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 range (0.0006-0.15) and c4k=-(1100-0.05). In the case of shifted [smooth] FHI, the GUT scale can be identified with its SUSY value for c4k=-16 [c4k=-1/16].
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.
In this paper, I show that type I hilltop inflation under the current observational constaints could have $M_P^2 \frac{V^{\prime\prime}}{V} \sim -\mathcal{O}(10^{-2})$ in the parameter space which is in tension with the refined swampland criteria. On the other hand, $M_P^2 \frac{V^{\prime\prime}}{V} \sim -\mathcal{O}(1)$ can be achieved if type I hilltop inflation on the brane is considered.
The scale of small-field inflation cannot be constrained via primordial gravitational waves through measurement of tensor-to-scalar ratio $r$. In this study, I show that if cosmic strings are produced after symmetry breaking at the end of hilltop supernatural inflation, this small-field inflation model can be tested through the production of gravitational waves from cosmic strings. Future experiments of gravitational wave detectors will determine or further constrain the parameter space in the model.
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 present $\mathcal{N}=1$ supergravity models of mutated hilltop inflation (MHI) for both large and small field sectors. Models with canonical kinetic terms are developed based on a shift symmetric Kähler potential in inflaton superfield, and with a superpotential linear in Goldstino superfield. We also construct models with non-canonical kinetic terms for MHI by generalizing the shift symmetry. We found that a good fraction of the models can address the entire branch of MHI in a single framework.
In 'hilltop inflation', inflation takes place when the inflaton field slowly rolls from close to a maximum of its potential (i.e. the 'hilltop') towards its minimum. When the inflaton potential is associated with a phase transition, possible topological defects produced during this phase transition, such as domain walls, are efficiently diluted during inflation. It is typically assumed that they also do not reform after inflation, i.e. that the inflaton field stays on its side of the 'hill', finally performing damped oscillations around the minimum of the potential. In this paper we study the …
Quartic hilltop inflation remains one of the most successful inflationary models. Yet, the expectations of early treatments of hilltop inflation would contradict the observations and render the model excluded. However, recent numerical treatment has demonstrated that quartic hilltop inflation actually fares well with observations. In this work, a fully analytic treatment of the model aims to dispel the mystery surrounding the behaviour of quartic hilltop inflation. The results obtained are in excellent agreement with numerical works on the subject, yet offer simple analytic formulas to calcula…
State Key Laboratory of Dark Matter Physics, Tsung-Dao Lee Institute and School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院、李政道研究所暗物质全国重点实验室）；Key Laboratory for Particle Astrophysics and Cosmology (MOE), and Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong University（上海交通大学粒子天体物理与宇宙学教育部重点实验室、上海粒子物理与宇宙学重点实验室）；School of Physics and Astronomy, University of Southampton（南安普顿大学物理与天文学院）；Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università degli Studi di Padova（帕多瓦大学伽利略·伽利莱物理与天文系）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院基础科学与数学学院）
The swampland criteria put significant constraints on inflation models. In this paper, I show that hilltop inflation on the brane may provide an initial condition for hilltop inflation and produce topological eternal inflation without violating the swampland distance and refined de Sitter criteria. This shows a way that string theory may not be incompatible with eternal inflation.
We study inflation with the non-minimally coupled Standard Model Higgs in the case when quantum corrections generate a hilltop in the potential. We consider both the metric and the Palatini formulation of general relativity. We investigate hilltop inflation in different parts of the Higgs potential and calculate predictions for CMB observables. We run the renormalization group equations up from the electroweak scale and down from the hilltop, adding a jump in-between to account for unknown corrections in the intermediate regime. Within our approximation, no viable hilltop inflation is possible…
In this paper, we consider high scale (100 TeV) supersymmetry (SUSY) breaking and realize the idea of hilltop supernatural inflation in concrete particle physics models based on flipped-SU(5) and Pati-Salam models in the framework of supersymmetric grand unified theories (SUSY GUTs). The inflaton can be a flat direction including right-handed sneutrino and the waterfall field is a GUT Higgs. The spectral index is $n_s=0.96$ which fits very well with recent data by PLANCK satellite. There is no both thermal and non-thermal gravitino problems. Non-thermal leptogenesis can be resulted from the de…
We study `hilltop' inflation, in which inflation takes place near a maximum of the potential. Viewed as a model of inflation after the observable Universe leaves the horizon (observable inflation) hilltop inflation is rather generic. If the potential steepens monotonically, observable hilltop inflation gives a tiny tensor fraction (r< 0.002). The usual F- and D-term models may easily be transmuted to hilltop models by Planck-suppressed terms, making them more natural. The only commonly-considered model of observable inflation which is definitely not hilltop is tree-level hybrid inflation. View…
In this paper, we explore the parameter space of hilltop supernatural inflation model and show the regime within which there is no gravitino problem even if we consider both thermal and nonthermal production mechanisms. We make plots for the allowed reheating temperature as a function of gravitino mass by constraints from big-bang nucleosynthesis. We also plot the constraint when gravitino is assumed to be stable and plays the role of dark matter.
