String theory generically predicts the coupling between the Affleck-Dine field and axion field through higher-dimensional operators. We thus explore the Affleck-Dine baryogenesis on an axion background. It turns out that the axion oscillation produces an enough amount of baryon asymmetry of the Universe just after the inflation, even without a soft supersymmetry-breaking $A$-term. This baryogenesis scenario is applicable to the string axion inflation.
Modulated reheating scenario is one of the most attractive models that predict possible detections of not only the primordial non-Gaussianity but also the tensor fluctuation through future CMB observations such as the Planck satellite, the PolarBeaR and the LiteBIRD satellite experiments. We study the baryonic-isocurvature fluctuations in the Affleck-Dine baryogenesis with the modulated reheating scenario. We show that the Affleck-Dine baryogenesis can be consistent with the modulated reheating scenario with respect to the current observational constraint on the baryonic-isocurvature fluctuati…
We study the dynamics of the Affleck-Dine field after inflation in more detail. After inflation, the Affleck-Dine field inevitably oscillates around the potential minimum. This oscillation is hard to decay and can cause accidental suppression of the consequential baryon asymmetry. This suppression is most effective for the model with non-renormalizable superpotential $W_{AD}\sim Φ^4$ ($Φ$: Affleck-Dine field). It is found that the Affleck-Dine leptogenesis in high-scale inflation, which suffers from serious gravitino overproduction, becomes workable owing to this effect.
Affleck-Dine inflation is a recently proposed model in which a single complex scalar field, nonminimally coupled to gravity, drives inflation and simultaneously generates the baryon asymmetry of universe via Affleck-Dine mechanism. In this paper we investigate the supersymmetric implementation of Affleck-Dine inflation in the use of two chiral superfields with appropriate superpotential and Kähler potential. The scalar potential has a similar form to the potential of original Affleck-Dine inflation, and it gives successful inflation and baryogenesis. We also consider the isocurvature perturbat…
In this paper, we investigate the parameter space in the framework of hilltop supernatural inflation in which the inflaton field can play the role of Affleck-Dine field to produce successful baryogenesis. The suitable value of reheating temperature could coincide with the reheating temperature required to produce lightest supersymmetric particle dark matter. The baryon isocurvature perturbation is shown to be negligible. We consider $p=3$, $p=4$, and $p=6$ type III hilltop inflation and discuss how to connect the models to supersymmetric theories.
We investigate the backreaction of the Affleck-Dine leptogenesis to inflaton dynamics in the F-term hybrid and chaotic inflation models in supergravity. We determine the lightest neutrino mass in both models so that the predictions of spectral index, tensor-to-scalar ratio, and baryon abundance are consistent with observations.
Motivated by the coincidence between the Hubble scale during inflation and the typical see-saw neutrino mass scale, we present a supergravity model where the inflaton is identified with a linear combination of right-handed sneutrino fields. The model accommodates an inflaton potential that is flatter than quadratic chaotic inflation, resulting in a measurable but not yet ruled out tensor-to-scalar ratio. Small CP-violation in the neutrino mass matrix and supersymmetry breaking yield an evolution in the complex plane for the sneutrino fields. This induces a net lepton charge that, via the Affle…
We propose a new scenario of Affleck-Dine baryogenesis where a flat direction in the MSSM generates B-L asymmetry just after the end of inflation. The resulting amount of baryon asymmetry is independent of low-energy supersymmetric models but is dependent on inflation models. We consider the hybrid and chaotic inflation models and find that reheating temperature is required to be higher than that in the conventional scenario of Affleck-Dine baryogenesis. In particular, non-thermal gravitino-overproduction problem is naturally avoided in the hybrid inflation model. Our results imply that Afflec…
Affleck-Dine baryogenesis is preconditioned on a certain structure of non-renormalizable operators in the Kahler potential. In this paper, we geometrically characterize the resulting constraint on the field space Kahler geometry and survey the Lagrangian for correlated predictions. The Affleck-Dine field backreacts on the inflaton, and by mapping the backreacted potential to an inflaton potential with a step, we find that current CMB data severely constrain some versions of the scenario.
