We present new constraints on spectator axion-${\rm U}(1)$ gauge field interactions during inflation using the latest $Planck$ (PR4) and BICEP/Keck 2018 data releases. This model can source tensor perturbations from amplified gauge field fluctuations, driven by an axion rolling for a few e-folds during inflation. The gravitational waves sourced in this way have a strongly scale-dependent (and chiral) spectrum, with potentially visible contributions to large/intermediate scale $B$-modes of the CMB. We first derive theoretical bounds on the model imposing validity of the perturbative regime and negligible backreaction of the gauge field on the background dynamics. Then, we determine bounds from current CMB observations, adopting a frequentist profile likelihood approach. We study the behaviour of constraints for typical choices of the model's parameters, analyzing the impact of different dataset combinations. We find that observational bounds are competitive with theoretical ones and together they exclude a significant portion of the model's parameter space. We argue that the parameter space still remains large and interesting for future CMB experiments targeting large/intermediate scales $B$-modes.
We discuss implications of the latest BICEP/Keck data release for inflationary models, with special emphasis on the cosmological attractors which can describe all presently available inflation-related observational data. These models are compatible with any value of the tensor to scalar ratio $r$, all the way down to $r = 0$. Some of the string theory motivated models of this class predict $10^{-3} \leq r \leq 10^{-2}$. The upper part of this range can be explored by the ongoing BICEP/Keck observations.
In this paper we demonstrate that in the context of mimetic $F(R)$ gravity with Lagrange multiplier, it is possible to realize cosmologies which are compatible with the recent BICEP2/Keck Array data. We provide some characteristic examples for which the predicted scalar to tensor ratio can be quite smaller in comparison to the upper limit imposed by the BICEP2/Keck Array observations.
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…
The recent results of the BICEP and Keck collaborations have put stringent bounds on many inflationary models, including some well-motivated ones. This is certainly the case when gravity remains described by Einstein's theory up to the inflationary scale, but can be avoided by introducing quadratic-in-curvature terms that are effective at that scale. Recently it has also been shown that these terms can UV complete gravity respecting stability and unitarity. Here the predictions of such quadratic gravity are computed and compared with the BICEP/Keck constraints by focusing on some of the inflat…
A joint analysis of data collected by the Planck and BICEP2+Keck teams has previously given $r = 0.09^{+0.06}_{-0.04}$ for BICEP2 and $r = 0.02^{+0.04}_{-0.02}$ for Keck. Analyzing BICEP2 using its published noise estimate, we had earlier (Colley & Gott 2015) found $r = 0.09 \pm 0.04$, agreeing with the final joint results for BICEP2. With the Keck data now available, we have done something the joint analysis did not: a correlation study of the BICEP2 vs. Keck B-mode maps. Knowing the correlation coefficient between the two and their amplitudes allows us to determine the noise in each map (whi…
We derive a new upper bound on the tensor-to-scalar ratio parameter $r$ using the frequentist profile likelihood method. We vary all the relevant cosmological parameters of the $Λ$CDM model, as well as the nuisance parameters. Unlike the Bayesian analysis using Markov Chain Monte Carlo (MCMC), our analysis is independent of the choice of priors. Using $Planck$ Public Release 4, BICEP/Keck Array 2018, $Planck$ CMB lensing, and BAO data, we find an upper limit of $r<0.037$ at 95% C.L., similar to the Bayesian MCMC result of $r<0.038$ for a flat prior on $r$ and a conditioned $Planck$ lowlEB cova…
Recent BICEP/Keck data on the cosmic microwave background, in combination with previous WMAP and Planck data, impose strong new constraints on the tilt in the scalar perturbation spectrum, $n_s$, as well as the tensor-to-scalar ratio, $r$. These constrain the number of e-folds of inflation, $N_*$, the magnitude of the inflaton coupling to matter, $y$, and the reheating temperature, $T_{\rm reh}$, which we evaluate in attractor models of inflation as formulated in no-scale supergravity. The 68% C.L. region of $(n_s, r)$ favours large values of $N_*, y$ and $T_{\rm reh}$ that are constrained by …
The Hubble tension that the standard $Λ$CDM model is suffering from can be resolved with pre-recombination early dark energy. We present the first constraint on the tensor-to-scalar ratio $r$ in corresponding Hubble-tension-free cosmologies using the most recent BICEP/Keck cosmic microwave background (CMB) B-mode polarization data. We find, combining BICEP/Keck with Planck18 CMB and baryon acoustic oscillation data, that the models with larger Hubble constant $H_0$ will have tighter upper bound on $r$, and resolution $H_0\sim73$ km/s/Mpc of the Hubble tension tightens the upper bound to $r<0.0…