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 propose a scenario to flatten inflaton potential for a small-field slow-roll inflation from the origin. In the scenario, inflaton mass-square gets through a renormalization group running which depends on not only inflaton field but also an assisting field. Thanks to the assisting field participating in the running, initial condition for a slow-roll inflation can be set naturally, and inflaton potential can be flattened by the vacuum expectation value of the field. Applying this idea, we propose a scenario of inflation, dubbed here as \textit{assisted hilltop inflation}, which is free from t…
In this talk, I will explain how to reduce the spectral index to be n_s=0.96 for supernatural inflation. I will also show the constraint to the reheating temperature from Big Bang Nucleosynthesis of both thermal and non-thermal gravitino production.
We study preheating after hilltop inflation where the inflaton couples to another scalar field, e.g. a right-handed sneutrino, which provides a mechanism for generating the correct initial conditions for inflation and also a decay channel for the inflaton that allows for reheating and non-thermal leptogenesis. In the presence of such a coupling, we find that after the phases of tachyonic preheating and tachyonic oscillations, during which the inflaton field becomes inhomogeneous, there can be a subsequent preheating phase where the fluctuations of the other field get resonantly enhanced, from …
Using analytic expressions, we explore the parameter space for hilltop inflation models with a potential of the form $V_0\pm m^2ϕ^2 -aϕ^p$. With the positive sign and p>2 this converts the original hybrid inflation model into a hilltop model, allowing the spectral index to agree with the observed value n=0.95. In some cases the observed value is theoretically favored, while in others there is only the generic prediction $|n-1|\lsim 1$.
We propose a class of models of supersymmetric hilltop inflation (also called "new inflation") where the initial conditions of the inflaton close to the hilltop are generated through "matter field preinflation". This is achieved via a coupling term between the inflaton and matter fields (i.e. Standard Model fields or a right-handed neutrino). The same coupling also opens up a decay channel for the inflaton into Standard Model fields, which allows efficient reheating of the universe. We discuss the multifield dynamics of the inflaton and matter fields during inflation using the delta N formalis…
Oscillons are spatially localized and relatively stable field fluctuations which can form after inflation under suitable conditions. In order to reheat the universe, the fields which dominate the energy density after inflation have to couple to other degrees of freedom and finally produce the matter particles present in the universe today. In this study, we use lattice simulations in 2+1 dimensions to investigate how such couplings can affect the formation and stability of oscillons. We focus on models of hilltop inflation, where we have recently shown that hill crossing oscillons generically …
The recent BICEP2 report on the CMB B-mode polarization hints an early Universe energy density at the GUT scale. We add a new 'chaoton' term to our recently proposed hilltop potential to have a large tensor mode fluctuation. The chaoton field slides down from the hilltop when the inflaton field value is small so that an enough e-folding is possible. We also comment how the trans-Planckian decay constant is obtained from some discrete symmetries of ultra-violet completed models.
