I study the post-inflation oscillation and decay of light coherent scalar field condensates that may develop during an inflationary phase of the universe. In particular, the light scalars studied are a composition of the scalar particles of a supersymmetric theory which correspond to the flat directions of the theory's scalar potential. Some toy models that possess supersymmetric flat directions are presented and numerical solutions for the evolution of the scalar fields are obtained. Both analytic and numeric results suggest that such condensates, if they existed in the early universe, can decay through a rapid and nonperturbative process long before these condensates could significantly affect the thermalization of the universe.
Flat directions are a generic feature of supersymmetric theories. They are of cosmological interest because they can lead to coherent production of scalars. In the early universe such flat directions could be dangerous due to the potentially large energy density and the late decay of the associated scalars when they have only $1/M_p$ couplings (Polonyi problem). On the other hand, flat directions among the standard model fields can carry baryon number and lead to a possible mechanism for baryogenesis (Affleck Dine baryogenesis). When considering the cosmological consequences of the flat direct…
We re-examine Affleck-Dine baryo/leptogenesis from the oscillation of condensates along flat directions of the supersymmetric standard model, which attained large vevs at the end of inflationary epoque. The key observation is that superpotential interactions couple the flat directions to other fields, which acquire masses induced by the flat-direction vev that may be sufficiently small for them to be kinematically accessible to inflaton decay. The resulting plasma of inflaton decay products then may act on the flat directions via these superpotential Yukawa couplings, inducing thermal masses a…
In supersymmetric generalizations of the Standard Model, all stable Q-balls are associated with some flat directions. We show that, if the flat direction has both the baryon number and the lepton number, the scalar field inside the Q-ball can deviate slightly from the flat direction in the ground state. We identify the true ground states of such nontopological solitons, including the electrically neutral and electrically charged Q-balls.
We show that a contribution to the total curvature perturbation may be due to the presence of flat directions in supersymmetric models. It is generated at the first os- cillation of the flat direction condensate when the latter relaxes to the minimum of its potential after the end of inflation. We also point out that, if the contribution to the total curvature perturbation from supersymmetric flat direction is the dominant one, then a significant level of non-Gaussianity in the cosmological perturbation is also naturally expected.
We show that the natural presence of flat directions in supersymmetric theories allows for nonrestoration of global and/or gauge symmetries. This has important cosmological consequences for supersymmetric GUTs and in particular it offers a solution of the monopole problem.
The scalar potential of the Minimal Supersymmetric Standard Model (MSSM) is nearly flat along many directions in field space. We provide a catalog of the flat directions of the renormalizable and supersymmetry-preserving part of the scalar potential of the MSSM, using the correspondence between flat directions and gauge-invariant polynomials of chiral superfields. We then study how these flat directions are lifted by non-renormalizable terms in the superpotential, with special attention given to the subtleties associated with the family index structure. Several flat directions are lifted only …
Flat manifold leptogenesis a la Affleck-Dine is investigated with the slepton and Higgs fields, L, H_u, H_d, in the supersymmetric standard model. The multi-dimensional motion of these scalar fields is realized in the case that the L H_u and H_u H_d directions are comparably flat with the relevant non-renormalizable superpotential terms. Soon after the inflation, the lepton number asymmetry appears to fluctuate due to this multi-dimensional motion involving certain CP violating phases. Then, it is fixed to some significant non-zero value for the successful baryogenesis when the scalar fields b…
We study resonant gravitino production in the early Universe in the presence of SUSY flat directions whose large VEVs break some but not all gauge symmetries. We find that for a large region of parameter space the gravitino abundance is several orders of magnitude larger than the cosmological upper bound. Since flat directions with large VEVs are generically expected in supersymmetric theories this result further exacerbates the gravitino problem.
