Constraining Post-Inflationary Axions with Pulsar Timing Arrays

Models that produce Axion-Like-Particles (ALP) after cosmological inflation due to spontaneous $U(1)$ symmetry breaking also produce cosmic string networks. Those axionic strings lose energy through gravitational wave emission during the whole cosmological history, generating a stochastic background of gravitational waves that spans many decades in frequency. We can therefore constrain the axion decay constant and axion mass from limits on the gravitational wave spectrum and compatibility with dark matter abundance as well as dark radiation. We derive such limits from analyzing the most recent NANOGrav data from Pulsar Timing Arrays (PTA). The limits are compatible with the slightly stronger $N_{\rm eff}$ bounds on dark radiation for ALP masses $m_a \lesssim 10^{-10}$ eV. On the other hand, for heavy ALPs with $m_a\gtrsim 0.1$ GeV and $N_{\rm DW}\neq 1$, new regions of parameter space can be probed by PTA data due to the dominant Domain-Wall contribution to the gravitational wave background.Comment: 8 pages, 4 figures + supplemental material (2 pages, 2 figures

The Stochastic Relaxion

We revisit the original proposal of cosmological relaxation of the electroweak scale by Graham, Kaplan and Rajendran in which the Higgs mass is scanned during inflation by an axion field, the relaxion. We investigate the regime where the relaxion is subject to large fluctuations during inflation. The stochastic dynamics of the relaxion is described by means of the Fokker-Planck formalism. We derive a new stopping condition for the relaxion taking into account transitions between the neighboring local minima of its potential. Relaxion fluctuations have important consequences even in the "classical-beats-quantum" regime. We determine that for a large Hubble parameter during inflation, the random walk prevents the relaxion from getting trapped at the first minimum. The relaxion stops much further away, where the potential is less shallow. Interestingly, this essentially jeopardises the "runaway relaxion" threat from finite-density effects, restoring most of the relaxion parameter space. We also explore the "quantum-beats-classical" regime, opening large new regions of parameter space. We investigate the consequences for both the QCD and the non-QCD relaxion. The misalignment of the relaxion due to fluctuations around its local minimum opens new phenomenological opportunities.Comment: 35 pages and 16 figures in main text, and 15 pages and 2 figures in appendice

Gravitational wave generation from bubble collisions in first-order phase transitions: an analytic approach

Gravitational wave production from bubble collisions was calculated in the early nineties using numerical simulations. In this paper, we present an alternative analytic estimate, relying on a different treatment of stochasticity. In our approach, we provide a model for the bubble velocity power spectrum, suitable for both detonations and deflagrations. From this, we derive the anisotropic stress and analytically solve the gravitational wave equation. We provide analytical formulae for the peak frequency and the shape of the spectrum which we compare with numerical estimates. In contrast to the previous analysis, we do not work in the envelope approximation. This paper focuses on a particular source of gravitational waves from phase transitions. In a companion article, we will add together the different sources of gravitational wave signals from phase transitions: bubble collisions, turbulence and magnetic fields and discuss the prospects for probing the electroweak phase transition at LISA.Comment: 48 pages, 14 figures. v2 (PRD version): calculation refined; plots redone starting from Fig. 4. Factor 2 in GW energy spectrum corrected. Main conclusions unchanged. v3: Note added at the end of paper to comment on the new results of 0901.166

Warped Unification, Proton Stability and Dark Matter

Many extensions of the Standard Model have to face the problem of new unsuppressed baryon-number violating interactions. In supersymmetry, the simplest way to solve this problem is to assume R-parity conservation. As a result, the lightest supersymmetric particle becomes stable and a well-motivated dark matter candidate. In this paper, we show that solving the problem of baryon number violation in non supersymmetric grand unified theories (GUT's) in warped higher-dimensional spacetime can lead to a stable Kaluza-Klein particle. This exotic particle has gauge quantum numbers of a right-handed neutrino, but carries fractional baryon-number and is related to the top quark within the higher-dimensional GUT. A combination of baryon-number and SU(3) color ensures its stability. Its relic density can easily be of the right value for masses in the 10 GeV--few TeV range. An exciting aspect of these models is that the entire parameter space will be tested at near future dark matter direct detection experiments. Other exotic GUT partners of the top quark are also light and can be produced at high energy colliders with distinctive signatures.Comment: 4 pages, 4 figures; v2: some comments added, figures updated; v3: Final version to appear in Phys. Rev. Let

ALP dark matter with non-periodic potentials: parametric resonance, halo formation and gravitational signatures

Axion-like particles (ALPs) are leading candidates to explain the dark matter in the universe. Their production via the misalignment mechanism has been extensively studied for cosine potentials characteristic of pseudo-Nambu-Goldstone bosons. In this work we investigate ALPs with non-periodic potentials, which allow for large misalignment of the field from the minimum. As a result, the ALP can match the relic density of dark matter in a large part of the parameter space. Such potentials give rise to self-interactions which can trigger an exponential growth of fluctuations in the ALP field via parametric resonance, leading to the fragmentation of the field. We study these effects with both Floquet analysis and lattice simulations. Using the Press-Schechter formalism, we predict the halo mass function and halo spectrum arising from ALP dark matter. These halos can be dense enough to produce observable gravitational effects such as astrometric lensing, diffraction of gravitational wave signals from black hole mergers, photometric microlensing of highly magnified stars, perturbations of stars in the galactic disk or stellar streams. These effects would provide a probe of dark matter even if it does not couple to the Standard Model. They would not be observable for halos predicted for standard cold dark matter and for ALP dark matter in the standard misalignment mechanism. We determine the relevant regions of parameter space in the (ALP mass, decay constant)-plane and compare predictions in different axion fragmentation models.Comment: 50 pages and 22 figures in the main text, and 15 pages and 2 figures in appendices, v2: As published in JCA

Gravitational signatures of ALP dark matter fragmentation

The misalignment mechanism for axion-like particles (ALPs) is a leading explanation for dark matter. In this work we investigate ALPs with non-periodic potentials, which allow for large misalignment of the field from the minimum and make it possible for ALPs to match the relic density of dark matter in a large part of the parameter space. Such potentials give rise to self-interactions which can trigger an exponential growth of fluctuations in the ALP field via parametric resonance, leading to the fragmentation of the field. The fluctuations later collapse to halos that can be dense enough to produce observable gravitational effects. These effects would provide a probe of dark matter even if it does not couple to the Standard Model (or too feebly). We determine the relevant regions of parameter space in the (ALP mass, decay constant)-plane and compare predictions in different axion fragmentation models. These proceedings are a short version of arXiv:2305.03756Comment: 6 pages, 5 figures. Contribution to the proceedings of EPS-HEP202