We consider the impact of a kinetic pole of order one or two on the non-supersymmetric model of hybrid inflation. These poles arise due to logarithmic Kaehler potentials which control the kinetic mixing of the inflaton field and parameterize hyperbolic manifolds with scalar curvature related to the coefficient (-N)<0 of the logarithm. Inflation is associated with the breaking of a local SU(2)xU(1) symmetry, which does not produce any cosmological defects after it, and remains largely immune from the minimal possible radiative corrections to the inflationary potential. For N=1 and equal values of the relevant coupling constants, lambda and kappa, the achievement of the observationally central value of ns requires the mass parameter, m, and the symmetry breaking scale, M, to be of the order of 10^12 GeV and 10^17 GeV respectively. Increasing N above unity the tensor-to-scalar ratio r increases above 0.002 and reaches its maximal allowed value for N~10-20.
In string-inspired supergravity theory, Kähler metric of chiral matter fields often has a pole. Such Kähler metric is interesting from the viewpoint of the framework of the pole inflation, where the scalar potential can be stretched out to be flat around the pole for a canonically normalized field and inflation can be realized. However, when Kähler metric has a pole, the scalar potential can also have a pole at the same point in supergravity theory. We study such supergravity models with the pole, and provide numerical analysis of inflationary dynamics and resultant density perturbation. In co…
A reformulation of inflationary model analyses appeared recently, in which inflationary observables are determined by the structure of a pole in the inflaton kinetic term rather than the shape of the inflaton potential. We comprehensively study this framework with an arbitrary order of the pole taking into account possible additional poles in the kinetic term or in the potential. Depending on the setup, the canonical potential becomes the form of hilltop or plateau models, variants of natural inflation, power-law inflation, or monomial/polynomial chaotic inflation. We demonstrate attractor beh…
We present novel realizations of Higgs inflation within Supergravity which are largely tied to the existence of a pole of order two in the kinetic term of the inflaton field. This pole arises due to the selected Kaehler potentials which parameterize the (SU(1,1)/U(1))^2 or SU(2,1)/(SU(2)xU(1)) manifolds with scalar curvatures R_{(11)^2}=-4/N or R_{21}=-3/N respectively. The associated superpotential includes, in addition to the Higgs superfields, a stabilizer superfield, respects the gauge and an R symmetries and contains the first allowed nonrenormalizable term. If the coefficient of this ter…
Transforming canonical scalars to the Einstein frame can give a multi-field generalization of pole inflation (namely, a scalar with a divergent kinetic term) at vanishing field-dependent Planck mass. However, to obtain an attractor, the scalar potential must obey certain non-generic conditions. These are automatically satisfied in Quantum Field Theories with dimension-less couplings. The resulting models of pole inflation have special inflationary predictions determined by the full RG running of couplings. Acceptable predictions for the tensor/scalar ratio arise for perturbative but moderately…
A second order pole in the scalar kinetic term can lead to a class of inflation models with universal predictions referred to as pole inflation or $α$-attractors. While this kinetic structure is ubiquitous in supergravity effective field theories, realising a consistent UV complete model in e.g. string theory is a non-trivial task. For one, one expects quantum corrections arising in the vicinity of the pole which may spoil the typical attractor dynamics. As a conservative estimate of the range of validity of supergravity models of pole inflation we employ the weak gravity conjecture (WGC). We …
We show how we can implement within Supergravity chaotic inflation in the presence of a pole of order one or two in the kinetic mixing of the inflaton sector. This pole arises due to the selected logarithmic Kahler potentials K, which parameterize hyperbolic manifolds with scalar curvature related to the coefficient -N of the logarithmic term. The associated superpotential W exhibits the same R charge with the inflaton-accompanying superfield and includes all the allowed terms. The role of the inflaton can be played by a gauge singlet or non-singlet superfield. Models with one logarithmic term…
We investigate inflation models in Jordan frame supergravity, in which an inflaton non-minimally couples to the scalar curvature. By imposing the condition that an inflaton would have the canonical kinetic term in the Jordan frame, we construct inflation models with asymptotically flat potential through pole inflation technique and discuss their relation to the models based on Einstein frame supergravity. We also show that the model proposed by Ferrara et al. has special position and the relation between the Kähler potential and the frame function is uniquely determined by requiring that scala…
A new scenario of hybrid-like inflation is considered without using hybrid-type potential. Radiation raised continuously by a dissipating inflaton field keeps symmetry restoration in a remote sector, and the false-vacuum energy of the remote sector dominates the energy density during inflation. Remote inflation is terminated when the temperature reaches the critical temperature, or when the slow-roll condition is violated. Without introducing a complex form of couplings, inflaton field may either roll-in (like a standard hybrid inflation) or roll-out (like an inverted-hybrid model or quintesse…
We show that the free light scalar fields that may exist in the inflationary Universe can change the predictions of the hybrid inflation model. Possible signatures are discussed, which can be used to discriminate the sources of the spectrum.
