Axion Potential Research Articles

The QCD axion at finite density

We show how the properties of the QCD axion change in systems at finite baryonic density, such as neutron stars. At nuclear saturation densities, where corrections can be reliably computed, we find a mild reduction of the axion mass and up to an order of magnitude enhancement in the model-independent axion coupling to neutrons. At moderately higher densities, if realized, meson (kaon) condensation can trigger axion condensation. We also study the axion potential at asymptotically large densities, where the color-superconducting phase of QCD potentially leads to axion condensation, and the mass of the axion is generically several orders of magnitude smaller than in vacuum due to the suppressed instantons. Several phenomenological consequences of the axion being sourced by neutron stars are discussed, such as its contribution to their total mass, the presence of an axionic brane, or axion-photon conversion in the magnetosphere.

Bifurcations of a soliton model of dark matter towards natural inflation

Axion-like scalar fields with a periodic potential provide a solitonic model of dark matter halos of galaxies. Here we point out that their stability analysis bridges over, via bifurcations, to natural inflation. Then the (pseudo-) scalar part of the Lagrangian can be mapped into a gravity model mildly nonlinear in the scalar curvature. In the case of an axionic periodic potential, the equivalent Lagrangian L(R) exhibits a combination of swallow tail cusps with transitions of stability, well-known from catastrophe theory. The resulting almost Einsteinian branches indicate a ‘unification’ of dark matter, dark energy and inflation.

QCD \u03b8-vacuum energy and axion properties

At low energies, the strong interaction is governed by the Goldstone bosons associated with the spontaneous chiral symmetry breaking, which can be systematically described by chiral perturbation theory. In this paper, we apply this theory to study the θ-vacuum energy density and hence the QCD axion potential up to next-to-leading order with N non-degenerate quark masses. By setting N = 3, we then derive the axion mass, self-coupling, topological susceptibility and the normalized fourth cumulant both analytically and numerically, taking the strong isospin breaking effects into account. In addition, the model-independent part of the axion-photon coupling, which is important for axion search experiments, is also extracted from the chiral Lagrangian supplemented with the anomalous terms up to mathcal{O}left({p}^6right) .

Probing the weak gravity conjecture in the cosmic microwave background

The weak gravity conjecture imposes severe constraints on natural inflation. A trans-Planckian axion decay constant can only be realized if the potential exhibits an additional (subdominant) modulation with sub-Planckian periodicity. The resulting wiggles in the axion potential generate a characteristic modulation in the scalar power spectrum of inflation which is logarithmic in the angular scale. The compatibility of this modulation is tested against the most recent Cosmic Microwave Background (CMB) data by Planck and BICEP/Keck. Intriguingly, we find that the modulation completely resolves the tension of natural inflation with the CMB. A Bayesian model comparison reveals that natural inflation with modulations describes all existing data equally well as the cosmological standard model $\Lambda$CDM. In addition, the bound of a tensor-to-scalar ratio r > 0.002 correlated with a striking small-scale suppression of the scalar power spectrum occurs. Future CMB experiments could directly probe the modulation through their improved sensitivity to smaller angular scales and possibly the measurement of spectral distortions. They could, thus, verify a key prediction of the weak gravity conjecture and provide dramatic new insights into the theory of quantum gravity.

Constraints on ultralight axions from compact binary systems

Ultra light particles $(m_a \sim 10^{-21}eV-10^{-22}eV)$ with axion-like couplings to other particles can be candidates for fuzzy dark matter (FDM) if the axion decay constant $f_a\sim 10^{17}GeV$. If a compact star is immersed in such a low mass axionic potential it develops a long range field outside the star. This axionic field is radiated away when the star is in a binary orbit. The orbital period of a compact binary decays mainly due to the gravitational wave radiation, which was confirmed first in the Hulse-Taylor binary pulsar. The orbital period can also decay by radiation of other light particles like axions and axion like particles(ALPs). For axionic radiation to take place, the orbital frequency of the periodic motion of the binary system should be greater than the mass of the scalar particle which can be radiated. This implies that, for most of the observed binaries, particles with mass $m_a< 10^{-19}eV$ can be radiated, which includes FDM particles. In this paper, we consider four compact binary systems: PSR J0348+0432, PSR J0737-3039, PSR J1738+0333, and PSR B1913+16 (Hulse Taylor Binary) and show that the observations of the decay in orbital period put the bound on axion decay constant, $f_a\lesssim \mathcal{O}(10^{11}GeV)$. This implies that Fuzzy Dark Matter cannot couple to gluons.