We present both analytically and numerically the consistent analysis from the Affleck-Dine (AD) dynamics to the subsequent semiclassical evolution in both gravity-mediated and gauge-mediated models. We obtain analytically the elliptic motions in the AD dynamics as the analogy of the well-known Kepler-problem, and by solving the equations of motion in a lattice, we find that the semiclassical evolution goes through three distinct stages as a nonequilibrium process of reheating the Universe: pre-thermalisation, bubble collisions and thermalisation. We report that the second stage of our case las…
The similarity of the visible and dark matter abundances indicates that they may originate via the same mechanism. If both the dark and the visible matter are charged under a generalized baryon number which remains always conserved, then the asymmetry of the visible sector may be compensated by an asymmetry in the dark sector. We show how the separation of baryonic and antibaryonic charge can originate in the vacuum, via the Affleck-Dine mechanism, due to the breaking of a symmetry orthogonal to the baryon number. Symmetry restoration in the current epoch guarantees the individual stability of…
We study the Affleck-Dine (AD) baryogenesis in the inflating curvaton scenario, when the curvaton is a moduli field with O($10-10^2$TeV) mass. A moduli field with such mass is known to be free from the Polonyi problem, and furthermore its decay products can explain the present cold dark matter abundance. In our scenario, it further explains the primordial curvature perturbation and the present baryon density all together. The current observational bound on the baryon isocurvature perturbation, which severely constrains the AD baryogenesis with the original oscillating moduli curvaton scenario,…
We investigate the baryon asymmetry in the supersymmetry Dine-Fischler-Srednicki-Zhitnitsky axion model without R-parity. It turns out that the R-parity violating terms economically explain the atmospheric mass-squared difference of neutrinos and the appropriate amount of baryon asymmetry through the Affleck-Dine mechanism. In this model, the axion is a promising candidate for the dark matter and the axion isocurvature perturbation is suppressed due to the large field values of Peccei-Quinn fields. Remarkably, in some parameter regions explaining the baryon asymmetry and the axion dark matter …
We investigate the viability of Affleck-Dine baryogenesis in D=4, N=1 supergravity descending from string theory. The process relies on an initial condition where visible sector supersymmetric flat directions obtain tachyonic masses during inflation. We discuss this condition for a variety of cases where supersymmetry is broken during inflation by a geometric modulus or hidden sector scalar, and outline scenarios where the initial condition is satisfied.
We propose a novel scenario for Affleck-Dine baryogenesis in the braneworld, considering the hybrid potential for the Affleck-Dine field. Destabilization of the flat direction is not due to the Hubble parameter, but is induced by a trigger field. The moduli for the brane distance plays the role of the trigger field. Q-balls are unstable in models with large extra dimensions.
Low-scale supersymmetry breaking in string motivated theories implies the presence of O(100) TeV scale moduli, which generically lead to a significant modification of the history of the universe prior to Big Bang Nucleosynthesis. Such an approach implies a non-thermal origin for dark matter resulting from scalar decay, where the lightest supersymmetric particle can account for the observed dark matter relic density. We study the further effect of the decay on the baryon asymmetry of the universe, and find that this can satisfactorily address the problem of the over-production of the baryon asy…
Working in $D=4, N=1$ supergravity, we utilize relations between holomorphic sectional and bisectional curvatures of Kahler manifolds to constrain Affleck-Dine baryogenesis. We show the following No-Go result: Affleck-Dine baryogenesis cannot be performed if the holomorphic sectional curvature at the origin is isotropic in tangent space; as a special case, this rules out spaces of constant holomorphic sectional curvature (defined in the above sense) and in particular maximally symmetric coset spaces. We also investigate scenarios where inflationary supersymmetry breaking is identified with the…
We introduce a class of non-supersymmetric models explaining baryogenesis a la Affleck-Dine, which use a decay of two superheavy scalar fields with close masses. These scalars acquire non-zero expectation values during inflation through linear couplings to a function of an inflaton. After the inflaton decay, the model possesses approximate U(1)-invariance, explicitly broken by a small mass splitting. This splitting leads to the baryogenesis in the early Universe. Resulting baryon asymmetry is automatically small for the scalars with the masses about the Grand Unification scale and larger. It i…
We compute the stochastic gravitational wave production from Affleck-Dine condensate fragmentation in the early universe, focusing on an effective potential with a logarithmic mass correction that typically arises in gravity mediated supersymmetry breaking scenarios. We find that a significant gravitational wave background can be generated when Q-balls are being formed out of the condensate fragmentation. This gravitational wave background has a distinct multi-peak power spectrum where the trough is closely linked to the supersymmetry breaking scale and whose frequencies are peaked around kHz …
We propose a novel framework in which the observed baryon and dark matter abundances are simultaneously generated via the Affleck-Dine mechanism. In its simplest realization, Affleck-Dine cogenesis is accomplished by a single superpotential operator and its A-term counterpart. These operators explicitly break B-L and X, the dark matter number, to the diagonal B-L+X. In the early universe these operators stabilize supersymmetric flat directions carrying non-zero B-L and X, and impart the requisite CP violation for asymmetry generation. Because B-L+X is preserved, the resulting B-L and X asymmet…
We propose a new scenario of Affleck-dine baryogenesis in the context of theories with large extra dimensions. In this paper we consider baryogenesis after thermal brane inflation and show how our mechanism works. We specifically consider models in which supersymmetry is broken at the distant brane.
