Conventional wisdom says that a chaotic inflation model with a power-law potential is ruled out by the recent Planck-BICEP/Keck results. We find, however, that the model can be assisted by a non-minimally coupled scalar field and still provides a successful inflation. Considering a power-law chaotic inflation model of the type $V\sim φ^n$ with $n=\{2, 4/3, 1, 2/3, 1/3\}$, we show that $n=1/3$ ($n=\{2/3, 1/3\}$) may be revived with the help of the quadratic (quartic) non-minimal coupling of the assistant field to gravity.
The $β$-exponential inflation is driven by a class of primordial potentials, derived in the framework of braneworld scenarios, that generalizes the well-known power law inflation. In this paper we update previous constraints on the minimal coupled $β$-exponential model [1] and extend the results also deriving the equations for the non-minimal coupled scenario. The predictions of both models are tested in light of the latest temperature and polarization maps of the Cosmic Microwave Background and clustering data. We also compare the predictions of these models with the standard $Λ$CDM cosmology…
We consider two classes of non-minimally coupled inflation models; those with a quadratic coupling of the inflaton to gravity, and the `Universal Attractor' models where the coupling is connected to the potential. We make a detailed analysis of the attractor structure in the latter case, identifying a shift of the attractor from the Starobinsky point and determining conditions for approach to the attractor. We then assess the viability of the models under different interpretations of the BICEP2 experiment's detection of B-mode polarisation, finding strong constraints on the non-minimal couplin…
We derive the general formulae for the the scalar and tensor spectral tilts to the second order for the inflationary models with non-minimally derivative coupling without taking the high friction limit. The non-minimally kinetic coupling to Einstein tensor brings the energy scale in the inflationary models down to be sub-Planckian. In the high friction limit, the Lyth bound is modified with an extra suppression factor, so that the field excursion of the inflaton is sub-Planckian. The inflationary models with non-minimally derivative coupling are more consistent with observations in the high fr…
We consider the late time one-loop quantum backreaction from inflationary fluctuations of a non-minimally coupled, massless scalar field. The scalar is assumed to be a spectator field in an inflationary model with a constant principal slow roll $ε$ parameter. We regulate the infrared by matching onto a pre-inflationary radiation era. We find a large late time backreaction when the nonminimal coupling $ξ$ is negative (in which case the scalar exhibits a negative mass term during inflation). The one-loop quantum backreaction becomes significant today for moderately small non-minimal couplings, $…
We argue that double inflation may occur when a spectator field is non-minimally coupled to gravity. As a concrete example, we study a two-field inflationary model where the initial spectator field is non-minimally coupled to gravity while the initial inflaton field is minimally coupled. The non-minimal coupling results in the growth of the spectator field which, in turn, drives the second stage of inflation in a significant region of parameter space. The isocurvature fluctuations originating from the spectator field source adiabatic ones, and hence the spectator non-minimal coupling can modif…
We have investigated inflationary model constructed from minimally modified gravity (MMG) theories. The MMG theory in the form of $f({\bf H}) \propto {\bf H}^{1+p}$ gravity where, ${\bf H}$ is the Hamiltonian constraint in the Einstein gravity and $p$ is constant, has been studied. An inflation is difficult to be achieved in this theory of gravity unless an additional scalar field playing a role of inflaton is introduced in the model. We have found that the inflaton with exponential potential can drive inflation with graceful exist different from the case of Einstein gravity. The slow-roll par…
The action of loop quantum gravity includes the Holst term and/or the Nieh-Yan term in addition to the Ricci scalar. These terms are expected to couple non-minimally to the Higgs. Thus the Holst and Nieh-Yan terms contribute to the classical equations of motion, and they can have a significant impact on inflation. We derive inflationary predictions in the parameter space of the non-minimal couplings, including non-minimally coupled terms up to dimension 4. Successful inflation is possible even with zero or negative coupling of the Ricci scalar. Notably, inflation supported by the non-minimally…
We study the inflation in a model with a Gauss-Bonnet term which is non-minimally coupled to a DBI field. We study the spectrum of the primordial perturbations in detail. The non-Gaussianity of this model is considered and the amplitude of the non-Gaussianity is studied in both the equilateral and orthogonal configurations. By taking various functions of the DBI field, inflaton potential and the Gauss-Bonnet coupling term, we test the model with observational data and find some constraints on the Gauss-Bonnet coupling parameter.