We consider observational limits on a proposed model of the string landscape in inflation. In this scenario, effects from the decoherence of entangled quantum states in long-wavelength modes in the universe result in modifications to the Friedmann Equation and a corresponding modification to inflationary dynamics. Previous work by Holman, Mersini-Houghton, and Takahashi suggested that such effects could provide an explanation for well-known anomalies in the Cosmic Microwave Background (CMB), such as the lack of power on large scales and the "cold spot" seen by both the WMAP and Planck satellit…
Supersymmetric versions of induced-gravity inflation are formulated within Supergravity (SUGRA) employing two gauge singlet chiral superfields. The proposed superpotential is uniquely determined by applying a continuous R and a discrete Z_2 symmetry. We also employ a logarithmic Kahler potential respecting the symmetries above and including all the allowed terms up to fourth order in powers of the various fields. When the Kahler manifold exhibits a no-scale-type symmetry, the model predicts spectral index ns=0.963 and tensor-to-scalar r=0.004. Beyond no-scale SUGRA, ns and r depend crucially o…
Comment on: "Third-order corrections to the slow-roll expansion: Calculation and constraints with Planck, ACT, SPT, and BICEP/Keck [2025 PDU 47 101813]"
Institut d’Astrophysique de Paris（巴黎天体物理学研究所）；University of Louvain（鲁汶大学）
We examine further the ability of the New Early Dark Energy model (NEDE) to resolve the current tension between the Cosmic Microwave Background (CMB) and local measurements of $H_0$ and the consequences for inflation. We perform new Bayesian analyses, including the current datasets from the ground-based CMB telescopes Atacama Cosmology Telescope (ACT), the South Pole Telescope (SPT), and the BICEP/Keck telescopes, employing an updated likelihood for the local measurements coming from the S$H_0$ES collaboration. Using the S$H_0$ES prior on $H_0$, the combined analysis with Baryonic Acoustic Osc…
The QCD axion solving the strong CP problem may originate from antisymmetric tensor gauge fields in compactified string theory, with a decay constant around the GUT scale. Such possibility appears to be ruled out now by the detection of tensor modes by BICEP2 and the PLANCK constraints on isocurvature density perturbations. A more interesting and still viable possibility is that the string theoretic QCD axion is charged under an anomalous U(1)_A gauge symmetry. In such case, the axion decay constant can be much lower than the GUT scale if moduli are stabilized near the point of vanishing Fayet…
BICEP/Keck XX: Component-separated maps of polarized CMB and thermal dust emission using Planck and BICEP/Keck Observations through the 2018 Observing Season
The polarization of cosmic microwave background (CMB) can be used to constrain cosmological birefringence, the rotation of the linear polarization of CMB photons potentially induced by parity violating physics beyond the standard model. This effect produces non-null CMB cross correlations between temperature and B mode-polarization, and between E- and B-mode polarization. Both cross-correlations are otherwise null in the standard cosmological model. We use the recently released 2015 Planck likelihood in combination with the Bicep2/Keck/Planck (BKP) likelihood to constrain the birefringence ang…
BICEP3 is a 520 mm aperture, compact two-lens refractor designed to observe the polarization of the cosmic microwave background (CMB) at 95 GHz. Its focal plane consists of modularized tiles of antenna-coupled transition edge sensors (TESs), similar to those used in BICEP2 and the Keck Array. The increased per-receiver optical throughput compared to BICEP2/Keck Array, due to both its faster f/1.7 optics and the larger aperture, more than doubles the combined mapping speed of the BICEP/Keck program. The BICEP3 receiver was recently upgraded to a full complement of 20 tiles of detectors (2560 TE…
We present results from an analysis of all data taken by the BICEP2, Keck Array and BICEP3 CMB polarization experiments up to and including the 2018 observing season. We add additional Keck Array observations at 220 GHz and BICEP3 observations at 95 GHz to the previous 95/150/220 GHz data set. The $Q/U$ maps now reach depths of 2.8, 2.8 and 8.8 $μ{\mathrm K}_{cmb}$ arcmin at 95, 150 and 220 GHz respectively over an effective area of $\approx 600$ square degrees at 95 GHz and $\approx 400$ square degrees at 150 & 220 GHz. The 220 GHz maps now achieve a signal-to-noise on polarized dust emission…
We reconstruct scalar field theories to realize inflation compatible with the BICEP2 result as well as the Planck. In particular, we examine the chaotic inflation model, natural (or axion) inflation model, and an inflationary model with a hyperbolic inflaton potential. We perform an explicit approach to find out a scalar field model of inflation in which any observations can be explained in principle.