We study charge-swapping Q-balls, a kind of composite Q-ball where positive and negative charges co-exist and swap with time, in models with a logarithmic potential that arises naturally in supersymmetric extensions of the Standard Model. We show that charge-swapping Q-balls can be copiously generated in the Affleck-Dine fragmentation process in the early universe. We find that the charge-swapping Q-balls with the logarithmic potential are extremely stable. By performing long time, parallelized lattice simulations with absorbing boundary conditions, we find that the lifetimes of such objects w…
We present a viable string embedding of Affleck-Dine baryogenesis in type IIB sequestered models where the late-time decay of the lightest modulus reheats the universe to relatively low temperatures. We show that if inflation is driven by a blow-up Kaehler modulus, the Affleck-Dine field can become tachyonic during inflation if the Kaehler metric for matter fields has an appropriate inflaton-dependent contribution. We find that the Affleck-Dine mechanism can generate the observed baryon asymmetry for natural values of the underlying parameters which lead also to successful inflation and low-en…
Certain exact results in supersymmetric gauge theories are generated by non-perturbative effects different from instantons. In supersymmetric QCD with N colours and Nf fundamental flavours we examine the Affleck-Dine-Seiberg (ADS) superpotential using controlled semi-classical analysis. We show how for Nf < N-1 the ADS superpotential arises from monopole contributions to the path integral of the supersymmetric gauge theory compactified on R^3*S^1. These are the monopole effects leading to gaugino condensation and confinement of the low-energy SU(N-Nf) supersymmetric gauge theory.
We present a novel Affleck-Dine scenario for the generation of the observed baryon asymmetry of the Universe based on the non-trivial interplay between quintessential inflationary models containing a kinetic dominated post-inflationary era and a non-minimally coupled $U(1)$ field with a weakly broken $B-L$ symmetry. The non-minimal coupling to gravity renders heavy the Affleck-Dine field during inflation and avoids the generation of isocurvature fluctuations. During the subsequent kinetic era the Ricci scalar changes sign and the effective mass term of the Affleck-Dine field becomes tachyonic.…
We discuss the curvaton scenario with the Affleck-Dine baryogenesis. In this scenario, non-vanishing baryonic entropy fluctuation may be generated even without primordial fluctuation of the Affleck-Dine field. Too large entropy fluctuation is inconsistent with the observations and hence constraints on the curvaton scenario with the Affleck-Dine baryogenesis are obtained. We calculate the baryonic entropy fluctuation (as well as other cosmological density fluctuations) in this case and derive constraints. Implications to some of the models of the curvaton are also discussed.
Primordial black hole (PBH) is a fascinating candidate for the origin of binary merger events observed by LIGO-Virgo collaboration. The spatial distribution of PBHs at formation is an important feature to estimate the merger rate. We investigate the clustering of PBHs formed by Affleck-Dine (AD) baryogenesis, where dense baryon bubbles collapse to form PBHs. We found that formed PBHs show a strong clustering due to the stochastic dynamics of the AD field. Including the clustering, we evaluate the merger rate and isocurvature perturbations of PBHs, which show significant deviations from those w…
It has been known that in anomaly-mediated SUSY breaking model Affleck-Dine baryogenesis does not work due to trapping of Affleck-Dine field into charge-breaking minima. We show that when finite-temperature effect is properly taken into account and if reheating temperature is relatively high, the problem of falling into charge breaking global minima can be avoided and hence Affleck-Dine baryogenesis works. Moreover, for the LH_u flat direction we obtain a constraint on the mass of neutrino.