Real-time dynamics of axion particle production due to spontaneous decay of a coherent axion field

We show that the coherent axion field spontaneously decays by emitting axion particles via quantum tunneling if axion potential has more than one minimum. By employing the $\hbar$-expansion and mean field approximation, we develop a formalism to trace the real-time dynamics of the axion particle production including its backreaction to the coherent axion field. We also present numerical results for the time evolution of various physical quantities including the strength of the coherent axion field, phase-space density of produced axion particles, energy density, and pressure. Phenomenological implications of our results are also discussed.

Dynamical axion misalignment with small instantons

We present a new mechanism to relax the initial misalignment angle of the QCD axion and raise the cosmological bound on the axion decay constant. The QCD axion receives a contribution from small UV instantons during inflation, which raises its mass to the inflationary Hubble scale. This makes the axion start rolling down its potential early on. In the scenario, the standard model Yukawa couplings of quarks are dynamical, being of order one during the inflationary era and reducing to their standard model values once it ends. This means that after inflation the contribution of the small instantons is suppressed, and the axion potential reduces to the standard one from the usual IR instantons. As a result, when the axion starts to oscillate again after inflation, the initial misalignment angle is suppressed due to the dynamics during inflation. While the general idea of dynamical axion misalignment has been discussed in the literature before, we present in detail the major bottleneck on the mismatching between the minima of the axion potentials during and after inflation, and how it is circumvented in our scenario via the Froggatt-Nielsen mechanism. Taking into account of all the constraints, we find that the axion decay constant could be raised to the GUT scale, 1015 GeV, in our scenario.

Gravitational waves induced from string axion model of inflation

We study the production of gravitational waves from primordial scalar perturbations in a string axion inflationary model with subleading nonperturbative corrections. In such a model, the subleading nonperturbative effects can superimpose steep cliffs and gentle plateaus onto the leading axion potential. Such an inflationary potential both matches the Planck observations at CMB scales and gives rise to an enhancement in the scalar power spectrum at small scales. We calculate the second-order gravitational wave signatures induced by the scalar density perturbations, and find that the signal can be detected by the space-based laser interferometers in the future.

Irrational monodromies of vacuum energy

We present a theory with axion flux monodromies coupled to gravity, that reduces to the local vacuum energy sequester below the axion mass scales. If the axion potentials include a term generated by nonperturbative couplings to gauge sectors, with a decay constant incommensurate with monodromy periods, the low energy potential germinates a landscape of irrational axion vacua, with arbitrarily small cosmological constants. The sensitivity of the values of cosmological constants to unknown UV physics can be greatly reduced. The variation of the cosmological constant in each vacuum, from one order in perturbation theory to the next, can be much smaller than the naïve cut­off. The nonperturbative transitions in the early universe between the vacua populate this landscape, similar to the case of irrational axion. In such a landscape of vacua a small cosmological constant can naturally emerge.

Axion hilltops, Kahler modulus quintessence and the swampland criteria

We study the interplay among extrema of axion potentials, Kahler moduli stabilization and the swampland criteria. We argue that moving away from the minima of nonperturbatively generated axion potentials can lead to a runaway behavior of moduli that govern the couplings in the effective field theory. The proper inclusion of these degrees of freedom resolves the conflict between periodic axion potentials and the gradient de Sitter criterion, without the need to invoke the refined de Sitter criterion. We investigate the possibility of including this runaway direction as a model of quintessence that satisfies the swampland criteria. Using a single nonperturbative effect, the maximum along the axion direction provides such a runaway direction, which is unstable in the axion directions, sensitive to initial conditions and too steep to allow for a Hubble time of expansion without violating the field excursion criterion. Adding a second nonperturbative effect generates a saddle point in the potential satisfying the refined de Sitter criterion, which solves the steepness problem and improves the initial conditions problem although some fine-tuning remains required.