We derive the supersymmetric low-energy effective theory of the D-flat directions of a supersymmetric gauge theory. The Kahler potential of Affleck, Dine and Seiberg is derived by applying holomorphic constraints which manifestly maintain supersymmetry. We also present a simple procedure for calculating all derivatives of the Kahler potential at points on the flat direction manifold. Together with knowledge of the superpotential, these are sufficient for a complete determination of the spectrum and the interactions of the light degrees of freedom. We illustrate the method on the example of a c…
Motivated by a recent discussion about the role of flat directions, a typical feature of supersymmetric models, in the process of particle production in the early universe a consistent model of inflation and preheating in supergravity with MSSM fields has been built. It is based on a model proposed by M. Kawasaki, M. Yamaguchi and T. Yanagida. In the inflationary stage, the flat directions acquire large vacuum expectation values (VEVs) without spoiling the background of slow-roll, high-scale inflation consistent with the latest WMAP5 observational data. In the stage of particle production, nat…
In an interesting class of models, non-renormalizable terms of the superpotential are responsible for the spontanteous breaking of Peccei-Quinn (PQ) symmetry as well as the generation of the $μ$ term. The flaton fields which break PQ symmetry are accompanied by flatinos, and the lightest flatino (the LSP) can be the stable, while the decay of the lightest neutralino (the NLSP) might be visible at colliders with a low axion scale. We examine the cosmology of these models, involving thermal inflation just after the PQ phase transition. The branching ratio of flatons into axions must be small so …
Baryogenesis from the coherent production of a scalar condensate along a flat direction of the supersymmetric extension of the standard model (Affleck-Dine mechanism) is investigated. Two important effects are emphasized. First, nonrenormalizable terms in the superpotential can lift standard model flat directions at large field values. Second, the finite energy density in the early universe induces soft potentials with curvature of order the Hubble constant. Both these have important implications for baryogenesis, which requires large squark or slepton expectation values to develop along flat …
The low energy effective theory of the N=1 supersymmetric SU(5) gauge theory with chiral superfields in the 5* and 10 representations is constructed. Instead of postulating the confinement of SU(5) (confining picture), only the confinement of its subgroup SU(4) is postulated (Higgs picture), and the effective fields are SU(4)-singlet but SU(5)-variant. The classical scalar potential which ensures unique supersymmetric vacuum at the classical level is incorporated into the Kaehler potential of the effective fields. We show that supersymmetry and all other global symmetry are spontaneously broke…
We consider a set of scalar fields, consisting of a single flat direction and one or several non-flat directions. We take our cue from the MSSM, considering separately D-flat and F-flat directions, but our results apply to any supersymmetric scenario containing flat directions. We study the field fluctuations during pure de Sitter Inflation, following the evolution of the infrared modes by numerically solving the appropriate Langevin equations. We demonstrate that for the Standard Model U(1), SU(2) or SU(3) gauge couplings, as well as for large enough Yukawa couplings, the fluctuations along t…
In this paper, we give a brief review of the Minimal Supersymmetric Standard Model (MSSM) and "$μ$ from $ν$" Supersymmetric Standard Model ($μν$SSM). Then we propose a generalization of $μν$SSM in order to explain the recent ATLAS, CMS and LHCb results. This "new" $μν$SSM generalizes the superpotential $W_{suppot}$ of $μν$SSM by including two terms that generate a mixing among leptons, gauginos and higgsinos while keeping the charginos and neutralinos masses unchanged. Also, it is potentially interesting for cosmological applications as it displays flat directions of the superpotential and a v…
We examine the fate of supersymmetric flat directions. We argue that the non-perturbative decay of the flat direction via preheating is an unlikely event. In order to address this issue, first we identify the physical degrees of freedom and their masses in presence of a large flat direction VEV (Vacuum Expectation Value). We explicitly show that the (complex) flat direction and its fermionic partner are the only light {\it physical} fields in the spectrum. If the flat direction VEV is much larger than the weak scale, and it has a rotational motion, there will be no resonant particle production…
Curvaton is an effectively massless field whose energy density during inflation is negligible but which later becomes dominant. This is a novel mechanism to generate the scale invariant perturbations. I discuss the possibility that the curvaton could be found among the fields of the minimally supersymmetric standard model (MSSM), which contains a number of flat directions along which the renormalizable potential vanishes. The requirements of late domination and the absence of damping of the perturbations pick out essentially a unique candidate for the MSSM curvaton. One must also require that …
