Multiple Axions Research Articles

Implications of protecting the QCD axion in the dual description

The QCD axion can be formulated in a dual description as a massive 2-form field. In this picture, the QCD axion quality problem translates into the question if there are additional 3-forms coupled to the axion other than the QCD 3-form that emerges at low energy. If such forms exist, the quality problem can be resolved via the introduction of other massive 2-forms (and thus corresponding axions), one for each additional 3-form. This can motivate an “axiverse from a high quality QCD axion”. In this work, we discuss this issue in the general case where the QCD axion couples to arbitrarily many 3-forms. Given the multiple axion solution, we discuss the phenomenological implications of the enhanced quality of the QCD axion in the dual description. These include sub-eV axion-like particle search through the axion-photon coupling, the cosmological consistency of a large decay constant QCD axion, and a model for the observed cosmic birefringence.

Axion Wind Detection with the Homogeneous Precession Domain of Superfluid Helium-3

Axions and axionlike particles may couple to nuclear spins like a weak oscillating effective magnetic field, the "axion wind." Existing proposals for detecting the axion wind sourced by dark matter exploit analogies to nuclear magnetic resonance (NMR) and aim to detect the small transverse field generated when the axion wind resonantly tips the precessing spins in a polarized sample of material. We describe a new proposal using the homogeneous precession domain of superfluid ^{3}He as the detection medium, where the effect of the axion wind is a small shift in the precession frequency of a large-amplitude NMR signal. We argue that this setup can provide broadband detection of multiple axion masses simultaneously and has competitive sensitivity to other axion wind experiments such as CASPEr-Wind at masses below 10^{-7} eV by exploiting precision frequency metrology in the readout stage.

Novel multilepton signatures of dark sectors in light meson decays

We point out kaon decays to multiple charged leptons as a novel probe of light dark particles $X$. Previously neglected channels, such as ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}(XX\ensuremath{\rightarrow}2({e}^{+}{e}^{\ensuremath{-}}))$, ${K}_{L}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}(XX\ensuremath{\rightarrow}2({e}^{+}{e}^{\ensuremath{-}}))$, and ${K}_{S}\ensuremath{\rightarrow}(XX\ensuremath{\rightarrow}2({e}^{+}{e}^{\ensuremath{-}}))$ may have very large rates, exceeding not only the Standard Model expectations but also possible backgrounds, such as Dalitz decays of neutral pions. We apply this idea to dark sector models where the production of dark Higgses or heavy neutral leptons leads to final states with several visible dark photons. We also investigate a recently proposed model of an MeV-scale QCD axion, where the rates for kaon decays to multiple axion states are large due to the nonlinear interactions of the axion with the light mesons. In addition, we point out new probes of this axion in pion decays, such as the single production of $a$ in ${\ensuremath{\pi}}^{+}\ensuremath{\rightarrow}\ensuremath{\nu}(({e}^{+}{)}^{*}\ensuremath{\rightarrow}{e}^{+}a\ensuremath{\rightarrow}{e}^{+}{e}^{+}{e}^{\ensuremath{-}})$, double production in pion capture ${\ensuremath{\pi}}^{\ensuremath{-}}+(p\text{ }\text{or}\text{ }\mathrm{D})\ensuremath{\rightarrow}aa+(n\text{ }\mathrm{or}\text{ }nn)\ensuremath{\rightarrow}\phantom{\rule{0ex}{0ex}}2({e}^{+}{e}^{\ensuremath{-}})+(n\text{ }\mathrm{or}\text{ }nn)$, as well as ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}aaa\ensuremath{\rightarrow}3({e}^{+}{e}^{\ensuremath{-}})$. The latter decay is fixed at $\mathcal{B}({\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}aaa)=1.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ for a 17 MeV axion.

Aligned natural inflation in the Large Volume Scenario

We embed natural inflation in an explict string theory model and derive observables in cosmology. We achieve this by compactifying the type IIB string on a Calabi-Yau orientifold, stabilizing moduli via the Large Volume Scenario, and configuring axions using D7-brane stacks. In order to obtain a large effective decay constant, we employ the Kim-Nilles-Peloso alignment mechanism, with the required multiple axions arising naturally from generically anisotropic bulk geometries. The bulk volumes, and hence the axion decay constants, are stabilized by generalized one-loop corrections and subject to various conditions: the Kähler cone condition on the string geometry; the convex hull condition of the weak gravity conjecture; and the constraint from the power spectrum of scalar perturbations. We find that all constraints can be satisfied in a geometry with relatively small volume and thus heavy bulk axion mass. We also covariantize the convex hull condition for the axion-dilaton-instanton system and verify the normalization of the extremal bound.