Pangenesis is the mechanism for jointly producing the visible and dark matter asymmetries via Affleck-Dine dynamics in a baryon-symmetric universe. The baryon-symmetric feature means that the dark asymmetry cancels the visible baryon asymmetry and thus enforces a tight relationship between the visible and dark matter number densities. The purpose of this paper is to analyse the general dynamics of this scenario in more detail and to construct specific models. After reviewing the simple symmetry structure that underpins all baryon-symmetric models, we turn to a detailed analysis of the required…
We study the Affleck-Dine mechanism with various types of the Kahler potential, and investigate whether or not the Affleck-Dine field could acquire a large VEV as an initial condition for successful baryogenesis. In addition to a negative Hubble-induced mass term, we find that large enough Hubble-induced A-terms could also develop the minimum at large amplitude of the field. Therefore, the Affleck-Dine mechanism works for broader classes of the theories.
In the version 1, we proposed a mechanism to create baryon asymmetry in a conformally sequestered supersymmetry (SUSY) breaking scenario through the Affleck-Dine (AD) mechanism. After the submission, however, we found a critical error in our discussion. This is a note on the article of version 1.
We reconsider the Affleck-Dine mechanism for baryogenesis and show that the baryonic isocurvature fluctuations are generated in many inflation models in supergravity. The inflationary scale and the reheating temperature must satisfy certain constraints to avoid too large baryonic isocurvature fluctuations.
In Affleck-Dine baryogenesis, the observed baryon asymmetry of the Universe is generated through the evolution of the vacuum expectation value (VEV) of a scalar condensate. This scalar condensate generically fragments into non-topological solitons (Q-balls). If they are sufficiently long-lived, they lead to an early matter domination epoch, which enhances the primordial gravitational wave signal for modes that enter the horizon during this epoch. The sudden decay of the Q-balls into fermions results in a rapid transition from matter to radiation domination, producing a sharp peak in the gravit…
The Affleck-Dine mechanism creates the baryon asymmetry of the universe from an angular motion of a complex scalar field. The mechanism is efficient and allows for a low reheating temperature of the universe if the scalar field has a flat potential along its radial direction. We consider a possibility where the scalar field is a pseudo-Nambu-Goldstone boson arising from spontaneous breaking of an approximate global symmetry, so that the flatness of the potential is naturally understood. We construct a concrete realization of the idea based on chiral symmetry breaking in an SU(N) gauge theory. …
Previously, we proposed a model of low energy Affleck-Dine leptogenesis in the context of thermal inflation. The lepton asymmetry is generated at the end of thermal inflation, which occurs at a relatively low energy scale with the Hubble parameter somewhere in the range $1 \keV \lesssim H \lesssim 1 \MeV$. Thus Hubble damping will be ineffective in bringing the Affleck-Dine field into the lepton conserving region near the origin, leaving the possibility that the lepton number could be washed out. Previously, we suggested that preheating could damp the amplitude of the Affleck-Dine field allowi…
We examine the conditions for a viable Affleck-Dine baryogenesis in supergravity (SUGRA) scenarios, finding surprisingly strong constraints on the type of SUGRA theory. These constraints are beautifully fulfilled by string-based SUGRA models provided that inflation is driven by a modulus (T) field.