In this work, we consider a hilltop version of the (supersymmetric) sneutrino hybrid inflation where the right-handed sneutrino field plays the role of the inflaton field. This model is a type III hilltop inflation that can produce a spectral index $n_s=0.96$ which fits perfectly to experimental observations without fine-tuning of parameters. We also briefly consider nonthermal leptogenesis via the decay of the right-handed sneutrino inflaton field after inflation.
Quasi-pole quintessential inflation in metric-affine gravity
Consortium for Fundamental Physics, School of Physics and Astronomy, Lancaster University（兰开斯特大学物理与天文学院基础物理学联盟）；National Institute of Chemical Physics and Biophysics（国家化学物理和生物物理研究所）；Tallinn University of Technology（塔尔图理工大学）
We consider D-term hybrid inflation in the framework of superconformal supergravity. In part of the parameter space, inflation continues for subcritical inflaton field value. Consequently, a new type of inflation emerges, which gives predictions for the scalar spectral index and the tensor-to-scalar ratio that are consistent with the Planck 2015 results. The potential in the subcritical regime is found to have a similar structure to one in the simplest class of superconformal alpha attractors.
We offer a geometric interpretation of attractor theories with singular kinetic terms as a union of multiple canonical models. We demonstrate that different domains (separated by poles) can drastically differ in their phenomenology. We illustrate this with the help of a "master model" that leads to distinct predictions depending on which side of the pole the field evolves before examining the more realistic example of $α$-attractor models. Such models lead to quintessential inflation within the poles when featuring an exponential potential. However, beyond the poles, we discover a novel behavi…
In hybrid inflation, the inflaton generically has a tadpole due to gravitational effects in supergravity, which significantly changes the inflaton dynamics in high-scale supersymmetry. We point out that the tadpole can be cancelled if there is a supersymmetry breaking singlet with gravitational couplings, and in particular, the cancellation is automatic in no-scale supergravity. We consider the LARGE volume scenario as a concrete example and discuss the compatibility between the hybrid inflation and the moduli stabilization. We also point out that the dark radiation generated by the overall vo…
We study the supergravity hybrid inflation model of Ref.[1] in the presence of a modulus field. The eta-problem is solved by a shift symmetry for the inflaton, which protects the inflaton mass even in the presence of the modulus field. Inflation is (nearly) unaffected by moduli stabilization, provided the scale of supersymmetry breaking in the post-inflation vacuum is small. Therefore the model has the nice phenomenology that it combines low scale supersymmetry breaking with high scale (grand unification scale) inflation.
Motivated by the reported discovery of inflationary gravity waves by the BICEP2 experiment, we propose an inflationary scenario in supergravity, based on the standard superpotential used in hybrid inflation. The new model yields a tensor-to-scalar ratio r ~ 0.14 and scalar spectral index ns ~ 0.964, corresponding to quadratic (chaotic) inflation. The important new ingredients are the high-scale, (1.6-10) x 10^13 GeV, soft supersymmetry breaking mass for the gauge singlet inflaton field and a shift symmetry imposed on the Kähler potential. The end of inflation is accompanied, as in the earlier …
We discuss the waterfall that ends hybrid inflation. Making some simplifying assumptions, that may be satisfied by GUT inflation models, two issues are addressed. First, the procedure of keeping the quantum fluctuation of the waterfall field only in the regime where it can be regarded as classical. Second, the contribution to the primordial curvature perturbation that is generated during the waterfall. Because the waterfall field is heavy during inflation, the spectrum of this contribution is strongly blue and hence is negligible on cosmological scales.
