semi-implicit time discretization scheme constructed on a smoother version of our problem, itself obtained by a regularization "\`a la Moreau-Yosida" of the subdifferential term. The key point of our approach consists in finding a clever relation between the time step denoted $\tau$ and the Moreau-Yosida regularization parameter denoted $\epsilon$ in view to pass simultaneously to the limit with respect to $\tau$ and $\epsilon$. On the other hand, the uniqueness of the solution is proved by standard arguments.

math.AP↗

arXiv2024

Scalar perturbations from inflation in the presence of gauge fields

We study how Abelian-gauge-field production during inflation affects scalar perturbations in the case when the gauge field interacts with the inflaton directly (by means of generic kinetic and axial couplings) and via gravity. The homogeneous background solution is defined by self-consistently taking into account the backreaction of the gauge field on the evolution of the inflaton and the scale factor. For the perturbations on top of this background, all possible scalar contributions coming from the inflaton, the metric, and the gauge field are considered. We derive a second-order differential equation for the curvature perturbation, $\zeta$, capturing the impact of the gauge field, both on the background dynamics and on the evolution of scalar perturbations. The latter is described by a source term in the $\zeta$ equation, which is quadratic in the gauge-field operators and leads to non-Gaussianities in the curvature perturbations. We derive general expressions for the induced scalar power spectrum and bispectrum. Finally, we apply our formalism to the well-known case of axion inflation without backreaction. Numerical results show that, in this example, the effect of including metric perturbations is small for values of the gauge-field production parameter $\xi> 3$. This is in agreement with the previous results in the literature. However, in the region of smaller values, $\xi\lesssim 2$, our new results exhibit order-of-unity deviations when compared to previous results.

astro-ph.CO↗

arXiv2022

Hypermagnetogenesis from axion inflation: Model-independent estimates

Axion inflation coupled to the Standard Model (SM) hypercharge gauge sector represents an attractive scenario for the generation of primordial hypermagnetic fields. The description of this scenario is, however, complicated by the Schwinger effect, which gives rise to highly nonlinear dynamics. Hypermagnetogenesis during axion inflation in the absence of nonlinear effects is well studied and known to result in a hypermagnetic energy density that scales like $H^4\,e^{2πξ}/ξ^5$, where $ξ$ is proportional to the time derivative of the axion-vector coupling in units of the Hubble rate $H$. In this paper, we generalize this result to the full SM case by consistently taking into account the Schwinger pair production of all SM fermions. To this end, we employ the novel gradient-expansion formalism that we recently developed in [2109.01651], and which is based on a set of vacuum expectation values for bilinear hyperelectromagnetic functions in position space. We parametrize the numerical output of our formalism in terms of three parameters ($ξ$, $H$, and $Δ$, where the latter accounts for the damping of subhorizon gauge-field modes because of the finite conductivity of the medium) and work out semianalytical fit functions that describe our numerical results with high accuracy. Finally, we validate our results by comparing them to existing estimates in the literature as well as to the explicit numerical results in a specific inflationary model, which leads to good overall agreement. We conclude that the systematic uncertainties in the description of hypermagnetogenesis during axion inflation, which previously spanned up to several orders of magnitude, are now reduced to typically less than 1 order of magnitude, which paves the way for further phenomenological studies.

hep-ph↗

arXiv2022

The International Pulsar Timing Array second data release: Search for an isotropic Gravitational Wave Background

We searched for an isotropic stochastic gravitational wave background in the second data release of the International Pulsar Timing Array, a global collaboration synthesizing decadal-length pulsar-timing campaigns in North America, Europe, and Australia. In our reference search for a power law strain spectrum of the form $h_c = A(f/1\,\mathrm{yr}^{-1})^α$, we found strong evidence for a spectrally-similar low-frequency stochastic process of amplitude $A = 3.8^{+6.3}_{-2.5}\times10^{-15}$ and spectral index $α= -0.5 \pm 0.5$, where the uncertainties represent 95\% credible regions, using information from the auto- and cross-correlation terms between the pulsars in the array. For a spectral index of $α= -2/3$, as expected from a population of inspiralling supermassive black hole binaries, the recovered amplitude is $A = 2.8^{+1.2}_{-0.8}\times10^{-15}$. Nonetheless, no significant evidence of the Hellings-Downs correlations that would indicate a gravitational-wave origin was found. We also analyzed the constituent data from the individual pulsar timing arrays in a consistent way, and clearly demonstrate that the combined international data set is more sensitive. Furthermore, we demonstrate that this combined data set produces comparable constraints to recent single-array data sets which have more data than the constituent parts of the combination. Future international data releases will deliver increased sensitivity to gravitational wave radiation, and significantly increase the detection probability.

astro-ph.HE↗

arXiv2021

Gauge-field production during axion inflation in the gradient expansion formalism

