Waterfall Field Research Articles

Walking-dilaton hybrid inflation with B − L Higgs embedded in dynamical scalegenesis

We propose a hybrid inflationary scenario based on eight-flavor hidden QCD with the hidden colored fermions being in part gauged under U(1)B−L. This hidden QCD is almost scale-invariant, so-called walking, and predicts the light scalar meson (the walking dilaton) associated with the spontaneous scale breaking, which develops the Coleman-Weinberg (CW) type potential as the consequence of the nonperturbative scale anomaly, hence plays the role of an inflaton of the small-field inflation. The U(1)B−L Higgs is coupled to the walking dilaton inflaton, which is dynamically induced from the so-called bosonic seesaw mechanism. We explore the hybrid inflation system involving the walking dilaton inflaton and the U(1)B−L Higgs as a waterfall field. We find that observed inflation parameters tightly constrain the U(1)B−L breaking scale as well as the walking dynamical scale to be ~ 109 GeV and ~ 1014 GeV, respectively, so as to make the waterfall mechanism worked. The lightest walking pion mass is then predicted to be around 500 GeV. Phenomenological perspectives including embedding of the dynamical electroweak scalegenesis and possible impacts on the thermal leptogenesis are also addressed.

Primordial black holes and scalar-induced gravitational waves in radiative hybrid inflation

We study the possibility that primordial black holes (PBHs) can be formed from large curvature perturbations generated during the waterfall phase transition due to the effects of one-loop radiative corrections of Yukawa couplings between the inflaton and a dark fermion in a non-supersymmetric hybrid inflationary model. We obtain a spectral index ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}, and a tensor-to-scalar ratio r, consistent with the current Planck data. Our findings show that the abundance of PBHs is correlated to the dark fermion mass mN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_N$$\\end{document} and peak in the GW spectrum. We identify parameter space where PBHs can be the entire dark matter (DM) candidate of the universe or a fraction of it. Our predictions are consistent with any existing constraints of PBH from microlensing, BBN, CMB, etc. Moreover, the scenario is also testable via induced gravitational waves (GWs) from first-order scalar perturbations detectable in future observatories such as LISA and ET. For instance, with inflaton mass m∼2×1012\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m \\sim 2\ imes 10^{12}$$\\end{document} GeV, mN∼5.4×1015\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_N \\sim 5.4\ imes 10^{15}$$\\end{document} GeV, we obtain PBHs of around 10-13M⊙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-13}\\, M_\\odot $$\\end{document} mass that can explain the entire abundance of DM and predict GWs with amplitude ΩGWh2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _\ extrm{GW}h^2$$\\end{document}∼10-9\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim 10^{-9}$$\\end{document} with peak frequency f∼\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim $$\\end{document} 0.1 Hz in LISA. By explicitly estimating fine-tuning we show that the model has very mild tuning. We discuss successful reheating at the end of the inflationary phase via the conversion of the waterfall field into standard model (SM) particles. We also briefly speculate a scenario where the dark fermion can be a possible heavy right-handed neutrino (RHN) which is responsible for generating the SM neutrino masses via the seesaw mechanism. The RHN can be produced due to waterfall field decay and its subsequent decay may also explain the observed baryon asymmetry in the universe via leptogenesis. We find the reheat temperature TR≲5×109\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_R\\lesssim 5\ imes 10^9$$\\end{document} GeV that explains the matter-anti-matter asymmetry of the universe.

Primordial monopoles, black holes and gravitational waves

We show how topologically stable superheavy magnetic monopoles and primordial black holes can be generated at observable levels by the waterfall field in hybrid inflation models based on grand unified theories. In SU(5) ×U(1) χ grand unification, the monopole mass is of order 4 × 1017 GeV, and it carries a single unit (2 π /e) of Dirac magnetic charge as well as screened color magnetic charge. The monopole density is partially diluted to an observable value, and accompanied with the production of primordial black holes with mass of order 1017–1019 g which may make up the entire dark matter in the universe. The tensor to scalar ratio r is predicted to be of order 10-5–10 -4 which should be testable in the next generation of CMB experiments such as CMB-S4 and LiteBIRD. The gravitational wave spectrum generated during the waterfall transition is also presented. The observed baryon asymmetry can be explained via leptogenesis.