The decay of massive particles during inflation generates characteristic signals in the squeezed limit of the primordial bispectrum. These signals are in particular distinctive in the regime of the quasi-single field inflation, where particles are oscillating with masses comparable to the Hubble scale. We apply the investigation to a class of scalar particles that experience a so-called waterfall phase transition in the isocurvature direction driven by the symmetry-breaking mechanism based on the hybrid inflation scenario. With a time-varying mass, a novel shape of oscillatory bispectrum is pr…
In sneutrino hybrid inflation the superpartner of one of the right-handed neutrinos involved in the seesaw mechanism plays the role of the inflaton field. It obtains its large mass after the "waterfall" phase transition which ends hybrid inflation. After this phase transition the oscillations of the sneutrino inflaton field may dominate the universe and efficiently produce the baryon asymmetry of the universe via nonthermal leptogenesis. We investigate the conditions under which inflation, with primordial perturbations in accordance with the latest WMAP results, as well as successful nontherma…
A new scenario of hybrid-like inflation is considered for sneutrino and MSSM fields. Contrary to the usual hybrid inflation model, the direct coupling between a trigger field and the sneutrino/MSSM inflaton field is not necessary for the scenario. The dissipation and the radiation from the sneutrino/MSSM inflaton can be written explicitly by using the Yukawa couplings. Remote inflation does not require the shift symmetry or cancellation in solving the eta-problem.
We study a generalized superconformal model that gives rise to a subcritical regime of $D$-term hybrid inflation. Exhibiting the model both in a Jordan frame and in the Einstein frame, the effective potential of the subcritical regime is derived in the Einstein frame. It turns out the inflaton-waterfall field dynamics leads to various types of inflaton potential. Consequently the tensor-to-scalar ratio is found to range from $10^{-4}$ ($10^{-3}$) to $0.1$ for getting 60 (50) $e$-folds before the end of 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 le…
We propose a new model of the D-term hybrid inflation in the framework of supergravity. Although our model introduces, analogously to the conventional D-term inflation, the inflaton and a pair of scalar fields charged under a $U(1)$ gauge symmetry, we study the logarithmic and exponential dependence on the inflaton field, respectively, for the Kähler and superpotential. This results in a characteristic one-loop scalar potential consisting of linear and exponential terms, which realizes the small-field inflation dominated by the Fayet-Iliopoulos term. With the reasonable values for the coupling…
Supersymmetric hybrid inflation is an exquisite framework to connect inflationary cosmology to particle physics at the scale of grand unification. Ending in a phase transition associated with spontaneous symmetry breaking, it can naturally explain the generation of entropy, matter and dark matter. Coupling F-term hybrid inflation to soft supersymmetry breaking distorts the rotational invariance in the complex inflaton plane---an important fact, which has been neglected in all previous studies. Based on the delta-N formalism, we analyze the cosmological perturbations for the first time in the f…
We consider a supersymmetric hybrid inflation model with two inflaton fields. The superpotential during inflation is dominated by W=(κS+κ' S')M^2, where S, S' are inflatons carrying the same U(1)_R charge, κ, κ' are dimensionless couplings, and M (\sim 10^{15-16} GeV) is a dimensionful parameter associated with a symmetry breaking scale. One light mass eigenstate drives inflation, while the other heavier mass eigenstate is stuck to the origin. The smallness of the lighter inflaton mass for the scalar spectral index n_s\approx 0.96, which is the center value of WMAP7, can be controlled by the r…
We present a mechanism for realizing hybrid inflation using two axion fields with a purely non-perturbatively generated scalar potential. The structure of scalar potential is highly constrained by the discrete shift symmetries of the axions. We show that harmonic hybrid inflation generates observationally viable slow-roll inflation for a wide range of initial conditions. This is possible while accommodating certain UV arguments favoring constraints $f\lesssim M_{\rm P}$ and $Δϕ_{60}\lesssim M_{\rm P}$ on the axion periodicity and slow-roll field range, respectively. We discuss controlled $\mat…
We estimate large-scale curvature perturbations from isocurvature fluctuations in the waterfall field during hybrid inflation, in addition to the usual inflaton field perturbations. The tachyonic instability at the end of inflation leads to an explosive growth of super-Hubble scale perturbations, but they retain the steep blue spectrum characteristic of vacuum fluctuations in a massive field during inflation. The power spectrum thus peaks around the Hubble-horizon scale at the end of inflation. We extend the usual delta-N formalism to include the essential role of these small fluctuations when…
We study symmetry breaking and topological defects in a supersymmetric model with gauge group $\text{U}(2)$, which can be identified with the right-handed part $\text{SU}(2)_R \times \text{U}(1)_{B-L}$ of an extended electroweak symmetry of the Standard Model. The model has two phases of hybrid inflation terminated by tachyonic preheating where either monopoles and strings or, alternatively, dumbbells are formed. In the first case a stochastic gravitational wave background is predicted in the LIGO-Virgo band, possibly extending to the LISA frequency band and to nanohertz frequencies, which is …