The only string models known to reproduce the Minimal Supersymmetric Standard Model in the low energy effective field theory are those constructed in the free fermionic formulation. We demonstrate the existence of quasi-realistic free fermionic heterotic-string models in which supersymmetric singlet flat directions do not exist. This raises the possibility that supersymmetry is broken perturbatively in such models by the one-loop Fayet-Iliopoulos term. We show, however, that supersymmetric flat directions that utilize VEVs of some non-Abelian fields in the massless string spectrum do exist in …
It has been recently realized that within the Minimal Supersymmetric Standard Model, for certain patterns of superpartner masses, consistent with all the present experimental constraints, the scalar potential may develop at some scale $Q_0$ unbounded color/charge breaking directions involving the sfermion fields, and that these patterns are then excluded unless some new physics is invoked at or below the scale $Q_0$. We reanalyze this observation and point out that such patterns of superpartner masses at the weak scale are {\it not} ruled out when taking into account the probability of decay f…
Leptogenesis in supersymmetric model is discussed comprehensively and in detail. In the first half, we discuss several leptogenesis mechanisms by the decay of heavy right-handed neutrino, which include the standard thermal leptogenesis, leptogenesis via inflaton decay, and leptogenesis from the coherent oscillation of the right-handed sneutrino. In the second half, we perform a detailed analysis on the leptogenesis via the LHu flat direction (Affleck-Dine leptogenesis).
We make a critical reappraisal of `unbounded-from-below' (UFB) constraints in the MSSM and R-parity violating models. We explain why the `traditional' UFB bounds are neither necessary nor sufficient and propose, instead, a sufficient condition which ensures that there are no local minima along the flat directions. This conservative (but meaningful) condition divides the parameter space into regions which are allowed, regardless of cosmology, and regions in which cosmology is expected to play a major role. We study both conditions at low tan-beta and obtain analytic approximations to the UFB bo…
We present a covariant, supersymmetric and kappa-symmetric action for non-Abelian multiwave system (nAmW) in D=3 AdS superspace. Its flat superspace limit provides a simplest counterpart of the recently proposed action for 11 dimensional system of N nearly coincident M-waves (multiple M0-branes), which is presently known for the case of flat target superspace only.
One interpretation of proton stability is the existence of extra-flat directions of the MSSM, in particular $u^{c}u^{c}d^{c}e^{c}$ and $QQQL$, where the operators lifting the potential are suppressed by a mass scale $Λ$ which is much larger than the Planck mass, $ Λ\gae 10^{26} \GeV$. Using D-term hybrid inflation as an example, we show that such flat directions can serve as the inflaton in SUSY inflation models. The resulting model is a minimal version of D-term inflation which requires the smallest number of additional fields. In the case where $Q$-balls form from the extra-flat direction co…
It has recently been shown that specific non-perturbative effects may lead to an explosive decay of flat direction condensates in supersymmetric theories. We confirm explicitly the efficiency of this process with lattice simulations: after few rotations of the condensates in their complex plane, most of their energy is quickly converted into inhomogeneous fluctuations. We then point out that this generates a gravitational wave background which depends on the inflaton sector and falls in the Hz-kHz frequency range today. We compute the resulting spectrum and study how it depends on the paramete…
Supersymmetric thermal leptogenesis with a hierarchical right-handed neutrino mass spectrum requires the mass of the lightest right-handed neutrino to be heavier than about 10^9 GeV. This is in conflict with the upper bound on the reheating temperature which is found by imposing that the gravitinos generated during the reheating stage after inflation do not jeopardize successful nucleosynthesis. In this paper we show that a solution to this tension is actually already incorporated in the framework, because of the presence of flat directions in the supersymmetric scalar potential. Massive right…
We consider BPS domain walls in the four dimensional N=1 supersymmetric models with continuous global symmetry. Since the BPS equation is covariant under the global transformation, the solutions of the BPS walls also have the global symmetry. The moduli space of the supersymmetric vacua in such models have non-compact flat directions, and the complex BPS walls interpolating between two disjoint flat directions can exist. We examine this possibility in two models with global O(2) symmetry, and construct the solution of such BPS walls.