Hilltop inflation models are often described by potentials $V = V_{0}(1-{ϕ^{n}\over m^{n}}+...)$. The omitted terms indicated by ellipsis do not affect inflation for $m \lesssim 1$, but the most popular models with $n =2$ and $4$ for $m \lesssim 1$ are ruled out observationally. Meanwhile in the large $m$ limit the results of the calculations of the tensor to scalar ratio $r$ in the models with $V = V_{0}(1-{ϕ^{n}\over m^{n}})$, for all $n$, converge to $r= 4/N \lesssim 0.07$, as in chaotic inflation with $V \sim ϕ$, suggesting a reasonably good fit to the Planck data. We show, however, that t…
We discuss how the non-minimal coupling $ξϕ^2R$ between the inflaton and the Ricci scalar affects the predictions of single field inflation models where the inflaton has a non-zero vacuum expectation value (VEV) $v$ after inflation. We show that, for inflaton values both above the VEV and below the VEV during inflation, under certain conditions the inflationary predictions become approximately the same as the predictions of the Starobinsky model. We then analyze inflation with double-well and Coleman-Weinberg potentials in detail, displaying the regions in the $v$-$ξ$ plane for which the spect…
F-term hybrid inflation (FHI) of the hilltop type can generate a scalar spectral index, ns, in agreement with the fitting of the seven-year Wilkinson microwave anisotropy probe data by the standard power-law cosmological model with cold dark matter and a cosmological constant, LambdaCDM. We investigate the realization of this type of FHI by using quasi-canonical Kahler potentials with or without the inclusion of extra hidden-sector fields. In the first case, acceptable results can be obtained by constraining the coefficients of the quadratic and/or quartic supergravity correction to the inflat…
We study the low-temperature limit of warm inflation in a hilltop model. This limit remains valid up to the end of inflation, allowing an analytic description of the entire inflationary stage. In the weak dissipative regime, if the kinetic density of the inflaton dominates after inflation, low scale inflation is attained with Hubble scale as low as 1 GeV. In the strong dissipative regime, the model satisfies the observational requirements for the spectral index with a mild tuning of the model parameters, while also overcoming the $η$-problem of inflation. However, there is some danger of gravi…
We consider a cosmological inflation with two inflatons, $ϕ$ and $X$. The inflation potential is a hilltop form in the $ϕ$ space and $X$ is a sideway down-fall field in the region $ϕ\ge m$. In this model, we calculate the $e$-fold number numerically starting from the intitial point which is in the vicinity of the hilltop point. Firstly, by varying parameters and initial conditions the inflaton path field $φ$ for the BICEP2 point, $φ_{\rm BCP2}$, is found to give $ n_s\simeq 0.96$ and $r\simeq 0.16$. Next, from the point $φ_{\rm BCP2}$ to the end of inflation the e-fold number is obtained. We f…
We analyse non-thermal leptogenesis after models of Majoron hilltop inflation, where the scalar field that provides masses for the right-handed neutrinos and sneutrinos via its vacuum expectation value acts as the inflaton. We discuss different realisations of Majoron inflation models with different hilltop shapes and couplings to the right-handed (s)neutrinos. To study the non-thermally produced baryon asymmetry in these models, we numerically solve the relevant Boltzmann equations. In contrast to previous studies, we include the effects from resonant sneutrino particle production during preh…
It has been shown that black holes would have formed in the early Universe if, on any given scale, the spectral amplitude of the Cosmic Microwave Background (CMB) exceeds 10^(-4). This value is within the bounds allowed by astrophysical phenomena for the small scale spectrum of the CMB, corresponding to scales which exit the horizon at the end of slow-roll inflation. Previous work by Kohri et. al. (2007) showed that for black holes to form from a single field model of inflation, the slope of the potential at the end of inflation must be flatter than it was at horizon exit. In this work we show…
In this paper, we consider logarithmic radiative corrections and higher order terms to the supersymmetric hilltop F- and D-term hybrid inflation models. Conventional F- and D-term hybrid inflation only predicts $n_s \gae 0.98$. We show that via a positive quadratic and a negative quartic correction the spectral index can be reduced to $n_s=0.96$ suggested from latest WMAP result and also cosmic string problem appeared in SUSY hybrid inflation can be solved with mild tuning of the parameters if $κ\lae 0.01$ for F-term inflation and $g \lae 0.05$ for D-term inflation.