We consider the basic supersymmetric (SUSY) models of F-term hybrid inflation (FHI). We show that a simple class of Kaehler potentials ensures a resolution to the ηproblem and allows for inflation of hilltop type. As a consequence, observationally acceptable values for the spectral index, ns, can be achieved constraining the coefficient c4k of the quartic supergravity correction to the inflationary potential. For about the central value of ns, in the case of standard FHI, the grand unification (GUT) scale turns out to be well below its SUSY value with the relevant coupling constant κin the ran…
We present novel realizations of E-model inflation within Supergravity which are largely associated with the existence of a pole of order one in the kinetic term of the (gauge-singlet) inflaton superfield. This pole arises due to the selected logarithmic Kahler potentials K1 and ~K1, which parameterize the same hyperbolic manifold with scalar curvature R=-2/N, where N>0 is the coefficient of a logarithmic term. The associated superpotential W exhibits the same R charge with the inflaton-accompanying superfield and includes all the allowed renormalizable terms. For K=K1, inflation can be attain…
Without demanding a specific form for the inflaton potential, we obtain an estimate of the contribution to the curvature perturbation generated during the linear era of the hybrid inflation waterfall. The spectrum of this contribution peaks at some wavenumber $k=k_*$, and goes like $k^3$ for $k\ll k_*$, making it typically negligible on cosmological scales. The scale $k_*$ can be outside the horizon at the end of inflation, in which case $ζ=- (g^2 - \vev{g^2})$ with $g$ gaussian. Taking this into account, the cosmological bound on the abundance of black holes is likely to be satisfied if the c…
We analyze the dynamics and observational predictions of supersymmetric hybrid inflation in the warm regime, where dissipative effects are mediated by the waterfall fields and their subsequent decay into light degrees of freedom. This produces a quasi-thermal radiation bath with a slowly-varying temperature during inflation and further damps the inflaton's motion, thus prolonging inflation. As in the standard supercooled scenario, inflation ends when the waterfall fields become tachyonic and can no longer sustain a nearly constant vacuum energy, but the interaction with the radiation bath make…
We present a realization of Higgs inflation within Supergravity which is largely tied to the existence of a pole of order two in the kinetic term of the inflaton field. This pole arises due to the selected Kaehler potential which parameterizes the SU(2,1) / (SU(2) x U(1)) manifold with scalar curvature R_{21}=-6/N. The associated superpotential includes, in addition to the Higgs superfields, a stabilizer superfield, respects a B-L gauge and an R symmetries and contains the first allowed nonrenormalizable term. If the coefficient of this term is almost equal to that of the others within about 1…
Hybrid inflation is a two field model where inflation ends due to an instability. In the neighborhood of the instability point, the potential is very flat and the quantum fluctuations dominate over the classical motion of the inflaton and waterfall fields. In this article, we study this regime in the framework of stochastic inflation. We numerically solve the two coupled Langevin equations controlling the evolution of the fields and compute the probability distributions of the total number of e-folds and of the inflation exit point. Then, we discuss the physical consequences of our results, in…
A contribution $ζ_χ$ to the curvature perturbation will be generated during the waterfall that ends hybrid inflation, that may be significant on small scales. In particular, it may lead to excessive black hole formation. We here consider standard hybrid inflation, where the tachyonic mass of the waterfall field is much bigger than the Hubble parameter. We calculate $ζ_χ$ in the simplest case, and see why earlier calculations of $ζ_χ$ are incorrect.
It is known that supersymmetric hybrid inflation model may require severe tunings on the initial condition for large gravitino mass of order 100 - 1000 TeV due to the constant term in the superpotential. We propose a modified hybrid inflation model, where the constant term is suppressed during inflation and generated after inflation by replacing a constant term with dynamical field. In this modified model, successful inflation consistent with large gravitino mass takes place without severe tunings on the initial condition. Constraint from cosmic strings is also relaxed.
Recent detection of $B$-mode polarization induced from tensor perturbations by the BICEP2 experiment implies so-called large field inflation, where an inflaton field takes super-Planckian expectation value during inflation, at a high energy scale. We show however, if another inflation follows hybrid inflation, the hybrid inflation can generate a large tensor perturbation with not super-Plankian but Planckian field value. This scenario would relax the tension between BICEP2 and Planck concerning the tensor-to-scalar ratio, because a negative large running can also be obtained for a certain numb…
We revisit the hybrid inflation model focusing on the dynamics of the waterfall field in an analytical way. It is shown that inflation may last long enough during the waterfall regime for some parameter regions, confirming the claim of Clesse. In this case the scalar spectral index becomes red, and can fall into the best fit range of the WMAP observation.