Galactic condensates composed of multiple axion species

Ultralight scalar dark matter has been proposed to constitute a component of dark matter, though the minimal scenarios have increasingly become constrained. In this work, we analyze scenarios where the dark matter consists of more than one ultralight boson, each with different masses. This potentially leads to formation of gravitationally-bound Bose-Einstein condensates with structures that are very different from condensates composed of a single scalar field. By generalizing from the well-understood single-flavor case, we explore a large range of input parameters, subject to stability criteria, and determine the allowed parameter space for two-flavor condensates as a function of particle physics parameters, paying particular attention to cases where such condensates could compose galactic cores. We also analyze single-flavor condensates subject to external gravity from massive inner bodies and find that such systems may mimic the size of galactic cores as well.

Relaxing the cosmological moduli problem by low-scale inflation

We show that the cosmological abundance of string axions is much smaller than naive estimates if the Hubble scale of inflation, Hinf , is sufficiently low (but can still be much higher than the axion masses) and if the inflation lasts sufficiently long. The reason is that the initial misalignment angles of the string axions follow the Bunch-Davies distribution peaked at the potential minima. As a result, the cosmological moduli problem induced by the string axions can be significantly relaxed by low-scale inflation, and astrophysical and cosmological bounds are satisfied over a wide range of the mass without any fine-tuning of the initial misalignment angles. Specifically, the axion with its decay constant fϕ = 1016 GeV satisfies the bounds over 10−18 eV ≲ mϕ ≲ 10 TeV for Hinf ≲ 10 keV-106 GeV. We also discuss cases with multiple axions and the QCD axion.

Phases of inflation

Motivated by the 4d effective field theories for closed string axions in Type II string compactifications with D-branes, we consider chiral gauge theories coupled to multiple axions. We discuss how well-known non-perturbative dynamical phenomena, such as gauge instantons, fermion confinement and Nambu-Jona-Lasinio interactions, give rise to non-trivial vacuum configurations in the IR. The fluctuations about the IR vacuum are captured by some remaining closed string axions and infladrons (scalar chiral condensate excitations), which acquire dynamical masses. By employing the full power of the effective field theory, we investigate the applicability of these IR theories as inflationary models (natural, monodromy, Starobinsky) and connect different types of inflationary scenarios to different phases of the non-Abelian gauge theory or the Nambu-Jona-Lasinio four-fermion couplings. The back-reaction of the infladrons flattens the axion potential in natural-like inflationary models, such that the tension with current CMB data with respect to the spectral index and the tensor-to-scalar ratio can be partially alleviated.

Multiple-axion framework

We provide a systematic framework for theories of multiple axions. We discover a novel type of "alignment" that renders even very complex theories analytically tractable. Theories with about 100 axions and random parameters have an exponential number of meta-stable vacua and accommodate a diverse range of inflationary observables. Very light fields can serve as dark matter with the correct abundance. Tunneling from a minimum with large vacuum energy can occur via a thin-wall instanton and be followed by a sufficient period of slow-roll inflation that ends in a vacuum containing axion dark matter and a cosmological constant with a value consistent with observation. Hence, this model can reproduce many macroscopic features of our universe without tuned parameters.

The photo-philic QCD axion

We propose a framework in which the QCD axion has an exponentially large coupling to photons, relying on the “clockwork” mechanism. We discuss the impact of present and future axion experiments on the parameter space of the model. In addition to the axion, the model predicts a large number of pseudoscalars which can be light and observable at the LHC. In the most favorable scenario, axion Dark Matter will give a signal in multiple axion detection experiments and the pseudo-scalars will be discovered at the LHC, allowing us to determine most of the parameters of the model.

Quality of the Peccei-Quinn symmetry in the aligned QCD axion and cosmological implications

We show that the required high quality of the Peccei-Quinn symmetry can be naturally explained in the aligned QCD axion models where the QCD axion arises from multiple axions with decay constants much smaller than the axion window, e.g., around the weak scale. Even in the presence of general Planck-suppressed Peccei-Quinn symmetry breaking operators, the effective strong CP phase remains sufficiently small in contrast to the standard axion models without the alignment. The QCD axion potential has small or large modulations due to the symmetry breaking operators, which can significantly affect the axion cosmology. When the axions are trapped in different minima, domain walls appear and their scaling behavior suppresses the axion isocurvature perturbations at super-horizon scales. Our scenario predicts many axions and saxions coupled to gluons, and they may be searched for at collider experiments. In particular, the recently found diphoton excess at 750 GeV could be due to one of such (s)axions.