The BICEP2 and Keck Array experiments are designed to measure the polarization of the cosmic microwave background (CMB) on angular scales of 2-4 degrees (l=50-100). This is the region in which the B-mode signal, a signature prediction of cosmic inflation, is expected to peak. BICEP2 was deployed to the South Pole at the end of 2009 and is in the middle of its third year of observing with 500 polarization-sensitive detectors at 150 GHz. The Keck Array was deployed to the South Pole at the end of 2010, initially with three receivers--each similar to BICEP2. An additional two receivers have been …
We investigate the axion dark matter scenario (ADM), in which axions account for all of the dark matter in the Universe, in light of the most recent cosmological data. In particular, we use the Planck temperature data, complemented by WMAP E-polarization measurements, as well as the recent BICEP2 observations of B-modes. Baryon Acoustic Oscillation data, including those from the Baryon Oscillation Spectroscopic Survey, are also considered in the numerical analyses. We find that, in the minimal ADM scenario, the full dataset implies that the axion mass m_a = 82.2 pm 1.1 μeV (corresponding to th…
The BICEP and Keck Array experiments are a suite of small-aperture refracting telescopes observing the microwave sky from the South Pole. They target the degree-scale B-mode polarization signal imprinted in the Cosmic Microwave Background (CMB) by primordial gravitational waves. Such a measurement would shed light on the physics of the very early universe. While BICEP2 observed for the first time a B-mode signal at 150 GHz, higher frequencies from the Planck satellite showed that it could be entirely due to the polarized emission from Galactic dust, though uncertainty remained high. Keck Array…
We present results from an analysis of all data taken by the BICEP2/Keck CMB polarization experiments up to and including the 2015 observing season. This includes the first Keck Array observations at 220 GHz and additional observations at 95 & 150 GHz. The $Q/U$ maps reach depths of 5.2, 2.9 and 26 $μ$K$_{cmb}$ arcmin at 95, 150 and 220 GHz respectively over an effective area of $\approx 400$ square degrees. The 220 GHz maps achieve a signal-to-noise on polarized dust emission approximately equal to that of Planck at 353 GHz. We take auto- and cross-spectra between these maps and publicly avai…
BICEP3 is a $550~mm$ aperture telescope with cold, on-axis, refractive optics designed to observe at the $95~GHz$ band from the South Pole. It is the newest member of the BICEP/Keck family of inflationary probes specifically designed to measure the polarization of the cosmic microwave background (CMB) at degree-angular scales. BICEP3 is designed to house 1280 dual-polarization pixels, which, when fully-populated, totals to $\sim$9$\times$ the number of pixels in a single Keck $95~GHz$ receiver, thus further advancing the BICEP/Keck program's $95~GHz$ mapping speed. BICEP3 was deployed during t…
Constraints on non-canonical chaotic inflation from ACT DR6 and BICEP/Keck data
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；Key Laboratory of Aerospace Information Materials and Physics (NUAA), MIIT（工业和信息化部航空航天信息材料与物理重点实验室）
We examine the statistical properties of polarization maps from Planck 2018 within the patch of sky observed by the BICEP2/Keck experiment using the one point distribution function (1PDF), skewness, and kurtosis statistics. Our analysis is performed for the Q and U Stokes parameters and for the corresponding E- and B-modes of the CMB signals. We extend our analysis by studying the correlations between CMB polarization maps and residual maps (the difference between the full signal and the CMB map) for the frequency range of 100--217 GHz with both the Q/U and E/B approaches. Although all the CMB…
We report on the design and performance of the BICEP3 instrument and its first three-year data set collected from 2016 to 2018. BICEP3 is a 52cm aperture, refracting telescope designed to observe the polarization of the cosmic microwave background (CMB) on degree angular scales at 95GHz. It started science observation at the South Pole in 2016 with 2400 antenna-coupled transition-edge sensor (TES) bolometers. The receiver first demonstrated new technologies such as large-diameter alumina optics, Zotefoam infrared filters, and flux-activated SQUIDs, allowing $\sim 10\times$ higher optical throu…
We explore the thermal light sterile neutrino situation from cosmological perspective in the $Λ\textrm{CDM} + r_{0.05} + N_{\textrm{eff}} + m^{\textrm{eff}}_{\textrm{s}}$ model using combinations of latest data sets available. Here, $r_{0.05}$ is the tensor-to-scalar ratio at the pivot scale of $k_*=0.05h$ Mpc$^{-1}$, $N_{\textrm{eff}}$ is the effective number of relativistic species during recombination, and $m^{\textrm{eff}}_{\textrm{s}}$ is the effective mass of the sterile neutrino. Among Cosmic Microwave Background (CMB) datasets, we use Planck 2015 temperature and low-$l$ ($l <$ 30) pola…