We propose an inflationary model ("natural hybrid model"), which combines the supersymmetric hybrid model and the natural inflation model to achieve the spectral index of 0.96, and the axion decay constant smaller than the Planck scale, f<< M_P. By introducing both U(1)_R and a shift symmetry and employing the minimal Kahler potential, the eta-problem can be still avoided. The two inflaton fields in this model can admit large non-Gaussianity.
In this paper we show that certain types of cosmological brane configurations may induce topological inflation. In generic models for topological inflation, there is a strict bound for the potential of the inflaton field. Naively, it seems that these constraints can be removed if inflation starts with a hybrid potential. However, it is difficult to combine topological inflation and hybrid inflation, because of the difference in their initial conditions. In this paper, we show some examples in which a novel type of topological inflation is realized with the unconventional hybrid potential.
We propose a hybrid type of the conventional Higgs inflation and new Higgs inflation models. We perform a disformal transformation into the Einstein frame and analyze the background dynamics and the cosmological perturbations in the truncated model, in which we ignore the higher-derivative terms of the Higgs field. From the observed power spectrum of the density perturbations, we obtain the constraint on the non-minimal coupling constant $ξ$ and the mass parameter $M$ in the derivative coupling. Although the primordial tilt $n_s$ in the hybrid model barely changes, the tensor-to-scalar ratio $…
Process of preheating for supersymmetric hybrid model of inflation is generally analyzed in two different ways known as parametric resonance and tachyonic preheating. In a common frame-work, we study both the processes from the decay or growth of homogeneous inflaton field and inhomogeneous waterfall field. We find that these two processes in SUSY hybrid F-term inflation are not parameter independent; rather one process will be more preferable than the other depending on the values of parameters and Fourier mode of the waterfall field. Parameters of the inflationary potential are constrained f…
We identify models of supersymmetric hybrid inflation in which the tensor-to-scalar ratio, a canonical measure of gravity waves produced during inflation, can be as large as 0.03 or so, which will be tested by the Planck satellite experiment. The scalar spectral index lies within the WMAP one sigma bounds, while $|d n_s / d\ln k| \lesssim 0.01$.
We revisit two-field hybrid inflation as an effective field theory for low-scale inflation with sub-Planckian scalar field ranges. We focus on a prototype model by Stewart because it allows for a red spectral tilt, which still fits the current data. We describe the constraints on this model imposed by current CMB measurements. We then explore the stability of this model to quantum corrections. We find that for relevant, marginal, and at least a finite set of irrelevant operators, some additional mechanism is required to render the model stable to corrections from both quantum field theory and …
A model is presented in which a single scalar field is responsible for both primordial inflation at early times and then dark energy at late times. This field is coupled to a second scalar field which becomes unstable and starts to oscillate after primordial inflation, thus driving a reheating phase that can create a high post-inflation temperature. This model easily avoids overproduction of gravity waves, which is a problem in the original quintessential inflation model in which reheating occurs via gravitational particle production.
We demonstrate the existence of two-field Q-ball solutions of the scalar field equations of supersymmetric D- and F-term hybrid inflation. The solutions consist of a complex inflaton field together with a real symmetry breaking field. Such inflatonic Q-balls may play a fundamental role in reheating and the post-inflation era of supersymmetric hybrid inflation models.
In this paper we provide a no-scale supergravity scenario of hybrid inflation with R-symmetry being broken maximally. We investigate the inflation dynamics in details in both cases of pure F-term hybrid inflation and when adding constant Fayet-Iliopoulos D-terms. The effective inflation potential is asymptotically flat in a region of the parameter space in both cases. We explore all regions in the parameter space when discussing the constraints from the observables. We point out a connection between inflation, R-symmetry breaking and GUT scales. The moduli backreaction and SUSY breaking effect…
In this paper, we show that if we extend D-term hybrid inflation by adding a light scalar field which couples to a waterfall field, large non-Gaussianity can be generated at the end of inflation. Contribution of cosmic strings generated after D-term inflation to the Cosmic Microwave Background (CMB) angular power spectrum can be as low as 10% and this also evade the spectral index problem.
In the literature there have been incompatible estimates for the amount of non-Gaussianity in hybrid inflation. In this note we point out the sources for the discrepancies and show that the results for the amount of non-Gaussianity in hybrid inflation obtained by two different methods, namely, perturbing Einstein equation to second order and the separate universe approach, indeed are compatible. This provides confidence in the methods themselves and in the actual computation of non-Gaussianities.