We consider inflation within the context of what is arguably the simplest non-metric extension of Einstein gravity. There non-metricity is described by a single graviscalar field with a non-minimal kinetic coupling to the inflaton field $Ψ$, parameterized by a single parameter $γ$. We discuss the implications of non-metricity for chaotic inflation and find that it significantly alters the inflaton dynamics for field values $Ψ\gtrsim M_P/γ$, dramatically changing the qualitative behaviour in this regime. For potentials with a positive slope non-metricity imposes an upper bound on the possible n…
We study chaotic inflation with a Galileon-like self interaction $G(ϕ,X)\Box ϕ$, where $G(ϕ,X)\propto X^{n}$. General conditions required for successful inflation are deduced and discussed from the background and cosmological perturbations under slow-roll approximation. Interestingly, it is found that in the regime where the Galileon term dominates over the standard kinetic term, the tensor-to-scalar ratio becomes significantly suppressed in comparison to the standard expression in General Relativity (GR). Particularly, we find the allowed range in the space of parameters characterizing the ch…
The inflationary dynamics and preheating in a model with a non-minimally coupled inflaton field in the metric and Palatini formalisms are studied in this paper. We find that in both formalisms, irrespective of the initial conditions, our Universe will evolve into a slow-roll inflationary era and then the scalar field rolls into an oscillating phase. The value of the scalar field at the end of the inflation in the Palatini formalism is always larger than that in the metric one, which becomes more and more obvious with the increase of the absolute value of the coupling parameter $|ξ|$. During th…
Inflation due to a non-minimally coupled scalar field with a large non-minimal coupling, as first proposed by Salopek, Bardeen and Bond (SBB), is in good agreement with the observed value of the spectral index and constraints on the tensor-to-scalar ratio. Here we explore the possibility that SBB inflation represents the late stage of a Universe which emerges from an early contracting era. We present a model in which the Universe smoothly transitions from an anamorphic contracting era to late-time SBB inflation without encountering a singular bounce. This corresponds to a continuous expansion …
We calculate the quantum gravitational corrections to the Mukhanov-Sasaki equation obtained by the canonical quantization of the inflaton-gravity system. Our approach, which is based on the Born-Oppenheimer decomposition of the resulting Wheeler-DeWitt equation, was previously applied to a minimally coupled inflaton. In this article we examine the case of a non minimally coupled inflaton and, in particular, the induced gravity case is also discussed. Finally, the equation governing the quantum evolution of the inflationary perturbations is derived on a de Sitter background. Moreover the proble…
In this work, we show the effect of the non-minimal coupling $ξϕ^2 R$ on the inflationary parameters by considering the single-field inflation and present the inflationary predictions of the appealing potential for the particle physics viewpoint: Natural Inflation, an axion-like inflaton which has a cosine-type periodic potential and the inflaton naturally emerges as a pseudo-Nambu-Goldstone boson with a spontaneously broken global symmetry. We present the inflationary predictions for this potential, $n_s$, $r$, and $α=\mathrm{d}n_s/\mathrm{d}\ln k$. In addition, we assume standard thermal his…
Inflationary dynamics of non-minimally coupled $f(R)$ matter-curvature theories
Universidade do Porto（波尔图大学）；Centro de Física das Universidades do Minho e do Porto（米尼奥与波尔图大学物理中心）；Faculdade de Ciências e Tecnologia da Universidade de Coimbra（科英布拉大学科学与技术学院）
本研究探讨了非最小耦合 f(R) 理论对膨胀动力学的影响，发现负耦合模型可容纳稳定 de Sitter 解，并约束非最小耦合尺度高于 10^13 GeV。