Supersymmetric theories, including the minimal supersymmetric standard model, usually contain many scalar fields whose potentials are absent in the exact supersymmetric limit and within the renormalizable level. Since their potentials are vulnerable to the finite energy density of the Universe through supergravity effects, these flat directions have nontrivial dynamics in the early Universe. Recently, we have pointed out that a flat direction may have a positive Hubble induced mass term during inflation whereas a negative one after inflation. In this case, the flat direction stays at the origi…
Primordial features as probes of baryogenesis from supersymmetric flat directions
Institute of Physics, Academia Sinica（中央研究院物理研究所）；Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics（哈佛-史密森尼天体物理中心理论与计算研究所）；Department of Physics, Harvard University（哈佛大学物理系）；International Center of Theoretical Physics-Asia Pacific（理论物理中心亚太中心）；Institute of High Energy Physics（高能物理研究所）；Department of Physics, Brown University（布朗大学物理系）
We discuss a supersymmetric SU(6) grand unified theory with the GUT flat direction being lifted by soft supersymmetry breaking, and the doublet-triplet splitting being achieved with Higgs as a pseudo-Goldstone boson. The theory offers a simple solution to the false vacuum and monopole problems.
Flat directions are a generic feature of the scalar potential in supersymmetric gauge field theories. They can arise, for example, from D-terms associated with an extra abelian gauge symmetry. Even when supersymmetry is broken softly, there often remain directions in the scalar field space along which the potential is almost flat. Upon breaking a gauge symmetry along one of these almost flat directions, cosmic strings may form. Relative to the standard cosmic string picture based on the abelian Higgs model, these flat-direction cosmic strings have the extreme Type-I properties of a thin gauge …
Within supersymmetry we provide an example where the inflaton sector is derived from a gauge invariant polynomial of SU(N) or SO(N) gauge theory. Inflation in our model is driven by multi-flat directions, which assist accelerated expansion. We show that multi-flat directions can flatten the individual non-renormalizable potentials such that inflation can occur at sub-Planckian scales. We calculate the density perturbations and the spectral index, we find that the spectral index is closer to scale invariance for large N. In order to realize a successful cosmology we require large N of order, N~…
We address a supersymmetric embedding of domain walls with asymptotically anti-deSitter (AdS) space-times in five-dimensional simple, N=2 U(1) gauged supergravity theory constructed by Gunaydin, Townsend and Sierra. These conformally flat solutions interpolate between supersymmetric AdS vacua, satisfy the Killing spinor (first order) differential equations, and the four-dimensional world on the domain wall is a flat world with N=1 supersymmetry. Regular solutions in this class have the energy density related to the cosmological constants of the supersymmetric AdS vacua. An analysis of such sol…
We consider Dynamical Supersymmetry Breaking (DSB) in models with classical flat directions. We analyze a number of examples, and develop a systematic approach to determine if classical flat directions are stabilized in the full quantum theory, or lead to run-away behavior. In some cases pseudo-flat directions remain even at the quantum level before taking into account corrections to the Kähler potential. We show that in certain limits these corrections are calculable. In particular, we find that in the Intriligator-Thomas $SU(2)$ and its generalizations, a potential for moduli is generated. M…
We argue that supersymmetric flat direction vacuum expectation values can decay non-perturbatively via preheating. Considering a toy U(1) gauge theory, we explicitly calculate the scalar potential, in the unitary gauge, for excitations around several flat directions. We show that the mass matrix for the excitations has non-diagonal entries which vary with the phase of the flat direction vacuum expectation value. Furthermore, this mass matrix has zero eigenvalues whose eigenstates change with time. We show that these light degrees of freedom are produced copiously in the non-perturbative decay …