The observed baryon and dark matter densities are equal up to a factor of 5. This observation indicates that the baryon asymmetry and dark matter have the same origin. The Affleck-Dine baryogenesis is one of the most promising mechanisms in this context. Q balls, which are often formed in the early Universe associated with the Affleck-Dine baryogenesis, decay both into supersymmetric particles and into quarks. Recently, it was pointed out that annihilation of squarks into quarks gives a dominant contribution to the Q-ball decay rate and the branching ratio of Q-ball decay into supersymmetric p…
We study the conditions for successful Affleck-Dine baryogenesis and the origin of gravitino dark matter in GMSB models. AD baryogenesis in GMSB models is ruled out by neutron star stability unless Q-balls are unstable and decay before nucleosynthesis. Unstable Q-balls can form if the messenger mass scale is larger than the flat-direction field Phi when the condensate fragments. We provide an example based on AD baryogenesis along a d = 6 flat direction for the case where m_{3/2} \approx 2 GeV, as predicted by gravitino dark matter from Q-ball decay. Using a phenomenological GMSB potential whi…
We consider the Affleck-Dine baryogenesis comprehensively in the minimal supersymmetric standard model with gauge-mediated supersymmetry breaking. Considering the high temperature effects, we see that the Affleck-Dine field is naturally deformed into the form of the Q ball. In the natural scenario where the initial amplitude of the field and the A-terms are both determined by the nonrenormalizable superpotential, we obtain a narrow allowed region in the parameter space in order to explain the baryon number and the dark matter of the universe simultaneously. Therefore, the Affleck-Dine baryogen…
We study the supermassive black holes (SMBHs) observed in the galactic centers. Although the origin of SMBHs has not been well understood yet, previous studies suggest that seed black holes (BHs) with masses $10^{4-5}M_\odot$ exist at a high redshift ($z \sim 10$). We examine whether primordial black holes (PBHs) produced by inhomogeneous baryogenesis can explain those seed black holes. The inhomogeneous baryogenesis is realized in the modified Affleck-Dine mechanism. In this scenario, there is no stringent constraint from CMB $μ$-distortion in contrast to the scenario where Gaussian fluctuati…
We investigate the Affleck-Dine baryogenesis after D-term inflation with a positive Hubble-induced mass term for a B-L flat direction. It stays at a large field value during D-term inflation, and just after inflation ends it starts to oscillate around the origin of the potential due to the positive Hubble-induced mass term. The phase direction is kicked by higher-dimensional Kahler potentials to generate the B-L asymmetry. The scenario predicts nonzero baryonic isocurvature perturbations, which would be detected by future observations of CMB fluctuations. We also provide a D-term inflation mod…
Affleck-Dine (AD) baryogenesis along a d=6 flat direction in gauge-mediated supersymmetry-breaking (GMSB) models can produce unstable Q-balls which naturally have field strength similar to the messenger scale. In this case a new kind of Q-ball is formed, intermediate between gravity-mediated and gauge-mediated type. We study in detail these new Q-ball solutions, showing how their properties interpolate between standard gravity-mediated and gauge-mediated Q-balls as the AD field becomes larger than the messenger scale. It is shown that E/Q for the Q-balls can be greater than the nucleon mass bu…
The Affleck-Dine mechanism in its simplest form provides baryogenesis from the out-of-equilibrium evolution of a complex scalar field with a simple renormalizable potential. We show that such a model, supplemented by nonminimal coupling to gravity, can also provide inflation, consistent with Planck constraints, simultaneously with the generation of the baryon asymmetry. The predictions of the model include significant tensor-to-scalar ratio and possibly baryon isocurvature fluctuations. The reheating temperature is calculable, making the model fully predictive. We require color triplet scalars…
Thermal inflation can solve serious cosmological problems such as overproduction of gravitinos and moduli. However, it also dilutes the preexisting baryon asymmetry. We investigate a possibility that Affleck-Dine mechanism works after thermal inflation and generate the baryon number at an acceptable level using lattice calculation. We find that a proper amount of baryon number can be generated for appropriate model parameters.
The recent observations of the gravitational waves (GWs) by LIGO-Virgo collaboration infer the increasing possibility of the primordial black holes (PBHs). Recently it was pointed out that sufficient PBHs are produced by the Affleck-Dine mechanism where inhomogeneous baryogenesis takes place due to change of the Hubble induced mass during and after inflation and forms high baryon bubbles (HBBs). The produced HBBs have large density contrasts through the QCD phase transition or stable Q-ball formation, which leads to formation of the LIGO PBHs. Furthermore, in this model stringent constraints f…
We investigate how gravity affects "Q-balls" with the Affleck-Dine potential $V_{AD}(ϕ):=\frac{m^2}{2}ϕ^2[ 1+K\ln (\fracϕ{M})^2]$. Contrary to the flat case, in which equilibrium solutions exist only if $K<0$, we find three types of gravitating solutions as follows. In the case that $K<0$, ordinary Q-ball solutions exist; there is an upper bound of the charge due to gravity. In the case that K=0, equilibrium solutions called (mini-)boson stars appear due to gravity; there is an upper bound of the charge, too. In the case that $K>0$, equilibrium solutions appear, too. In this case, these soluti…
Quantum fluctuations in the post inflationary Affleck-Dine baryogenesis model are studied. The squeezed states formalism is used to give evolution equations for the particle and anti-particle modes in the early universe. The role of expansion and parametric amplification of the quantum fluctuations on the baryon asymmetry produced is investigated.