Gauge and gravitational instantons: from 3-forms and fermions to weak gravity and flat axion potentials

We investigate the role of gauge and gravitational instantons in the context of the Swampland program. Our focus is on the global symmetry breaking they induce, especially in the presence of fermions. We first recall and make more precise the description of the dilute instanton gas through a 3-form gauge theory. In this language, the familiar suppression of instanton effects by light fermions can be understood as the decoupling of the 3-form. Even if all fermions remain massive, such decoupling may occur on the basis of an explicitly unbroken but anomalous global symmetry in the fermionic sector. This should be forbidden by quantum gravity, which leads us to conjecture a related, cutoff-dependent lower bound on the induced axion potential. Finally, we note that the gravitational counterpart of the above are K3 instantons. These are small fluctuations of Euclidean spacetime with K3 topology, which induce fermionic operators analogous to the ’t Hooft vertex in gauge theories. Although Planck-suppressed, they may be phenomenologically relevant if accompanied by other higher-dimension fermion operators or if the K3 carries appropriate gauge fluxes.

A Strong Scalar Weak Gravity Conjecture and some implications

We propose a new version of the scalar Weak Gravity Conjecture (WGC) which would apply to any scalar field coupled to quantum gravity. For a single scalar it is given by the differential constraint (V″)2 ≤ (2V‴2 − V″V′′′′) {M}_{mathrm{p}}^2 , where V is the scalar potential. It corresponds to the statement that self-interactions of a scalar must be stronger than gravity for any value of the scalar field. We find that the solutions which saturate the bound correspond to towers of extremal states with mass {m}^2left(phi right)={m}_0^2/left({left(R/mright)}^2+1/{(nR)}^2right) , with R2 = eϕ, consistent with the emergence of an extra dimension at large or small R and the existence of extended objects (strings). These states act as WGC states for the scalar ϕ. It is also consistent with the distance swampland conjecture with a built-in duality symmetry. All of this is remarkable since neither extra dimensions nor string theory are put in the theory from the beginning, but they emerge. This is quite analogous to how the 11-th dimension appears in M-theory from towers of Type IIA solitonic D0-branes. From this constraint one can derive several swampland conjectures from a single principle. In particular one finds that an axion potential is only consistent if f ≤ Mp, recovering a result already conjectured from other arguments. The conjecture has far reaching consequences and applies to several interesting physical systems: i) Among chaotic inflation potentials only those asymptotically linear may survive. ii) If applied to the radion of the circle compactification of the Standard Model to 3D with Dirac neutrinos, the constraint implies that the 4D cosmological constant scale must be larger than the mass of the lightest neutrino, which must be in normal hierarchy. It also puts a constraint on the EW scale, potentially explaining the hierarchy problem. This recovers and improves results already obtained by applying the AdS swampland conjecture, but in a way which is independent from UV physics. iii) It also constraints simplest moduli fixing string models. The simplest KKLT model is compatible with the constraints but the latter may be relevant for some choices of parameters.

Tensor spectra templates for axion-gauge fields dynamics during inflation

SU(2) gauge fields can generate large gravitational waves during inflation, if they are coupled to an axion which can be either the inflaton or a spectator field. The shape of the produced tensor power spectrum \U0001d4abh depends on the form of the axion potential. We derive analytic expressions and provide general templates for \U0001d4abh for various types of the spectator axion potential. Furthermore, we explore the detectability of the oscillatory feature, which is present in \U0001d4abh in the case of an axion monodromy model, by possible future CMB B-mode polarization observations.

Deformation of axion potentials: Implications for spontaneous baryogenesis, dark matter, and isocurvature perturbations

We show that both the baryon asymmetry of the universe and dark matter (DM) can be accounted for by the dynamics of a single axion-like field. In this scenario, the observed baryon asymmetry is produced through spontaneous baryogenesis---driven by the early evolution of the axion---while its late-time coherent oscillations explain the observed DM abundance. Typically, spontaneous baryogenesis via axions is only successful in regions of parameter space where the axion is relatively heavy, rendering it highly unstable and unfit as a dark matter candidate. However, we show that a field-dependent wavefunction renormalization can arise which effectively "deforms" the axion potential, allowing for efficient generation of baryon asymmetry while maintaining a light and stable axion. Meanwhile, such deformations of the potential induce non-trivial axion dynamics, including a tracking behavior during its intermediate phase of evolution. This attractor-like dynamics dramatically reduces the sensitivity of the axion relic abundance to initial conditions and naturally suppresses DM isocurvature perturbations. Finally, we construct an explicit model realization, using a continuum-clockwork axion, and survey the details of its phenomenological viability.