We investigate the sources of the Hubble-induced mass for a flat direction in supersymmetric theories and show that the sign of the Hubble-induced mass generally changes just after the end of inflation. This implies that global cosmic strings generally form after the end of inflation in most supersymmetric models, including the Minimal Supersymmetric Standard Model. The cosmic strings emit gravitational waves whose frequency corresponds to the Hubble scale, until they disappear when the Hubble parameter decreases down to the soft mass of the flat direction. As a result, the peak frequency of g…
The minimal supersymmetric standard model (MSSM) has a truly supersymmetric way to explain both the baryon asymmetry and cold dark matter in the present Universe, that is, ``Affleck-Dine baryo/DM-genesis.'' The associated late-time decay of Q-balls directly connects the origins of the baryon asymmetry and dark matter, and also predicts a specific nature of the LSP. In this paper, we investigate the prospects for indirect detection of these dark matter candidates observing high energy neutrino flux from the Sun, and hard positron flux from the halo. We also update the previous analysis of the d…
Motivated by Refs \cite{am1,am2}, we analyze how the inflaton decay reheats the Universe within supersymmetry. In a non-supersymmetric case the inflaton usually decays via preheating unless its couplings to other fields are very small. Naively one would expect that supersymmetry enhances bosonic preheating as it introduces new scalars such as squarks and sleptons. On the contrary, we point out that preheating is unlikely within supersymmetry. The reason is that flat directions in the scalar potential, classified by gauge invariant combinations of slepton and squark fields, are generically disp…
A longstanding question in superstring/$M$ theory is does it predict supersymmetry below the string scale? We formulate and discuss a necessary condition for this to be true; this is the mathematical conjecture that all stable, compact Ricci flat manifolds have special holonomy in dimensions below eleven. Almost equivalent is the proposal that the landscape of all geometric, stable, string/$M$ theory compactifications to Minkowski spacetime (at leading order) are supersymmetric. For simply connected manifolds, we collect together a number of physically relevant mathematical results, emphasisin…
We consider the possibility of using one of the $D$-flat directions in the minimal supersymmetric standard model (MSSM) as the inflaton. We show that the flat direction consisting of (first generation) left- and right-handed up-squarks as well as the up-type Higgs boson may play the role of the inflaton if dominant part of the up-quark mass is radiatively generated from supersymmetric loop diagrams. We also point out that, if the R-parity violating Yukawa coupling is of $O(10^{-7})$, $R$-odd $D$-flat directions may be another possible candidate of the inflaton. Such inflation models using $D$-…
The possibility that both the baryon asymmetry and dark matter arise from the late decay of a population of supersymmetric particles is considered. If the decay takes place below the LSP freeze out temperature, a nonthermal distribution of LSPs results. With conserved $R$ parity these relic LSPs contribute to the dark matter density. A net asymmetry can exist in the population of decaying particles if it arises from coherent production along a supersymmetric flat direction. The asymmetry is transferred to baryons if the condensate decays through the lowest order nonrenormalizable operators whi…
We discuss, using the Hilbert basis method, how to efficiently construct a complete basis for D-flat directions in supersymmetric Abelian and non-Abelian gauge theories. We extend the method to discrete (R and non-R) symmetries. This facilitates the construction of a basis of all superpotential terms in a theory with given symmetries.
Natural Supercooling and Reheating along Supersymmetric Flat Directions and Observable Gravitational Waves at the Einstein Telescope and the Cosmic Explorer
Supersymmetric flat directions allow a generic counterexample to the phenomenon of symmetry restoration at high temperatures. We show that (exponentially) large VEVs can be developed along these directions through temperature-induced `dimensional transmutation'. A minimum with broken gauge charges (e.g. electric charge) can exist at arbitrarily high temperatures. In such a scenario magnetic monopoles are never formed, independent of whether inflation occurs before or after the GUT phase transition, or whether it occurs at all.
