Axion inflation represents an intriguing source of gravitational waves (GWs) from the early Universe. In a companion paper [1], 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, ∆$\textit{N}$ . 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 ∆$\textit{N}$ . 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.

Germany

Richard Eckardstein

Japan

Kai Schmitz

Ukraine

Oleksandr Sobol

Gravitational waves from axion inflation in the gradient expansion formalism. Part II. Fermionic 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 ∆$\textit{N}$ , 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.

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

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 <math altimg='si14.svg'><msub><mi>M</mi><mi>N</mi></msub></math> is subject to the Davidson&#8211;Ibarra bound, <math altimg='si15.svg'><mrow><msub><mi>M</mi><mi>N</mi></msub><mo>&#8819;</mo><msup><mn>10</mn><mn>9</mn></msup><mspace width='0.16em' /><mrow><mi mathvariant='normal'>GeV</mi></mrow></mrow></math>, which builds on the assumption that RHN decays are responsible for the violation of both charge-parity invariance ( <math altimg='si16.svg'><mrow><mi>C</mi><mi>P</mi></mrow></math>) and baryon-minus-lepton number ( <math altimg='si17.svg'><mrow><mi>B</mi><mspace width='-0.16em' /><mo linebreak='goodbreak'>&#8722;</mo><mspace width='-0.16em' /><mi>L</mi></mrow></math>). In this paper, we relax this assumption in the context of the more flexible framework of wash-in leptogenesis, in which <math altimg='si16.svg'><mrow><mi>C</mi><mi>P</mi></mrow></math> violation is encoded in the initial conditions and the only remaining task of the RHN decays is to violate <math altimg='si17.svg'><mrow><mi>B</mi><mspace width='-0.16em' /><mo linebreak='goodbreak'>&#8722;</mo><mspace width='-0.16em' /><mi>L</mi></mrow></math>. Solving the relevant set of Boltzmann equations for vanishing initial baryon and lepton numbers (i.e., <math altimg='si18.svg'><mrow><mi>B</mi><mo linebreak='goodbreak'>=</mo><msub><mi>L</mi><mi>e</mi></msub><mo linebreak='goodbreak'>=</mo><msub><mi>L</mi><mi>&#956;</mi></msub><mo linebreak='goodbreak'>=</mo><msub><mi>L</mi><mi>&#964;</mi></msub><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math> 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.

Martin A. Mojahed

Dominik Wilken

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

<p>Wash-in leptogenesis is an attractive mechanism to produce the baryon asymmetry of the Universe. It treats right-handed-neutrino interactions as spectator processes, on the same footing as electroweak sphalerons, that reprocess primordial charge asymmetries in the thermal plasma into a baryon-minus-lepton asymmetry. The origin of these primordial charges must be accounted for by new <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating dynamics at very high energies. In this paper, we propose such a scenario of chargegenesis that, unlike earlier proposals, primarily relies on new interactions in the gravitational sector. We point out that a coupling of a conserved current to the divergence of the Ricci scalar during reheating can lead to nonzero effective chemical potentials in the plasma that, together with a suitable charge-violating interaction, can result in the production of a primordial charge asymmetry. Gravitational chargegenesis represents a substantial generalization of the idea of gravitational baryogenesis. We provide a detailed analysis of a generic and minimal realization that is consistent with inflation and show that it can successfully explain the baryon asymmetry of the Universe.</p>

China

Xun-Jie Xu

Gravitational charge production

Pair-creation of charged particles in a strong gauge-field background — the renowned Schwinger effect — can strongly alter the efficiency of gauge-field production during axion inflation. It is therefore crucial to have a clear understanding and proper description of this phenomenon to obtain reliable predictions for the physical observables in this model. In the present work, we revisit the problem of Schwinger pair production during axion inflation in the presence of both electric and magnetic fields and improve on the state of the art in two ways: (i) taking into account that the electric- and magnetic-field three-vectors are in general not collinear, we derive the vector decomposition of the Schwinger-induced current in terms of these fields and determine the corresponding effective electric and magnetic conductivities; (ii) by identifying the physical momentum scale associated with the pair-creation process, we incorporate Schwinger damping of the gauge field in a scale-dependent fashion in the relevant equations of motion. Implementing this new description in the framework of the gradient-expansion formalism, we obtain numerical results in a benchmark scenario of axion inflation and perform a comprehensive comparison with earlier results in the literature. In some cases, the resulting energy densities of the produced gauge fields differ from the old results by more than one order of magnitude, which reflects the importance of taking the new effects into account.

On the Schwinger effect during axion inflation

Wash-in leptogenesis is a powerful mechanism to generate the baryon asymmetry of the Universe that treats right-handed-neutrino interactions on the same footing as electroweak sphaleron processes: as mere spectator processes acting on the background of chemical potentials in the Standard Model plasma. Successful wash-in leptogenesis requires this chemical background to be CP-violating, which can be achieved by violating any of the more than ten global charges that are conserved in the Standard Model at very high temperatures. In this paper, we demonstrate that the primordial charge asymmetries required for wash-in leptogenesis can be readily produced by evaporating primordial black holes (PBHs). Our argument is based on the fact that the Hawking radiation emitted by PBHs contains more or less any state in the particle spectrum. Therefore, if heavy states with CP-violating decays are present in the ultraviolet, PBH evaporation will unavoidably lead to the production of these states. We illustrate this scenario by means of a simple toy model where PBH evaporation leads to the production of heavy particles that we call asymmetrons and whose decay results in a primordial charge asymmetry for right-handed electrons, which in turn sets the initial conditions for wash-in leptogenesis. We focus on the parameter region where the decay of the initial thermal asymmetron abundance occurs long before PBH evaporation and only results in a negligible primordial charge asymmetry. PBH evaporation at later times then serves as a mechanism to resurrect the asymmetron abundance and ensure the successful generation of the baryon asymmetry after all. We conclude that PBHs can act as asymmetry-producing machines that grant access to whatever CP-violating physics may be present in the ultraviolet, rekindling it at lower energies where it can be reprocessed into a baryon asymmetry by right-handed neutrinos.