The QCD axion from aligned axions and diphoton excess

We argue that the QCD axion can arise from many aligned axions with decay constants much smaller than the conventional axion window. If the typical decay constant is of {\cal O}{(100)} GeV to 1 TeV, one or more of the axions or saxions may account for the recently found diphoton excess at \sim 750 GeV. Our scenario predicts many axions and saxions coupled to gluons with decay constants of order the weak scale, and therefore many collider signatures by heavy axions and saxions will show up at different energy scales. In particular, if the inferred broad decay width is due to multiple axions or saxions, a non-trivial peak structure may become evident when more data is collected. We also discuss cosmological implications of the aligned QCD axion scenario. In the Appendix we give a possible UV completion and argue that the high quality of the Peccei-Quinn symmetry is naturally explained in our scenario.

Large-field inflation with multiple axions and the weak gravity conjecture

In this note, we discuss the implications of the weak gravity conjecture (WGC) for general models of large-field inflation with a large number of axions $N$. We first show that, from the bottom-up perspective, such models admit a variety of different regimes for the enhancement of the effective axion decay constant, depending on the amount of alignment and the number of instanton terms that contribute to the scalar potential. This includes regimes of no enhancement, power-law enhancement and exponential enhancement with respect to $N$. As special cases, we recover the Pythagorean enhancement of $N$-flation, the $N$ and $N^{3/2}$ enhancements derived by Bachlechner, Long and McAllister and the exponential enhancement by Choi, Kim and Yun. We then analyze which top-down constraints are put on such models from the requirement of consistency with quantum gravity. In particular, the WGC appears to imply that the enhancement of the effective axion decay constant must not grow parametrically with $N$ for $N \gg 1$. On the other hand, recent works proposed that axions might be able to violate this bound under certain circumstances. Our general expression for the enhancement allows us to translate this possibility into a condition on the number of instantons that couple to the axions. We argue that, at large $N$, models consistent with quantum gravity must either allow super-Planckian field excursions or have an enormous, possibly even exponentially large, number of dominant instanton terms in the scalar potential.

Axionic band structure of the cosmological constant

We argue that theories with multiple axions generically contain a large number of vacua that can account for the smallness of the cosmological constant. In a theory with N axions, the dominant instantons with charges Q determine the discrete symmetry of vacua. Subleading instantons break the leading periodicity and lift the vacuum degeneracy. For generic integer charges the number of distinct vacua is given by |det(Q)|~exp(N). Our construction motivates the existence of a landscape with a vast number of vacua in a large class of four-dimensional effective theories.

Realizing the relaxion from multiple axions and its UV completion with high scale supersymmetry

We discuss a scheme to implement the relaxion solution to the hierarchy problem with multiple axions, and present a UV-completed model realizing the scheme. All of the $N$ axions in our model are periodic with a similar decay constant $f$ well below the Planck scale. In the limit $N\gg 1$, the relaxion $\phi$ corresponds to an exponentially long multi-helical flat direction which is shaped by a series of mass mixing between nearby axions in the compact field space of $N$ axions. With the length of flat direction given by $\Delta \phi =2\pi f_{\rm eff} \sim e^{\xi N} f$ for $\xi={\cal O}(1)$, both the scalar potential driving the evolution of $\phi$ during the inflationary epoch and the $\phi$-dependent Higgs boson mass vary with an exponentially large periodicity of ${\cal O}(f_{\rm eff})$, while the back reaction potential stabilizing the relaxion has a periodicity of ${\cal O}( f)$. A natural UV completion of our scheme can be found in high scale or (mini) split supersymmetry (SUSY) scenario with the axion scales generated by SUSY breaking as $f\sim \sqrt{m_{\rm SUSY}M_*}$, where the soft SUSY breaking scalar mass $m_{\rm SUSY}$ can be well above the weak scale, and the fundamental scale $M_*$ can be identified as the Planck scale or the GUT scale.

Fencing in the swampland: quantum gravity constraints on large field inflation

In this note we show that models of natural inflation based on closed string axions are incompatible with the weak gravity conjecture (WGC). Specifically, we use T- duality in order to map the bounds on the charge-to-mass ratio of particles imposed by the WGC, to constraints on the ratio between instanton actions and axion decay constants. We use this connection to prove that if the WGC holds, even when multiple axions are present and mix with each other, one cannot have large axion decay constants while remaining in a regime of perturbative control. We also discuss the extension of the WGC to discrete symmetries and its possible impact on models with axion monodromy, and the distinction between the strong and mild versions of the WGC. We argue that, if the strong version is violated, the constraints on large field inflation can be evaded while still satisfying the mild one. Finally, we offer some speculations regarding the import of these results to the general theory of inflation.

Special points of inflation in flux compactifications

We study the realization of axion inflation models in the complex structure moduli spaces of Calabi–Yau threefolds and fourfolds. The axions arise close to special points of these moduli spaces that admit discrete monodromy symmetries of infinite order. Examples include the large complex structure point and conifold point, but can be of more general nature. In Type IIB and F-theory compactifications the geometric axions receive a scalar potential from a flux-induced superpotential. We find toy variants of various inflationary potentials including the ones for natural inflation of one or multiple axions, or axion monodromy inflation with polynomial potential. Interesting examples are also given by mirror geometries of torus fibrations with Mordell–Weil group of rank N−1 or an N-section, which admit an axion if N>3.