We consider the non-supersymmetric models of chaotic (driven by a quadratic potential) and hybrid inflation, taking into account the minimal possible radiative corrections to the inflationary potential. We show that two simple coupling functions f(sigma) (with a parameter ck involved) between the inflaton field, sigma, and the Ricci scalar curvature ensure, for sub-Planckian values of the inflaton field, observationally acceptable values for the spectral index, ns, and sufficient reheating after inflation. In the case of chaotic inflation we consider two models with large ck's resulting to ns=…
We, in the first part, contemplate a massless minimally coupled scalar which is Yukawa-coupled to a massless Dirac fermion in a locally de Sitter background of an inflating spacetime. We compute the scalar's quantum corrected mode function, power spectrum, spectral index and the running of the spectral index at one-loop order. We find that the spectrum is slightly blue-tilted; hence, the amplitudes of fluctuations grow slightly toward the smaller scales. Then, in the second part, we apply the computation method used in the first part to a massless minimally coupled scalar with a quartic self-i…
We consider inflation driven by an axion-like particle coupled to an SU(2) gauge sector via a Chern-Simons term. Known as chromo-natural inflation, this scenario is in tension with CMB observations. In order to remedy this fact and preserve both the symmetries and the intriguing gravitational wave phenomenology exhibited by the model, we explore the non-minimal coupling of the axion-inflaton to the Einstein tensor. We identify regions of parameter space corresponding to a viable cosmology at CMB scales. We also highlight the possibility of a large and chiral gravitational wave signal at small …
We use the most recent cosmic microwave background (CMB) data to perform a Bayesian statistical analysis and discuss the observational viability of inflationary models with a non-minimal coupling,~$ξ$, between the inflaton field and the Ricci scalar. We particularize our analysis to two examples of small and large field inflationary models, namely, the Coleman-Weinberg and the chaotic quartic potentials. We find that (i) the $ξ$ parameter is closely correlated with the primordial amplitude; (ii) although improving the agreement with the CMB data in the $r - n_s$ plane, where $r$ is the tensor-…
We consider the non-minimal model of gravity in $Y(R) F^2$-form. We investigate a particular case of the model, for which the higher order derivatives are eliminated but the scalar curvature $R$ is kept to be dynamical via the constraint $Y_RF_{mn}F^{mn} =-\frac{2}{κ^2}$. The effective fluid obtained can be represented by interacting electromagnetic field and vacuum depending on $Y(R)$, namely, the energy density of the vacuum tracks $R$ while energy density of the conventional electromagnetic field is dynamically scaled with the factor $\frac{Y(R)}{2}$. We give exact solutions for anisotropic…
We show that an inflationary background might be realized by using any p-form non-minimally coupled to gravity. Standard scalar field inflation corresponds to the 0-form case and vector inflation to the 1-form. Moreover, we show that the 2- and 3-form fields are dual to a new vector and scalar inflationary theories where the kinetic terms are non-minimally coupled to gravity.
In this work, we revisit the Witten-O'Raifeartaigh model of inflation, in which the potential takes a $\operatorname{log}^2(ϕ/M)$ form, when the scalar field is non-minimally coupled to gravity. We investigate the impact of the coupling in the prediction of the inflationary parameters, thereby affecting the viability of the model. We find that a small coupling of order $ξ\sim10^{-3}$ is preferred by data at the $n_s-r$ plane level, and that the presence of a non-zero $ξ$ allows for a large interval of the mass scale $M$, in which it is possible to achieve a low tensor-to-scalar ratio. We also …
We describe a simple model of chaotic inflation in supergravity where one can easily tune not only the basic cosmological parameters such as n_{s}, r, and f_NL, but also a possible (subdominant) cosmic string contribution to the CMB anisotropy.
