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The first direct measurement of gravitational waves by the LIGO and Virgo collaborations has opened up new avenues to explore our Universe. This white paper outlines the challenges and gains expected in gravitational-wave searches at frequencies above the LIGO/Virgo band, with a particular focus on Ultra High-Frequency Gravitational Waves (UHF-GWs), covering the MHz to GHz range. The absence of known astrophysical sources in this frequency range provides a unique opportunity to discover physics beyond the Standard Model operating both in the early and late Universe, and we highlight some of the most promising gravitational sources. We review several detector concepts that have been proposed to take up this challenge, and compare their expected sensitivity with the signal strength predicted in various models. This report is the summary of the workshop “Challenges and opportunities of high-frequency gravitational wave detection” held at ICTP Trieste, Italy in October 2019, that set up the stage for the recently launched Ultra-High-Frequency Gravitational Wave (UHF-GW) initiative.

A bstract We study fermion number non-conservation (or chirality breaking) in Abelian gauge theories at finite temperature. We consider the presence of a chemical potential μ for the fermionic charge, and monitor its evolution with real-time classical lattice simula- tions. This method accounts for short-scale fluctuations not included in the usual effective magneto-hydrodynamics (MHD) treatment. We observe a self-similar decay of the chemi- cal potential, accompanied by an inverse cascade process in the gauge field that leads to a production of long-range helical magnetic fields. We also study the chiral charge dynamics in the presence of an external magnetic field B , and extract its decay rate Γ 5 ≡ d log μ dt . We provide in this way a new determination of the gauge coupling and magnetic field de- pendence of the chiral rate, which exhibits a best fit scaling as Γ 5 ∝ 11 2 B 2 . We confirm numerically the fluctuation-dissipation relation between Γ5 and Γ diff , the Chern-Simons diffusion rate, which was obtained in a previous study. Remarkably, even though we are outside the MHD range of validity, the dynamics observed are in qualitative agreement with MHD predictions. The magnitude of the chiral/diffusion rate is however a factor ∼ 10 times larger than expected in MHD, signaling that we are in reality exploring a dif- ferent regime accounting for short scale fluctuations. This discrepancy calls for a revision of the implications of fermion number and chirality non-conservation in finite tempera- ture Abelian gauge theories, though no definite conclusion can be made at this point until hard-thermal-loops are included in the lattice simulations.

A bstract We discuss the non-conservation of fermion number (or chirality breaking, depending on the fermionic charge assignment) in Abelian gauge theories at finite temperature. We study different mechanisms of fermionic charge disappearance in the high temperature plasma, using both analytical estimates and real-time classical lattice numerical simulations. We investigate the random walk of the Chern-Simons number Q ∝ ∫ d 4 x F μ ν F ˜ μ ν , and show that it has a diffusive behaviour in the presence of an external magnetic field B . This indicates that the mechanism for fermionic number non-conservation for B ≠ 0, is due to fluctuations of the gauge fields, similarly as in the case of non-Abelian gauge theories. We have determined numerically, with lattice simulations, the rate Γ of chirality non-conservation, extracting it from the diffusion process. We find that it is a factor ∼ 60 larger compared to previous theoretical estimates, what calls for a revision of the implications of Abelian fermion number and chirality non-conservation for baryogenesis, magnetogenesis and chiral symmetry evolution.

To confront the numerical results of Γ diff with the analytical results from section 2.3, we originally considered the theoretical prediction for the diffusion rate given by eq. (2.17), which we re-wrote in eq. (4.25).

A bstract Out-of-equilibrium fermions can be created in the early Universe by non-perturbative parametric effects, both at preheating or during the thermal era. An anisotropic stress is developed in the fermion distribution, acting as a source of a stochastic background of gravitational waves (GW). We derive a general formalism to calculate the spectrum of GW produced by an ensemble of fermions, which we apply to a variety of scenarios after inflation. We discuss in detail the regularization of the source, i.e. of the unequal-time-correlator of the fermions’ transverse-traceless anisotropic stress. We discuss how the GW spectrum builds up in time and present a simple parametrization of its final amplitude and peak frequency. We find that fermions may generate a GW background with a significant amplitude at very high frequencies, similarly to the case of preheating with scalar fields. A detection of this GW background would shed light on the physics of the very early Universe, but new technology at high frequencies is required, beyond the range accessible to currently planned detectors.

A bstract The stability of the Standard Model (SM) at high energies implies that the SM Higgs forms a condensate during inflation, which starts oscillating soon after the inflationary stage ends. This causes the Higgs to decay very fast, via non-perturbative effects, into all the SM fields coupled directly to it. The excited species act as a source of gravitational waves (GWs), and as a result, all Yukawa and SU(2) L gauge couplings of the SM are imprinted as features in the GW spectrum. In practice, the signal is dominated by the most strongly interacting species, rendering the information on the other species inaccessible. To detect this background new high frequency GW detection technology is required, beyond that of currently planned detectors. If detected, this signal could be used for measuring properties of high-energy particle physics, including beyond the SM scenarios.

The first direct measurement of gravitational waves by the LIGO and Virgo collaborations has opened up new avenues to explore our Universe. This White Paper outlines the challenges and gains expected in gravitational-wave searches at frequencies above the LIGO/Virgo band. The scarcity of possible astrophysical sources in most of this frequency range provides a unique opportunity to discover physics beyond the Standard Model operating both in the early and late Universe, and we highlight some of the most promising of these sources. We review several detector concepts that have been proposed to take up this challenge, and compare their expected sensitivity with the signal strength predicted in various models. This report is the summary of a series of workshops on the topic of high-frequency gravitational wave detection, held in 2019 (ICTP, Trieste, Italy), 2021 (online) and 2023 (CERN, Geneva, Switzerland).

The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational-wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational-wave observations by LISA to probe the universe.

The first direct measurement of gravitational waves by the LIGO and Virgo collaborations has opened up new avenues to explore our Universe. This White Paper outlines the challenges and gains expected in gravitational-wave searches at frequencies above the LIGO/Virgo band. The scarcity of possible astrophysical sources in most of this frequency range provides a unique opportunity to discover physics beyond the Standard Model operating both in the early and late Universe, and we highlight some of the most promising of these sources. We review several detector concepts that have been proposed to take up this challenge, and compare their expected sensitivity with the signal strength predicted in various models. This report is the summary of a series of workshops on the topic of high-frequency gravitational wave detection, held in 2019 (ICTP, Trieste, Italy), 2021 (online) and 2023 (CERN, Geneva, Switzerland).

We apply state-of-the-art, likelihood-free statistical inference (machine-learning-based) techniques for reconstructing the spectral shape of a gravitational wave background (GWB). We focus on the reconstruction of an arbitrarily shaped signal by the LISA detector, but the method can be easily extended to either template-dependent signals, or to other detectors, as long as a characterisation of the instrumental noise is available. As proof of the technique, we quantify the ability of LISA to reconstruct signals of arbitrary spectral shape (\\(ıt blind\\) reconstruction), considering a diversity of frequency profiles, and including astrophysical backgrounds in some cases. As a teaser of how the method can reconstruct signals characterised by a parameter-dependent template (\\(ıt template\\) reconstruction), we present a dedicated study for power-law signals. While our technique has several advantages with respect to traditional MCMC methods, we validate it with the latter for concrete cases. This work opens the door for both fast and accurate Bayesian parameter estimation of GWBs, with essentially no computational overhead during the inference step. Our set of tools are integrated into the package \\( GWBackFinder\\), which is publicly available in https://github.com/AndronikiDimitriou/GWBackFinder.