We investigate in detail solutions of supergravity that involve warped products of flat geometries of the type M(p+1) x R x T(D-p-2) depending on a single coordinate. In the absence of fluxes, the solutions include flat space and Kasner-like vacua that break all supersymmetries. In the presence of a symmetric flux, there are three families of solutions that are characterized by a pair of boundaries and have a singularity at one of them, the origin. The first family comprises supersymmetric vacua, which capture a universal limiting behavior at the origin. The first and second families also cont…
Quasi-realistic string models in the free fermionic formulation typically contain an anomalous U(1), which gives rise to a Fayet-Iliopoulos D-term that breaks supersymmetry at the one--loop level in string perturbation theory. Supersymmetry is traditionally restored by imposing F- and D-flatness on the vacuum. By employing the standard analysis of flat directions we present a quasi--realistic three generation string model in which stringent F- and D-flat solution do not appear to exist to all orders in the superpotential. We speculate that this result is indicative of the non-existence of supe…
We consider instant preheating as the mechanism for generating the curvature perturbation at the end of chaotic inflation. Then we examine if inflation could be driven by a Minimal Supersymmetric Standard Model (MSSM) flat direction or a sneutrino. Our simple mechanism relaxes some serious constraints that appeared in past studies, making inflation driven by a MSSM flat direction or a sneutrino more plausible.
We consider a possibility that one of the flat directions in the minimal supersymmetric standard model plays the role of the inflaton field and realizes large-field inflation. This is achieved by introducing a generalized shift symmetry on the flat direction, which enables us to control the inflaton potential over large field values. After inflation, higher order terms allowed by the generalized shift symmetry automatically cause a helical motion of the field to create the baryon number of the universe, while baryonic isocurvature fluctuations are suppressed.
We study $N=1$ supersymmetric $SO(10)$ gauge theory with a field in the spinorial representaition and $N_f$ ($\leq8$) fields in the defining representation. It is shown that this theory for $N_f=7,8$ has a dual description, which is $N=1$ supersymmetric $SU(N_f-5)$ gauge theory. Its matter content for $N_f=7$ is different {}from the one for $N_f=8$; for $N_f=7$, it contains $8$ fields in the anti-fundamental representation. For $N_f=8$, a rank-$2$ symmetric tensor and one field in the fundamental representation appears in addition to them. This duality connects along the flat direction to the …
In string theory compactifications it is common to find an effective Lagrangian for the scalar fields with a non-canonical kinetic term. We study the effective action of the scalar position moduli of Type II D$p$-branes. In many instances the kinetic terms are in fact modified by a term proportional to the scalar potential itself. This can be linked to the appearance of higher-dimensional supersymmetric operators correcting the Kähler potential. We identify the supersymmetric dimension-eight operators describing the $α'$ corrections captured by the D-brane Dirac-Born-Infeld action. Our analysi…
We examine whether F-term supersymmetric hybrid inflation can be embedded within the minimal SO(10) model, in a natural way. We show that none of the singlets of the Standard Model symmetries in the minimal set of SO(10) representations can satisfy the conditions which are necessary for a scalar field to play the role of the inflaton. As a consequence, one has to introduce an extra scalar field, which however may spoil the naturalness of inflation within the context of SO(10). Nevertheless, if we add an extra scalar field, we are then able to construct a model that can accommodate flat directi…
We present a field theory solution to the eta problem. By making the inflaton field the phase of a baryon of SU(N_c) supersymmetric Yang-Mills theory we show that all operators that usually spoil the flatness of the inflationary potential are absent. Our solution naturally generalizes to non-supersymmetric theories.
In this talk I will describe the role of supersymmetric flat directions in the early Universe cosmology. Particularly I will discuss how supergravity effects lift the flat direction potential and leads to interesting cosmological consequences.