Landscape tomography through primordial non-Gaussianity

In this paper, we show how the structure of the landscape potential of the primordial Universe may be probed through the properties of the primordial density perturbations responsible for the origin of the cosmic microwave background anisotropies and the large-scale structure of our Universe. Isocurvature fields -fields orthogonal to the inflationary trajectory- may have fluctuated across the barriers separating local minima of the landscape potential during inflation. We analyze how this process could have impacted the evolution of the primordial curvature perturbations. If the typical distance separating consecutive minima of the landscape potential and the height of the potential barriers are smaller than the Hubble expansion rate parametrizing inflation, the probability distribution function of isocurvature fields becomes non-Gaussian due to the appearance of bumps and dips associated to the structure of the potential. We show that this non-Gaussianity can be transferred to the statistics of primordial curvature perturbations if the isocurvature fields are coupled to the curvature perturbations. The type of non-Gaussian structure that emerges in the distribution of curvature perturbations cannot be fully probed with the standard methods of polyspectra; instead, the probability distribution function is needed. The latter is obtained by summing all the $n$-point correlation functions. To substantiate our claims, we offer a concrete model consisting of an axionlike isocurvature perturbation with a sinusoidal potential and a linear derivative coupling between the isocurvature and curvature fields. In this model, the probability distribution function of the curvature perturbations consists of a Gaussian function with small superimposed oscillations reflecting the isocurvature axion potential.

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.

Implications of Dilaton Couplings on the Axion Potential

In particle physics and cosmology, the dilaton is an hypothetical scalar field which can explain many physical phenomena. In this framework, we investigate an extended lagrangian of QCD which involves dilatonic degrees of freedom. Our approach is based on the relationship between the massive dilaton and the nonperturbative effects of QCD. We derive a general axion potential involving the dilaton properties and vacuum condensates.

Mechanisms for primordial black hole production in string theory

We consider mechanisms for producing a significant population of primordial black holes (PBHs) within string inspired single field models of inflation. The production of PBHs requires a large amplification in the power spectrum of curvature perturbations between scales associated with CMB and PBH formation. In principle, this can be achieved by temporarily breaking the slow-roll conditions during inflation. In this work, we identify two string setups that can realise this process. In string axion models of inflation, subleading non-perturbative effects can superimpose steep cliffs and gentle plateaus onto the leading axion potential. The cliffs can momentarily violate the slow-roll conditions, and the plateaus can lead to phases of ultra slow-roll inflation. We thus achieve a string motivated model which both matches the Planck observations at CMB scales and produces a population of light PBHs, which can account for an order one fraction of dark matter. In DBI models of inflation, a sharp increase in the speed of sound sourced by a steep downward step in the warp factor can drive the amplification. In this scenario, discovery of PBHs could indicate non-trivial dynamics in the bulk, such as flux-antibrane annihilation at the tip of a warped throat.

Probing axions with neutron star inspirals and other stellar processes

In certain models of a QCD axion, finite density corrections to the axion potential can result in the axion being sourced by large dense objects. There are a variety of ways to test this phenomenon, but perhaps the most surprising effect is that the axion can mediate forces between neutron stars that can be as strong as gravity. These forces can be attractive or repulsive and their presence can be detected by Advanced LIGO observations of neutron star inspirals. By a numerical coincidence, axion forces between neutron stars with gravitational strength naturally have an associated length scale of tens of kilometers or longer, similar to that of a neutron star. Future observations of neutron star mergers in Advanced LIGO can probe many orders of magnitude of axion parameter space. Because the axion is only sourced by large dense objects, the axion force evades fifth force constraints. We also outline several other ways to probe this phenomenon using electromagnetic signals associated with compact objects.

Universality of multi-field α-attractors

We study a particular version of the theory of cosmological α-attractors with α=1/3, in which both the dilaton (inflaton) field and the axion field are light during inflation. The kinetic terms in this theory originate from maximal \U0001d4a9=4 superconformal symmetry and from maximal \U0001d4a9=8 supergravity. We show that because of the underlying hyperbolic geometry of the moduli space in this theory, it exhibits double attractor behavior: their cosmological predictions are stable not only with respect to significant modifications of the dilaton potential, but also with respect to significant modifications of the axion potential: ns≃1−2/N, r≃4/N2. We also show that the universality of predictions extends to other values of α ≲ \U0001d4aa(1) with general two-field potentials that may or may not have an embedding in supergravity. Our results support the idea that inflation involving multiple, not stabilized, light fields on a hyperbolic manifold may be compatible with current observational constraints for a broad class of potentials.