We present a novel realization of Starobinsky-type inflation within Supergravity using two chiral superfields. The proposed superpotential is inspired by induced-gravity models. The Kaehler potential contains two logarithmic terms, one for the inflaton T and one for the matter-like field S, parameterizing the SU(1,1)/U(1)x SU(2)/U(1) Kaehler manifold. The two factors have constant curvatures -m/n and 2/n2, where n, m are the exponents of T in the superpotential and Kaehler potential respectively, and 0<n2<=6. The inflationary observables depend on the ratio 2n/m only. Essentially they coincide…
In this work, we study inflation with the non-minimally coupled quadratic, Standard Model (SM) Higgs and hilltop potentials through $ξϕ^2R$ term in the Palatini gravity. We first analyze observational parameters of Palatini quadratic potential as functions of $ξ$ for high-$N$ scenario and low-$N$ scenario. In addition to this, taking into account inflaton $ϕ$ has a non-zero vacuum expectation value $v$ afterwards inflation, we display observational parameters of well-known symmetry-breaking potentials type of Higgs potential and its generalizations which are hilltop potentials in the Palatini …
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…
We show that the recently proposed multi-natural inflation can be realized within the framework of 4D ${\cal N}=1$ supergravity. The inflaton potential mainly consists of two sinusoidal potentials that are comparable in size, but have different periodicity with a possible non-zero relative phase. For a sub-Planckian decay constant, the multi-natural inflation model is reduced to axion hilltop inflation. We show that, taking into account the effect of the relative phase, the spectral index can be increased to give a better fit to the Planck results, with respect to the hilltop quartic inflation…
We study non-Gaussianity of density perturbations generated by an axionic curvaton, focusing on the case that the curvaton sits near the hilltop of the potential during inflation. Such hilltop curvatons can generate a red-tilted density perturbation spectrum without invoking large-field inflation. We show that, even when the curvaton dominates the Universe, the non-Gaussianity parameter fNL is positive and mildly increases towards the hilltop of the curvaton potential, and that fNL = O(10) is a general and robust prediction of such hilltop axionic curvatons. In particular, we find that the non…
We show that the initial misalignment angle of the QCD axion (or axion-like particles) can be set very close to $π$, if the QCD axion has a mixing with another heavy axion which induces the phase shift $\approx π$ after inflation. In the simplest case, the heavy axion plays the role of the inflaton, and we call such inflation as "$π$nflation." The basic idea was first proposed by Daido and the present authors in Ref. [1702.03284] in 2017 and more recently discussed in Ref. [1903.00462]. We show that the QCD axion with a decay constant $f_a \gtrsim 3 \times 10^9\,$ GeV can explain dark matter b…
We present constraints on inflationary dynamics and features in the primordial power spectrum of scalar perturbations using the Cosmic Microwave Background temperature, polarization data from Planck 2018 data release and updated likelihoods. We constrain the slow-roll dynamics using Hilltop Quartic Potential and Starobinsky $R+R^2$ model in the Einstein frame using the Planck 2018 binned Plik likelihood. Using the Hilltop as base potential we construct Whipped Inflation potential to introduce suppression in the scalar power spectrum at large angular scales. We notice marginal (68% C.L.) prefer…
Oscillons are spatially localised strong fluctuations of a scalar field. They can e.g. form after inflation when the scalar field potential is shallower than quadratic away from the minimum. Although oscillons are not protected by topology, they can be remarkably stable and have a significant impact on the (p)reheating phase. In this work we investigate the properties of oscillons in hilltop-shaped potentials, in particular the typical energies, shapes and lifetimes. In the first part of the paper, we simulate oscillon creation and stabilization with (3+1)-dimensional classical lattice simulat…
In this paper we consider a class of inflation models on the brane where the dominant part of the inflaton scalar potential does not depend on the inflaton field value during inflation. In particular, we consider supernatural inflation, its hilltop version, A-term inflation, and supersymmetric (SUSY) D- and F-term hybrid inflation on the brane. We show that the parameter space can be broadened, the inflation scale generally can be lowered, and still possible to have the spectral index $n_s=0.96$.
We construct explicit examples of fibre inflation models which are globally embedded in type IIB orientifolds with chiral matter on D7-branes and full closed string moduli stabilisation. The minimal setup involves a Calabi-Yau threefold with h^{1,1}=4 Kaehler moduli which features multiple K3 fibrations and a del Pezzo divisor supporting non-perturbative effects. We perform a consistent choice of orientifold involution, brane setup and gauge fluxes which leads to chiral matter and a moduli-dependent Fayet-Iliopoulos term. After D-term stabilisation, the number of Kaehler moduli is effectively …
We study ``hilltop'' curvatons that evolve on a convex potential. Hilltop curvatons evolving on the Hubble-induced potential are generic if supergravity is assumed in the theory. We do not consider curvatons whose potential is protected from $O(H)$ corrections, where $H$ is the Hubble parameter. We assume that the effective mass of a curvaton is expressed as $m_σ= c H$, where the coefficient varies within $0.2 \le c \le 5$ depending on the circumstances. A negative mass term may lead to enhancement of curvaton fluctuation, which has a significant impact on the energy bound for low-scale inflat…