We illustrate a framework for constructing models of chaotic inflation where the inflaton is the position of a D3 brane along the universal cover of a string compactification. In our scenario, a brane rolls many times around a non-trivial one-cycle, thereby unwinding a Ramond-Ramond flux. These "flux monodromies" are similar in spirit to the monodromies of Silverstein, Westphal, and McAllister, and their four-dimensional description is that of Kaloper and Sorbo. Assuming moduli stabilization is rigid enough, the large-field inflationary potential is protected from radiative corrections by a di…
This thesis presents research exploring aspects of inflation and cosmology in the context of inflation models in which an inflaton is non-minimally coupled to the Ricci scalar, or is considered in conjunction with a term quadratic in the Ricci scalar. We consider a $ϕ^{2}$ Palatini inflation model in $R^{2}$ gravity and investigate whether this model can overcome some of the problems of the original $ϕ^{2}$ chaotic inflation model. We investigate the compatibility of this model with the observed CMB when treated as an effective theory of inflation in quantum gravity by examining the constraint…
We investigate the effect of adiabatic regularization on both the tensor- and scalar-perturbation power spectra in \textit{nonminimally} coupled chaotic inflation. Similar to that of the \textit{minimally} coupled general single-field inflation, we find that the subtraction term is suppressed by an exponentially decaying factor involving the number of $ e $-folds. By following the subtraction term long enough beyond horizon crossing, the regularized power spectrum tends to the "bare" power spectrum. This study justifies the use of the unregularized ("bare") power spectrum in standard calculati…
We investigate inflationary attractor points by analyzing non-minimally coupled single field inflation models in two opposite limits; the `flat' limit in which the first derivative of the conformal factor is small and the `steep' limit, in which the first derivative of the conformal factor is large. We consider a subset of models that yield Starobinsky inflation in the steep conformal factor, strong coupling, limit and demonstrate that they result in chaotic inflation in the opposite flat, weak coupling, limit. The suppression of higher order powers of the inflaton field in the potential is sh…
In this work we investigate the inflationary era in the presence of a canonical scalar field and Chern-Simons parity violating corrections. It was also assumed that a non minimal coupling between curvature and the scalar field is present. For the shake of completeness, the slow-roll and the constant-roll scenarios were examined separately. In the context of this scalar-tensor theory, inflation can be viable for both scenarios since the observational indices take acceptable values according to the most recent Planck data. Furthermore, the involvement of the Chern-Simons term has no effect on th…
In this work we introduce a new plateau-like inflationary model including a quadratic scalar potential coupled non-minimally to gravity. This potential has a dominant constant energy density at early times which can realize successful inflation. It also includes an infinitesimal non-zero term $V_0$ responsible for explaining dark energy which causing the universe to expand accelerating at the late time. We show that this model predicts small tensor-to-scalar ratio of the order of $r\approx 0.01$ which is fully consistent with Planck constraints. Using the lower and upper bounds on reheating te…
We discuss the hybrid inflation model where the inflaton field is nonminimally coupled to gravity. In the Jordan frame, the potential contains $ϕ^4$ term as well as terms in the original hybrid inflation model. In our model, inflation can be classified into the type (I) and the type (II). In the type (I), inflation is terminated by the tachyonic instability of the waterfall field, while in the type (II) by the violation of slow-roll conditions. In our model, the reheating takes place only at the true minimum and even in the case (II) finally the tachyonic instability occurs after the terminati…
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 show that "spiralized" models of new-inflation can be experimentally identified mostly by their positive spectral running in direct contrast with most chaotic-inflation models which have negative runnings typically in the range of $\mathcal{O}(10^{-4}-10^{-3})$.
We discuss the general structure and observational consequences of some of the simplest versions of chaotic inflation in supergravity in relation to the data by Planck 2013 and BICEP2. We show that minimal modifications to the simplest quadratic potential are sufficient to provide a controllable tensor mode signal and a suppression of CMB power at large angular scales.
It is well known that light scalar fields present during inflation are coherently excited. We show that if the field couples to gravity in a non-minimal way, the fluctuations at large scales are suppressed with respect to the small scales ones. This fact allows for the field excitations to make a sizeable contribution to the energy density of the universe without generating too large isocurvature fluctuations at observable scales. We show that this mechanism could generate all the observed dark matter and study the main cosmological implications of this setup.