Axion landscape and natural inflation

Multiple axions form a landscape in the presence of various shift symmetry breaking terms. Eternal inflation populates the axion landscape, continuously creating new universes by bubble nucleation. Slow-roll inflation takes place after the tunneling event, if a very flat direction with a super-Planckian decay constant arises due to the alignment mechanism. We study the vacuum structure as well as possible inflationary dynamics in the axion landscape scenario, and find that the inflaton dynamics is given by either natural or multi-natural inflation. In the limit of large decay constant, it is approximated by the quadratic chaotic inflation, which however is disfavored if there is a pressure toward shorter duration of inflation. Therefore, if the spectral index and the tensor-to-scalar ratio turn out to be different from the quadratic chaotic inflation, there might be observable traces of the bubble nucleation. Also, the existence of small modulations to the inflaton potential is a common feature in the axion landscape, which generates a sizable and almost constant running of the scalar spectral index over CMB scales. Non-Gaussianity of equilateral type can also be generated if some of the axions are coupled to massless gauge fields.

Natural inflation with multiple sub-Planckian axions

We extend the Kim-Nilles-Peloso (KNP) alignment mechanism for natural inflation to models with $N>2$ axions, which obtains super-Planckian effective axion decay constant ${f}_{\text{eff}}\ensuremath{\gg}{M}_{\mathrm{Pl}}$ through an alignment of the anomaly coefficients of multiple axions having sub-Planckian fundamental decay constants ${f}_{0}\ensuremath{\ll}{M}_{\mathrm{Pl}}$. The original version of the KNP mechanism realized with two axions requires that some of the anomaly coefficients should be of the order of ${f}_{\text{eff}}/{f}_{0}$, which would be uncomfortably large if ${f}_{\text{eff}}/{f}_{0}\ensuremath{\gtrsim}\mathcal{O}(100)$ as suggested by the recent BICEP2 results. We note that the KNP mechanism can be realized with the anomaly coefficients of $\mathcal{O}(1)$ if the number of axions $N$ is large as $N\mathrm{ln}N\ensuremath{\gtrsim}2\mathrm{ln}({f}_{\text{eff}}/{f}_{0})$, in which case the effective decay constant can be enhanced as ${f}_{\text{eff}}/{f}_{0}\ensuremath{\sim}\sqrt{N!}{n}^{N\ensuremath{-}1}$ for $n$ denoting the typical size of the integer-valued anomaly coefficients. Comparing to the other multiple axion scenario, the $N$-flation scenario which requires $N\ensuremath{\sim}{f}_{\text{eff}}^{2}/{f}_{0}^{2}$, the KNP mechanism has a virtue of not invoking to a too large number of axions, although it requires a specific alignment of the anomaly coefficients, which can be achieved with a probability of $\mathcal{O}({f}_{0}/{f}_{\text{eff}})$ under a random choice of the anomaly coefficients. We also present a simple model realizing a multiple axion monodromy along the inflaton direction.

Aligned natural inflation in string theory

The authors discuss type IIB string theory realizations of Kim-Nilles-Peloso (KNP) multiple axion inflation, which provides a super-Planckian effective axion decay constant, necessary for UV stable realistic slow roll inflation.

Non-Gaussianities in multi-field inflation

We compute the amplitude of the non-Gaussianities in inflationary models with multiple,uncoupled scalar fields. This calculation thus applies to all models of assisted inflation,including N-flation, where inflation is driven by multiple axion fields arising from shiftsymmetries in a flux stabilized string vacuum. The non-Gaussianities are associated withnonlinear evolution of the field (and density) perturbations, characterized by the parameterfNL. We derive a general expression for the nonlinear parameter, incorporating the evolution ofperturbations after horizon-crossing. This is valid for arbitrary separable potentialsduring slow roll. To develop an intuitive understanding of this system and todemonstrate the applicability of the formalism we examine several cases with quadraticpotentials: two-field models with a wide range of mass ratios, and a general -field model with a narrow mass spectrum. We uncover thatfNL is suppressed as the number of e-foldings grows, and that this suppression is increased inmodels with a broad spectrum of masses. On the other hand, we find no enhancement tofNL that increases with the number of fields. We thus conclude that the production of a largenon-Gaussian signal in multi-field models of inflation is very unlikely as long as fields areslowly rolling and potentials are of simple, quadratic form. Finally, we compute anexpression for the scalar spectral index that incorporates the nonlinear corrections to thefields’ evolution.