We propose a novel class of F-term hybrid inflation models in supergravity (SUGRA) where the $η$-problem is resolved using either a Heisenberg symmetry or a shift symmetry of the Kaehler potential. In addition to the inflaton and the waterfall field, this class (referred to as tribrid inflation) contains a third 'driving' field which contributes the large vacuum energy during inflation by its F-term. In contrast to the ''standard'' hybrid scenario, it has several attractive features due to the property of vanishing inflationary superpotential (W_inf=0) during inflation. While the symmetries of…
We review the realization of Starobinsky-type inflation within induced-gravity Supersymmetric (SUSY) and non-SUSY models. In both cases, inflation is in agreement with the current data and can be attained for subplanckian values of the inflaton. The corresponding effective theories retain perturbative unitarity up to the Planck scale and the inflaton mass is predicted to be 3x10^13 GeV. The supergravity embedding of these models is achieved by employing two gauge singlet chiral supefields, a superpotential that is uniquely determined by a continuous R and a discrete Zn symmetry, and several (s…
We examine the theoretical possibility for the heavy QCD axion to induce slow-roll inflation while solving the strong CP problem through the Peccei-Quinn mechanism. If the cancellation between contributions from a small-size instanton and another Peccei-Quinn symmetry breaking occurs with high accuracy, the potential can be flattened enough near its maximum to achieve hilltop inflation. This comes at the cost of severe fine-tuning of their relative size and phase, but it also allows us to relate the high quality problem of the Peccei-Quinn symmetry to the fine-tuning problem of the hilltop inf…
We propose a multi-natural inflation model in which the single-field inflaton potential consists of two or more sinusoidal potentials that are comparable in size, but have different periodicity with a possible non-zero relative phase. The model is versatile enough to realize both large-field and small-field inflation. We show that, in a model with two sinusoidal potentials, the predicted values of the spectral index and tensor-to-scalar ratio lie within the $1σ$ region of the Planck data. In particular, there is no lower bound on the decay constants in contrast to the original natural inflatio…
We show that the radion in a warped geometry bounded by two branes can have a potential suitable for inflation. Our construction is based upon a solution known in string theory as the linear dilaton, in which the back-reaction from a bulk scalar Φis exactly accounted for. The radion, stabilized by Φ, is much heavier than the TeV scale and its couplings to the standard model are much more suppressed than in the usual Randall-Sundrum solution. We present a new formalism for obtaining approximate time-dependent solutions, based on perturbing the exact solution to the coupled Einstein and scalar f…
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…
We propose a solution to the eta-problem in supergravity (SUGRA) hybrid inflation using a Nambu-Goldstone-like shift symmetry within a new class of models. The flatness of the tree-level inflaton potential is ensured by shift symmetry invariance of the Kaehler potential, while a small symmetry breaking term in the superpotential gives rise to a slope of the potential at loop-level. In the proposed class of inflation models, potentially dangerous couplings between the inflaton and the moduli sector are avoided. We also discuss under which conditions the predicted spectral index can be in agreem…
We investigate how long wavelength inflationary fluctuations can cause the background field to deviate from classical dynamics. For generic potentials, we show that, in the Hartree approximation, the long wavelength dynamics can be encapsulated by a two-field model operating in an effective potential. The latter is given by a simple Gaussian integral transformation of the original inflationary potential. We use this new expression to study backreaction effects in quadratic, hilltop, flattened, and axion monodromy potentials. We find that the net result of the altered dynamics is to slightly mo…
We consider Supersymmetric (SUSY) and non-SUSY models of chaotic inflation based on the phi^n potential with n=2 or 4. We show that the coexistence of an exponential nonminimal coupling to gravity, fR=Exp(cR phi^p), with a kinetic mixing of the form fK=cK fR^m can accommodate inflationary observables favored by the Planck and Bicep2/Keck Array results for p=1 and 2, 1<=m<=15 and 2.6x10^(-3)<=rRK=cR/cK^(p/2)<=1, where the upper limit is not imposed for p=1. Inflation is of hilltop type and it can be attained for subplanckian inflaton values with the corresponding effective theories retaining th…
What new physics can we extract from inflation using the ACT DR6 and DESI DR2 Observations?
SGT University（SGT大学）；Institute of Theoretical Physics, Faculty of Physics, University of Warsaw（华沙大学物理学院理论物理研究所）；Center for Theoretical Physics, L.N. Gumilyov Eurasian National University（L.N. 古米廖夫欧亚国立大学理论物理中心）；B.M.S. College of Engineering（B.M.S.工程学院）
We consider models of chaotic inflation driven by the real parts of a conjugate pair of Higgs superfields involved in the spontaneous breaking of a grand unification symmetry at a scale assuming its Supersymmetric value. Employing Kaehler potentials with a prominent shift-symmetric part proportional to c- and a tiny violation, proportional to c+, included in a logarithm we show that the inflationary observables provide an excellent match to the recent Planck and Bicep2/Keck Array results setting, e.g., 0.0064<= c+/c-<1/N where N=2 or 3 is the prefactor of the logarithm. Deviations of these pre…