We show that a non-minimal coupling to gravity can not only make some inflationary models consistent with cosmological data, similar to the case of Higgs inflation, but can also invoke slow-roll violation to realize graceful exit from inflation. In particular, this is the case in models where a destabilizing mechanism that ends inflation should be assumed when the model is minimally coupled to gravity. As explicit examples, we consider the power-law and inverse monomial inflation models with a non-minimal coupling to gravity. While these models are excluded in the minimally coupled case, we sh…
We discuss how the non-minimal coupling $ξϕ^2 R$ between the inflaton and the Ricci scalar affects predictions of single field inflation models in Palatini formalism. To transition radiation dominated era, the inflaton field $ϕ$ must interact to matter fields at the end of inflation. Interactions of the inflaton with other fields lead to radiative corrections to the inflationary potential. These radiative corrections can be explained at leading order by Coleman-Weinberg (CW) one-loop corrections. In this work, using two different prescriptions debated in the literature, the effect of radiative…
A classical evolution in chaotic inflationary models starts at high energy densities with semi-classical initial conditions presumably consistent with universal quantum nature of all the fundamental forces. That is each quantum contributes the same amount to the energy density. We point out the upper limit on this amount inherent in this approach, so that all the quanta are inside the weak-coupling domain. We discuss this issue in realistic models with modified gravity, $R^2$- and Higgs-inflations, emphasizing the specific change of the initial conditions with metric frame, while all the quant…
We study a nonminimal derivative inflationary model in the presence of the Gauss-Bonnet term. To have a complete treatment of the model, we consider a general form of the nonminimal derivative function and also the Gauss-Bonnet coupling term. By following the ADM formalism, expanding the action up to the third order in the perturbations and using the correlation functions, we study the perturbation and its non-Gaussian feature in details. We also study the consistency relation that gets modified in the presence of the Gauss-Bonnet term in the action. We compare the results of our consideration…
We explore the inflationary phase of a scalar field with a kinetic term non-minimally coupled to gravity. We find that one of the slow-roll conditions is naturally consequence of the equation of motion of the scalar field. Thus, slow-roll conditions impose fewer constraints on potentials than other inflationary models. Moreover, it is demonstrated that the inflationary phase can be described by just one slow-roll parameter. By investigating the metric perturbations, it is shown that except for one potential, almost all potentials have the same pattern in the ($n_{s}$, $r$) plane. We provide an…
Non-minimally coupled loop quantum inflation with inverse-volume corrections
Universidad de Tarapacá（塔拉帕卡大学）；Pontificia Universidad Católica de Valparaíso（瓦帕莱索天主教 Pontificia 大学）；Università degli Studi di Napoli “Federico II”（那不勒斯费德里科二世大学）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）
If the recent measurement of B-mode polarization by BICEP2 is due to primordial gravitational waves, it implies that inflation was driven by energy densities at the GUT scale $M_{GUT} \sim 2\times 10^{16} GeV$. This favors single-field chaotic inflation models. These models require transplanckian excursions of the inflaton, forcing one to address the UV completion of the theory. We use a benchmark 4d effective field theory of axion-4-form inflation to argue that inflation driven by a quadratic potential (with small corrections) is well motivated in the context of high-scale string theory model…
We introduce a new class of models of chaotic inflation inspired by the superconformal approach to supergravity. This class of models allows a functional freedom of choice of the inflaton potential V = |f(ϕ)|^2. The simplest model of this type has a quadratic potential m^2ϕ^2/2. Another model describes an inflaton field with the standard symmetry breaking potential λ^2 (ϕ^2-v^2)^2. Depending on the value of v and on initial conditions for inflation, the spectral index n_s may take any value from 0.97 to 0.93, and the tensor-to-scalar ratio r may span the interval form 0.3 to 0.01. A generalize…
We propose a chaotic inflation model in supergravity based on polynomial interactions of the inflaton. Specifically we study the chaotic inflation model with quadratic, cubic and quartic couplings in the scalar potential and show that the predicted scalar spectral index and tensor-to-scalar ratio can lie within the 1 sigma region allowed by the Planck results.
In this paper, we consider a chaotic inflation model where the role of inflaton is played by the Higgs triplet in type II seesaw mechanism for generating the small masses of left-handed neutrinos. Leptogenesis could happen after inflation. This model is constructed without introducing supersymmetry (SUSY).
When considered in the Palatini formalism, the Starobinsky model does not provide us with a mechanism for inflation due to the absence of a propagating scalar degree of freedom. By (non)--minimally coupling scalar fields to the Starobinsky model in the Palatini formalism we can in principle describe the inflationary epoch. In this article, we focus on the minimally coupled quartic and natural inflation models. Both theories are excluded in their simplest realization since they predict values for the inflationary observables that are outside the limits set by the Planck data. However, with the …
Non-Minimally Coupled Warm Inflation in the Defining Frame
Center for Physical Sciences and Technology (FTMC)（立陶宛物理与工程技术中心）；Faculdade de Ciências e Tecnologia and CFisUC, Departamento de Física, Universidade de Coimbra（科英布拉大学科学与技术学院及CFisUC物理系）
I describe the first model of chaotic inflation in supergravity, which was proposed by Goncharov and the present author in 1983. The inflaton potential of this model has a plateau-type behavior $V_{0} (1- {8\over 3}\, e^{-\sqrt 6 |ϕ|})$ at large values of the inflaton field. This model predicts $n_{s} = 1-{2\over N} \approx 0.967$ and $r = {4\over 3 N^{2}} \approx 4 \times 10^{-4}$, in good agreement with the Planck data. I propose a slight generalization of this model, which allows to describe not only inflation but also dark energy and supersymmetry breaking.