Hybrid inflation, reheating and dark radiation in a IIB perturbative moduli stabilization scenario

We study the cosmological implications of an effective field theory model derived within a configuration of D7 brane stacks in the framework of type-IIB string theory. We consider a suitable geometric setup where the Kähler moduli fields are stabilized and the parametric space is constrained so that a de Sitter vacuum is ensured. In addition to the moduli fields we also take into account the usual Higgs and matter fields included in the effective field theory. In this background, we implement the standard hybrid inflation scenario with a singlet scalar field acting as the inflaton and the Higgs states serving as waterfall fields. Radiative corrections and soft supersymmetry breaking terms play an essential role in the realization of a successful inflationary scenario consistent with the present cosmological data. Small tensor-to-scalar ratio values are predicted, which can be probed in future planned experiments. Further constraints on the model’s parameters are derived from bounds on dark radiation which is measured as a contribution to the effective number of neutrino species Neff. In particular, we find an excess of ∆Neff ≤ 0.95 at 2σ confidence level with natural values of the involved couplings.

Multifield stochastic dynamics in GUT hybrid inflation without monopole problem and with gravitational wave signatures of GUT Higgs representation

We revisit the hybrid inflation model within the framework of the Grand Unified Theory (GUT), focusing on cases where the waterfall phase transition extends over several e-foldings to dilute monopoles. Considering the stochastic effects of quantum fluctuations, we demonstrate that the waterfall fields (i.e., GUT Higgs) maintain a nonzero vacuum expectation value around the waterfall phase transition. By accurately accounting for the number of degrees of freedom of the GUT Higgs field, we establish that these fluctuations can produce observable gravitational waves without leading to an overproduction of primordial black holes. The amplitude of these gravitational waves is inversely proportional to the degrees of freedom of the waterfall fields, thereby providing a unique method to probe the representation of the GUT Higgs.

Hybrid inflation from supersymmetry breaking

We extend a recently proposed framework, dubbed inflation by supersymmetry breaking, to hybrid inflation by introducing a waterfall field that allows to decouple the supersymmetry breaking scale in the observable sector from the inflation scale, while keeping intact the inflation sector and its successful predictions: naturally small slow-roll parameters, small field initial conditions and absence of the pseudo-scalar companion of the inflaton, in terms of one free parameter which is the first order correction to the inflaton Kähler potential. During inflation, supersymmetry is spontaneously broken with the inflaton being the superpartner of the goldstino, together with a massive vector that gauges the R-symmetry. Inflation arises around the maximum of the scalar potential at the origin where R-symmetry is unbroken. Moreover, a nearby minimum with tuneable vacuum energy can be accommodated by introducing a second order correction to the Kähler potential. The inflaton sector can also play the role of the supersymmetry breaking ‘hidden’ sector when coupled to the (supersymmetric) Standard Model, predicting a superheavy superparticle spectrum near the inflation scale. Here we show that the introduction of a waterfall field provides a natural way to end inflation and allows for a scale separation between supersymmetry breaking and inflation. Moreover, the study of the global vacuum describing low energy Standard Model physics can be done in a perturbative way within a region of the parameter space of the model.

Spectators no more! How even unimportant fields can ruin your Primordial Black Hole model

In this work we terminate inflation during a phase of Constant Roll by means of a waterfall field coupled to the inflaton and a spectator field. The presence of a spectator field means that inflation does not end at a single point, ϕ e, but instead has some uncertainty resulting in a stochastic end of inflation. We find that even modestly coupled spectator fields can drastically increase the abundance of Primordial Black Holes (PBHs) formed by many orders of magnitude. The power spectrum created by the inflaton can be as little as 10-4 during a phase of Ultra Slow-Roll and still form a cosmologically relevant number of PBHs. We conclude that the presence of spectator fields, which very generically will alter the end of inflation, is an effect that cannot be ignored in realistic models of PBH formation.

Stochastic dynamics of multi-waterfall hybrid inflation and formation of primordial black holes

We show that a hybrid inflation model with multiple waterfall fields can result in the formation of primordial black holes (PBHs) with an astrophysical size, by using an advanced algorithm to follow the stochastic dynamics of the waterfall fields. This is in contrast to the case with a single waterfall field, where the wavelength of density perturbations is usually too short to form PBHs of the astrophysical scale (or otherwise PBHs are overproduced and the model is ruled out) unless the inflaton potential is tuned. In particular, we demonstrate that PBHs with masses of order 1020 g can form after hybrid inflation consistently with other cosmological observations if the number of waterfall fields is about 5 for the case of instantaneous reheating. Observable gravitational waves are produced from the second-order effect of large curvature perturbations as well as from the dynamics of texture or global defects that form after the waterfall phase transition.