For Affleck-Dine baryogenesis to proceed, there must have been two types of phase transitions. One is the destabilized-stabilized phase transition of the flat direction, which is in general induced by the Hubble parameter. The other is the phase transition related to the A-term, which induces the misalignment of the relative phase of the flat direction. In the conventional Affleck-Dine baryogenesis they are supposed to start almost simultaneously. Of course these phase transitions can take place separately, but the latter must not be later than the former because the phase transition of the A-…
In this talk we considered the Affleck-Dine mechanism with various types of the Kahler potential, and investigate whether or not the Affleck-Dine field could acquire a large VEV as an initial condition for successful baryogenesis. In addition to a negative Hubble-induced mass term, we found examples that large enough Hubble-induced A-terms could also develop the minima at large amplitude of the field. It is concluded, therefore, that the Affleck-Dine mechanism works for broader classes of the theories. This talk is based on Ref.[1]. Here I extend the discussion from more generic standpoint, an…
To date, the properties of Q-balls arising from an Affleck-Dine condensate in gravity-mediated SUSY breaking have been obtained primarily through numerical simulations. In this work, we will derive the expected charge of the Q-balls formed in such a scenario through an analytical treatment. We will also examine the numerically observed difference between Q-ball formation in weakly charged condensates and formation in strongly charged condensates.
Fragmentation of the Affleck-Dine condensate into Q-balls could fill the Universe with dark matter either in the form of stable baryonic balls, or LSP produced from the decay of unstable Q-balls. The dark matter and the ordinary matter in the Universe may share the same origin.
We present a minimal approach to the generation of the baryon ($B$) asymmetry of the Universe, in which the asymmetry is generated in a complex inflaton condensate via $B$-violating quadratic inflaton potential terms using the Affleck-Dine (AD) mechanism. We show that the $B$-violating quadratic mass terms create an oscillating asymmetry in the complex inflaton condensate at late times. The final asymmetry transferred to the Standard Model sector at reheating is naturally reduced to the magnitude of the observed $B$ asymmetry by the effect of averaging over the $B$ oscillations. This approach …
We study Affleck-Dine leptogenesis via the L H_u flat direction in supersymmetric theories. We find that the baryon asymmetry is enhanced when the energy scale of the inflation is sufficiently low. Especially, we consider models of low scale inflation in which the Hubble parameter during inflation is comparable to (but slightly larger than) the gravitino mass m_{3/2} \sim 1 \TeV. The observed cosmological baryon asymmetry is obtained with the lightest neutrino mass m_{ν_1} \sim 10^{-4} eV, if the reheating process is suddenly terminated after inflation.
We examine the viability of the Affleck-Dine mechanism for baryogenesis under radiatively induced running of soft breaking $({\rm mass})^2$ of the flat directions stemming from non-zero energy density of the inflaton during inflation. A major difference from analogous phenomenological studies is that the horizon radius provides a natural infrared cut-off to the quantum corrections in this case. We identify different scenarios which may arise and point out that the $H_{u}L$ flat direction remains the most promising flat direction, since it is largely independent of uncertainties about high scal…
In D-term inflation models, Affleck-Dine baryogenesis produces isocurvature density fluctuations. These can be perturbations in the baryon number, or, in the case where the present neutralino density comes directly from B-ball decay, perturbations in the number of dark matter neutralinos. The latter case results in a large enhancement of the isocurvature perturbation. The requirement that the deviation of the adiabatic perturbations from scale invariance due to the Affleck-Dine field is not too large then imposes a lower bound on the magnitude of the isocurvature fluctuation of about $10^{-2}$…
In the MSSM, cosmological scalar field condensates formed along flat directions of the scalar potential (Affleck-Dine condensates) are typically unstable with respect to formation of Q-balls, a type of non-topological soliton. I discuss the creation and growth of the quantum seed fluctuations which catalyse the collapse of the condensate. In D-term inflation models, the fluctuations of squark fields in the flat directions also give rise to isocurvature density fluctuations stored in the Affleck-Dine condensate. After the condensate breaks up, these can be perturbations in the baryon number, or…