Wash-in leptogenesis after the evaporation of primordial black holes

Axion inflation coupled to Abelian gauge fields via a Chern-Simons-like term of the form   <math> <mi>ϕF</mi> <mover> <mi>F</mi> <mo>~</mo> </mover> </math>  $$ \phi F\overset{\sim }{F} $$  represents an attractive inflationary model with a rich phenomenology, including the production of magnetic fields, black holes, gravitational waves, and the matter-antimatter asymmetry. In this work, we focus on a particular regime of axion inflation, the so-called Anber-Sorbo (AS) solution, in which the energy loss in the gauge-field production provides the dominant source of friction for the inflaton motion. We revisit the AS solution and confirm that it is unstable. Contrary to earlier numerical works that attempted to reach the AS solution starting from a regime of weak backreaction, we perform, for the first time, a numerical evolution starting directly from the regime of strong backreaction. Our analysis strongly suggests that, at least as long as one neglects spatial inhomogeneities in the inflaton field, the AS solution has no basin of attraction, not even a very small one that might have been missed in previous numerical studies. Our analysis employs an arsenal of analytical and numerical techniques, some established and some newly introduced, including (1) linear perturbation theory along the lines of ref. [1], (2) the gradient expansion formalism (GEF) developed in ref. [2], (3) a new linearized version of the GEF, and (4) the standard mode-by-mode approach in momentum space in combination with input from the GEF. All these methods yield consistent results confirming the instability of the AS solution, which renders the dynamics of axion inflation in the strong-backreaction regime even more interesting than previously believed.

Italy

Marco Peloso

United States

Lorenzo Sorbo

Axion inflation in the strong-backreaction regime: decay of the Anber-Sorbo solution

We study the evolution of magnetic fields coupled with chiral fermion asymmetry in the framework of chiral magnetohydrodynamics with zero initial total chirality. The initial magnetic field has a turbulent spectrum peaking at a certain characteristic scale and is fully helical with positive helicity. The initial chiral chemical potential is spatially uniform and negative. We consider two opposite cases where the ratio of the length scale of the chiral plasma instability (CPI) to the characteristic scale of the turbulence is smaller and larger than unity. These initial conditions might be realized in cosmological models, including certain types of axion inflation. The magnetic field and chiral chemical potential evolve with inverse cascading in such a way that the magnetic helicity and chirality cancel each other at all times, provided there is no spin flipping. The CPI timescale is found to determine mainly the time when the magnetic helicity spectrum attains negative values at high wave numbers. The turnover time of the energy-carrying eddies, on the other hand, determines the time when the peak of the spectrum starts to shift to smaller wave numbers via an inverse cascade. The onset of helicity decay is determined by the time when the chiral magnetic effect becomes efficient at the peak of the initial magnetic energy spectrum, provided the CPI does not grow much. When spin flipping is important, the chiral chemical potential vanishes at late times and the magnetic helicity becomes constant, which leads to a faster increase of the correlation length. This is in agreement with what is expected from magnetic helicity conservation and also happens when the initial total chirality is imbalanced. Our findings have important implications for baryogenesis after axion inflation.

Sweden

Georgia

Axel Brandenburg

Kohei Kamada

Kyohei Mukaida

Switzerland

Jennifer Schober

Chiral magnetohydrodynamics with zero total chirality

A chiral chemical potential present in the early Universe can source helical hypermagnetic fields through the chiral plasma instability. If these hypermagnetic fields survive until the electroweak phase transition, they source a contribution to the baryon asymmetry of the Universe. In this Letter, we demonstrate that lepton flavor asymmetries above <math><mo>|</mo><mi>μ</mi><mo>|</mo><mo>/</mo><mi>T</mi><mo>∼</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> trigger this mechanism even for vanishing total lepton number. This excludes the possibility of such large lepton flavor asymmetries present at temperatures above <math><mrow><msup><mrow><mn>10</mn></mrow><mrow><mn>6</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>, setting a constraint which is about 2 orders of magnitude stronger than the current CMB and BBN limits.

CERN

Valerie Domcke

Masaki Yamada

New Constraint on Primordial Lepton Flavor Asymmetries

We study the impact of sphaleron-induced thermal friction on the axion dark-matter abundance due to the interaction of an axion-like particle (ALP) with a dark non-abelian gauge sector in a secluded thermal bath. Thermal friction can either enhance the axion relic density by delaying the onset of oscillations or suppress it by damping them. We derive an analytical formula for the frictional adiabatic invariant, which remains constant along the axion evolution and which allows us to compute the axion relic density in a general set-up. Even in the most minimal scenario, in which a single gauge group is responsible for both the generation of the ALP mass and the friction force, we find that the resulting dark-matter abundance from the misalignment mechanism deviates from the standard scenario for axion masses m  a  ≳ 100 eV. We also generalize our analysis to the case where the gauge field that induces friction and the gauge sector responsible for the ALP mass are distinct and their couplings to the axion have a large hierarchy as can be justified by means of alignment or clockwork scenarios. We find that it is easy to open up the ALP parameter space where the resulting axion abundance matches the observed dark-matter relic density both in the traditionally over- and underabundant regimes. This conclusion also holds for the QCD axion.