Composite hybrid inflation: dilaton and waterfall pions

We investigate the possibility that inflation originates from a composite field theory, in terms of an effective chiral Lagrangian involving a dilaton and pions. The walking dynamics of the theory constrain the potential in a specific way, where the anomalous dimensions of operators involving pions play a crucial role. For realistic values of the anomalous dimensions, we find a successful hybrid inflation occurring via the dilaton-inflaton, with the pions acting as waterfall fields. Compositeness consistency strongly constrain the model, predicting a dilaton scale fχ ∼ 𝒪 (1) in unit of the Planck scale, an inflation scale H inf ∼ 1010 GeV, and the pion scale around 1014 GeV. We further discuss possible phenomenological consequences of this theory.

Detectable gravitational wave signals from inflationary preheating

We consider gravitational wave (GW) production during preheating in hybrid inflation models where an axion-like waterfall field couples to Abelian gauge fields. Based on a linear analysis, we find that the GW signal from such models can be within the reach of a variety of foreseeable GW experiments such as LISA, AEDGE, ET and CE, and is close to that of LIGO A+, both in terms of frequency range and signal strength. Furthermore, the resultant GW signal is helically polarized and thus may distinguish itself from other sources of stochastic GW background. Finally, such models can produce primordial black holes that can compose dark matter and lead to merger events detectable by GW detectors.

Subcritical regime of hybrid inflation with modular A4 symmetry

We consider a supergravity model that has the modular A4 symmetry and discuss the interplay between the neutrino mixing and inflation. The model contains right- handed neutrinos that have the Majorana masses and additional Yukawa couplings to the waterfall field. In the model an active neutrino is massless and we find that only the inverted hierarchy is allowed and the Majorana phase is predicted to be around ±(120–180)° from the observed neutrino mixing data. In the early universe, one of right-handed sneutrinos plays the role of the inflaton field. Focusing on the subcritical regime of the hybrid inflation that is consistent with the cosmic microwave background data, we analyze the dynamics of the scalar sector and derive an upper bound (1010) GeV on the scale of the Majorana mass.

Pseudo-Nambu-Goldstone inflation with twin waterfalls

We propose a pseudo-Nambu-Goldstone inflation where twin waterfall fields coupled to the inflaton are responsible for the graceful exit from inflation by a waterfall transition. In this scenario, the Z2 symmetry for the waterfall fields and the inflaton protects the inflaton potential against dangerous quantum corrections coming from the waterfall couplings. We show that there is a wide range of natural model parameters and initial conditions for a successful inflation and discuss the reheating process by the perturbative decay of the waterfall field with a Z2 invariant Higgs portal. We also present a microscopic model for the inflaton couplings to the twin waterfall fields in the context of a dark QCD with light and heavy quarks.

Waterfall stiff period can generate observable primordial gravitational waves

A toy-model is studied, which considers two flat directions meeting at an enhanced symmetry point such that they realise the usual hybrid inflation mechanism. The kinetic term of the waterfall field features a pole at its Planckian vacuum expectation value (VEV), as with α-attractors. Consequently, after the phase transition which terminates hybrid inflation, the waterfall field never rolls to its VEV. Instead, it drives a stiff period, where the barotropic parameter of the Universe w ≈ 1/2 results in a peak in the spectrum of primordial gravitational waves, which will be observable by the forthcoming LISA mission as well as by Advanced LIGO.

Type IIB moduli stabilization, inflation and waterfall fields

In this paper, we present a string realization of the hybrid inflationary scenario within type IIB effective string theory constructions and a geometric configuration of intersecting D7 branes. A metastable de Sitter minimum is ensured by perturbative logarithmic corrections and D-term contributions from abelian factors associated with the D7 branes. The inflaton is identified with the internal volume modulus whereas possible waterfall fields correspond to excitations of open strings attached to the magnetized D7 branes. By incorporating contributions of these fields in the scalar potential, inflation stops and the metastable vacuum settles to a minimum with the observed tunable value of the cosmological constant.