The phase-integral approximation devised by Fröman and Fröman, is used for computing cosmological perturbations in the quartic chaotic inflationary model. The phase-integral formulas for the scalar power spectrum are explicitly obtained up to fifth order of the phase-integral approximation. As in previous reports [1-3], we point out that the accuracy of the phase-integral approximation compares favorably with the numerical results and those obtained using the slow-roll and uniform approximation methods.
Chaotic inflation based on a simple monomial scalar potential, V(phi) ~ phi^p, is an attractive large-field model of inflation capable of generating a sizable tensor-to-scalar ratio r. Therefore, assuming that future CMB observations will confirm the large r value reported by BICEP2, it is important to determine what kind of dynamical mechanism could possibly endow the inflaton field with such a simple effective potential. In this paper, we answer this question in the context of field theory, i.e. in the framework of dynamical chaotic inflation (DCI), where strongly interacting supersymmetric …
Non-Minimally Coupled Chain Inflation at High Scales
Universidade do Porto（波尔图大学）；Centro de Física das Universidades do Minho e do Porto（米尼奥大学和波尔图大学物理中心）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Stockholm University（斯德哥尔摩大学）；Harvard University（哈佛大学）
A model of chaotic inflation based on the theory of a scalar field with potential λϕ^4 perfectly matches the observational data if one adds to it a tiny non-minimal coupling to gravity -ξ/2 ϕ^2 R with ξ> 0.002. We describe embedding of this model into the superconformal theory with spontaneous breaking of superconformal symmetry, and into supergravity. A model with small ξis technically natural: setting the small parameter ξto zero leads to a point of enhanced symmetry in the underlying superconformal theory.
We revisit a polynomial chaotic inflation model in supergravity which we proposed soon after the Planck first data release. Recently some issues have been raised in Ref.[12], concerning the validity of our polynomial chaotic inflation model. We study the inflaton dynamics in detail, and confirm that the inflaton potential is very well approximated by a polynomial potential for the parameters of our interest in any practical sense, and in particular, the spectral index and the tensor-to-scalar ratio can be estimated by single-field approximation. This justifies our analysis of the polynomial ch…
We point out that the prediction of the minimal chaotic inflation model is altered if a scalar field takes a large field value close to the Planck scale during inflation due to a negative Hubble induced mass. In particular, we show that the inflaton potential is effectively suppressed at a large inflaton field value in the presence of such a scalar field. The scalar field may be identified with the standard model Higgs field or flat directions in supersymmetric theory. With such spontaneous suppression, we find that the minimal chaotic inflation model, especially the model with a quadratic pot…
We consider the renormalization group improvement in the theory of the Standard Model Higgs boson playing the role of an inflaton with a strong non-minimal coupling to gravity. It suggests the range of the Higgs mass $135.6 {\rm GeV} \lesssim M_H\lesssim 184.5 {\rm GeV}$ compatible with the current CMB data (the lower WMAP bound on $n_s$), which is close to the widely accepted range dictated by the electroweak vacuum stability and perturbation theory bounds. We find the phenomenon of asymptotic freedom induced by this non-minimal curvature coupling, which brings the theory to the weak coupling…
The BICEP2 collaboration has recently reported a large tensor fluctuation in the cosmic microwave background, which suggests chaotic inflation models. In this letter, we reconsider the chaotic inflation model in the supergravity. We introduce a non-holomorphic shift-symmetry breaking parameter, which we expect to exist in general, and discuss its effect on the inflaton dynamics. We show that the model predicts a sizable deviation from the original chaotic inflation model and the predicted tensor fluctuation can lie between the BICEP2 result and the upper bound given by the Planck experiment wi…