We study the explosive production of gauge fields during axion inflation in a novel gradient expansion formalism that describes the time evolution of a set of bilinear electromagnetic functions in position space. Based on this formalism, we are able to simultaneously account for two important effects that have thus far been mostly treated in isolation: (i) the backreaction of the produced gauge fields on the evolution of the inflaton field and (ii) the Schwinger pair production of charged particles in the strong gauge-field background. This allows us to show that the suppression of the gauge-field production due to the Schwinger effect can prevent the backreaction in scenarios in which it would otherwise be relevant. Moreover, we point out that the induced current, $\boldsymbol{J} = σ\boldsymbol{E}$, also dampens the Bunch-Davies vacuum fluctuations deep inside the Hubble horizon. We describe this suppression by a new parameter $Δ$ that is related to the time integral over the conductivity $σ$ which hence renders the description of the entire system inherently nonlocal in time. Finally, we demonstrate how our formalism can be used to construct highly accurate solutions for the mode functions of the gauge field in Fourier space, which serves as a starting point for a wealth of further phenomenological applications, including the phenomenology of primordial perturbations and baryogenesis.

hep-ph↗

arXiv2020

Fluid leakage in metallic seals

Metallic seals are crucial machine elements in many important applications, e.g., in ultrahigh vacuum systems. Due to the high elastic modulus of metals, and the surface roughness which exists on all solid surfaces, if no plastic deformation would occur one expects in most cases large fluid flow channels between the contacting metallic bodies, and large fluid leakage. However, in most applications plastic deformation occurs, at least at the asperity level, which allows the surfaces to approach each other to such an extent that fluid leakage often can be neglected. In this study, we present an experimental set-up for studying the fluid leakage in metallic seals. We study the water leakage between a steel sphere and a steel body (seat) with a conical surface. The experimental results are found to be in good quantitative agreement with a (fitting-parameter-free) theoretical model. The theory predicts that the plastic deformations reduce the leak-rate by a factor $\approx 8$

cond-mat.soft↗

arXiv2014

The Chaotic Regime of D-Term Inflation

We consider D-term inflation for small couplings of the inflaton to matter fields. Standard hybrid inflation then ends at a critical value of the inflaton field that exceeds the Planck mass. During the subsequent waterfall transition the inflaton continues its slow-roll motion, whereas the waterfall field rapidly grows by quantum fluctuations. Beyond the decoherence time, the waterfall field becomes classical and approaches a time-dependent minimum, which is determined by the value of the inflaton field and the self-interaction of the waterfall field. During the final stage of inflation, the effective inflaton potential is essentially quadratic, which leads to the standard predictions of chaotic inflation. The model illustrates how the decay of a false vacuum of GUT-scale energy density can end in a period of `chaotic inflation'.

hep-ph↗

arXiv2013

Superconformal D-Term Inflation

We study models of hybrid inflation in the framework of supergravity with superconformal matter. F-term hybrid inflation is not viable since the inflaton acquires a large tachyonic mass. On the contrary, D-term hybrid inflation can successfully account for the amplitude of the primordial power spectrum. It is a two-field inflation model which, depending on parameters, yields values of the scalar spectral index down to n_s ~ 0.96. Generically, there is a tension between a small spectral index and the cosmic string bound albeit, within 2-sigma uncertainty, the current observational bounds can be simultaneously fulfilled.

hep-ph↗

arXiv2011

Entropy, Baryon Asymmetry and Dark Matter from Heavy Neutrino Decays

The origin of the hot phase of the early universe remains so far an unsolved puzzle. A viable option is entropy production through the decays of heavy Majorana neutrinos whose lifetimes determine the initial temperature. We show that baryogenesis and the production of dark matter are natural by-products of this mechanism. As is well known, the cosmological baryon asymmetry can be accounted for by leptogenesis for characteristic neutrino mass parameters. We find that thermal gravitino production then automatically yields the observed amount of dark matter, for the gravitino as the lightest superparticle and typical gluino masses. As an example, we consider the production of heavy Majorana neutrinos in the course of tachyonic preheating associated with spontaneous B-L breaking. A quantitative analysis leads to contraints on the superparticle masses in terms of neutrino masses: For a light neutrino mass of 10^{-5} eV the gravitino mass can be as small as 200 MeV, whereas a lower neutrino mass bound of 0.01 eV implies a lower bound of 9 GeV on the gravitino mass. The measurement of a light neutrino mass of 0.1 eV would rule out heavy neutrino decays as the origin of entropy, visible and dark matter.

hep-ph↗

arXiv2010

Matter and Dark Matter from False Vacuum Decay

We study tachyonic preheating associated with the spontaneous breaking of B-L, the difference of baryon and lepton number. Reheating occurs through the decays of heavy Majorana neutrinos which are produced during preheating and in decays of the Higgs particles of B-L breaking. Baryogenesis is an interplay of nonthermal and thermal leptogenesis, accompanied by thermally produced gravitino dark matter. The proposed mechanism simultaneously explains the generation of matter and dark matter, thereby relating the absolute neutrino mass scale to the gravitino mass.

hep-ph↗