Effective field theory of waterfall in hybrid inflation

We examine the validity of the classical approximation of the waterfall phase transition in hybrid inflation from an effective field theory (EFT) point of view. The EFT is constructed by integrating out the waterfall field fluctuations, up to one-loop order in the perturbative expansion. Assuming slow-roll conditions are obeyed, right after the onset of the waterfall phase, we find the backreaction of the waterfall field fluctuations to the evolution of the system can be dominant. In this case the classical approximation is completely spoiled. We derive the necessary constraint that ensures the validity of the EFT.

Hybrid inflation and waterfall field in string theory from D7-branes

We present an explicit string realisation of a cosmological inflationary scenario we proposed recently within the framework of type IIB flux compactifications in the presence of three magnetised D7-brane stacks. Inflation takes place around a metastable de Sitter vacuum. The inflaton is identified with the volume modulus and has a potential with a very shallow minimum near the maximum. Inflation ends due to the presence of “waterfall” fields that drive the evolution of the Universe from a nearby saddle point towards a global minimum with tuneable vacuum energy describing the present state of our Universe.

Axion-driven hybrid inflation over a barrier

We present a scenario where an axion-like field drives inflation until a potential barrier, which keeps a waterfall field at the origin, disappears and a waterfall transition occurs. Such a barrier separates the scale of inflation from that of the waterfall transition. We find the observed spectrum of the cosmic microwave background indicates that the decay constant of the inflaton is well below the Planck scale, with the inflationary Hubble parameter spanning a wide range. Further, our model involves dark matter candidates including the inflaton itself. Also, for a complex waterfall field, we can determine cosmologically the Peccei-Quinn scale associated with the strong CP problem.

Leptogenesis after superconformal subcritical hybrid inflation

We consider an extended version of superconformal subcritical hybrid inflation model by introducing three right-handed neutrinos that have the Majorana mass terms. In the model one of the right-handed sneutrinos plays a role of the inflaton field, and it decays to reheat the universe after inflation. The vacuum expectation value for the waterfall field gives an unconventional pattern of the light neutrino mass matrix, and the neutrino Yukawa couplings that determine the reheating temperature are not constrained by the neutrino oscillation data. Consequently thermal leptogenesis or sneutrino leptogenesis is realized.

General bounds in Hybrid Natural Inflation

Recently we have studied in great detail a model of Hybrid Natural Inflation (HNI) by constructing two simple effective field theories. These two versions of the model allow inflationary energy scales as small as the electroweak scale in one of them or as large as the Grand Unification scale in the other, therefore covering the whole range of possible energy scales. In any case the inflationary sector of the model is of the form V(ϕ)=V0 (1+a cos(ϕ/f)) where 0⩽ a<1 and the end of inflation is triggered by an independent waterfall field. One interesting characteristic of this model is that the slow-roll parameter ϵ(ϕ) is a non-monotonic function of ϕ presenting a maximum close to the inflection point of the potential. Because the scalar spectrum \U0001d4abs(k) of density fluctuations when written in terms of the potential is inversely proportional to ϵ(ϕ) we find that \U0001d4abs(k) presents a minimum at ϕmin. The origin of the HNI potential can be traced to a symmetry breaking phenomenon occurring at some energy scale f which gives rise to a (massless) Goldstone boson. Non-perturbative physics at some temperature T<f might occur which provides a potential (and a small mass) to the originally massless boson to become the inflaton (a pseudo-Nambu-Goldstone boson). Thus the inflaton energy scale Δ is bounded by the symmetry breaking scale, Δ≡ VH1/4 <f. To have such a well defined origin and hierarchy of scales in inflationary models is not common. We use this property of HNI to determine bounds for the inflationary energy scale Δ and for the tensor-to-scalar ratio r.

Thermal inflation with a thermal waterfall scalar field coupled to a light spectator scalar field

A new model of thermal inflation is introduced, in which the mass of the thermal waterfall field is dependent on a light spectator scalar field. Using the $\delta N$ formalism, the "end of inflation" scenario is investigated in order to ascertain whether this model is able to produce the dominant contribution to the primordial curvature perturbation. A multitude of constrains are considered so as to explore the parameter space, with particular emphasis to key observational signatures. For natural values of the parameters, the model is found to yield a sharp prediction for the scalar spectral index and its running, well within the current observational bounds.