BICEP3 is a 550 mm-aperture refracting telescope for polarimetry of radiation in the cosmic microwave background at 95 GHz. It adopts the methodology of BICEP1, BICEP2 and the Keck Array experiments - it possesses sufficient resolution to search for signatures of the inflation-induced cosmic gravitational-wave background while utilizing a compact design for ease of construction and to facilitate the characterization and mitigation of systematics. However, BICEP3 represents a significant breakthrough in per-receiver sensitivity, with a focal plane area 5$\times$ larger than a BICEP2/Keck Array …
By taking into account the contamination of foreground radiations, we employ the Fisher matrix to forecast the future sensitivity on the tilt of power spectrum of primordial tensor perturbations for several ground-based (AdvACT, CLASS, Keck/BICEP3, Simons Array, SPT-3G), balloon-borne (EBEX, Spider) and satellite (CMBPol, COrE, LiteBIRD) experiments of B-mode polarizations. For the fiducial model $n_t=0$, our results show that the satellite experiments give good sensitivity on the tensor tilt $n_t$ to the level $σ_{n_t}\lesssim0.1$ for $r\gtrsim2\times10^{-3}$, while the ground-based and ballo…
Current and future B-mode polarization data are the most powerful observables to constrain gravitational waves from the early Universe. We set conservative constraints on tensor modes when relaxing the inflationary consistency condition $n_t=-r/8$ between the tensor tilt $n_t$ and the tensor-to-scalar ratio r. By adding a power-law spectrum of tensor perturbations to $Λ$CDM, and parameterizing this tensor contribution by two independent primordial tensor-to-scalar ratios $(r_1,r_2)$ at $k_1 = 0.005$ Mpc$^{-1}$ and $k_2 = 0.02$ Mpc$^{-1}$, Planck and BICEP/Keck Array 2018 data (BK18) lead to co…
We characterize Galactic dust filaments by correlating BICEP/Keck and Planck data with polarization templates based on neutral hydrogen (H I) observations. Dust polarization is important for both our understanding of astrophysical processes in the interstellar medium (ISM) and the search for primordial gravitational waves in the cosmic microwave background (CMB). In the diffuse ISM, H I is strongly correlated with the dust and partly organized into filaments that are aligned with the local magnetic field. We analyze the deep BICEP/Keck data at 95, 150, and 220 GHz, over the low-column-density …
Natural (axionic) inflation can accommodate sizeable primordial tensor modes but suffers from the necessity of trans-Planckian variations of the inflaton field. This problem can be solved via the mechanism of aligned axions arXiv:hep-ph/0409138, where the aligned axion spirals down in the potential of other axions. We elaborate on the mechanism in view of the recently reported observations of the BICEP2 collaboration arXiv:1403.3985.
For the past decade, the BICEP/Keck collaboration has been operating a series of telescopes at the Amundsen-Scott South Pole Station measuring degree-scale $B$-mode polarization imprinted in the Cosmic Microwave Background (CMB) by primordial gravitational waves (PGWs). These telescopes are compact refracting polarimeters mapping about 2% of the sky, observing at a broad range of frequencies to account for the polarized foreground from Galactic synchrotron and thermal dust emission. Our latest publication "BK18" utilizes the data collected up to the 2018 observing season, in conjunction with t…
The recent BICEP2 result shows that the Universe once has gone through the vacuum with the GUT scale energy density. The implied high scale inflation nullifies the dilution idea of topological defects, strings and domain walls, of the axionic system. In particular, domain walls are disastrous if the domain wall problem with domain-wall number greater than 1 is present. We argue that the model-independent axion in string compactification with the anomalous U(1) gauge symmetry resolves the domain wall problem naturally with a symmetry principle.
We present results from an analysis of all data taken by the BICEP2 & Keck Array CMB polarization experiments up to and including the 2014 observing season. This includes the first Keck Array observations at 95 GHz. The maps reach a depth of 50 nK deg in Stokes $Q$ and $U$ in the 150 GHz band and 127 nK deg in the 95 GHz band. We take auto- and cross-spectra between these maps and publicly available maps from WMAP and Planck at frequencies from 23 GHz to 353 GHz. An excess over lensed-LCDM is detected at modest significance in the 95x150 $BB$ spectrum, and is consistent with the dust contribut…
The BICEP/Keck Array experiment is a series of small-aperture refracting telescopes observing degree-scale Cosmic Microwave Background polarization from the South Pole in search of a primordial $B$-mode signature. As a pair differencing experiment, an important systematic that must be controlled is the differential beam response between the co-located, orthogonally polarized detectors. We use high-fidelity, in-situ measurements of the beam response to estimate the temperature-to-polarization (T $\rightarrow$ P) leakage in our latest data including observations from 2016 through 2018. This incl…
We present a search for axion-like polarization oscillations in the cosmic microwave background (CMB) with observations from the Keck Array. A local axion field induces an all-sky, temporally sinusoidal rotation of CMB polarization. A CMB polarimeter can thus function as a direct-detection experiment for axion-like dark matter. We develop techniques to extract an oscillation signal. Many elements of the method are generic to CMB polarimetry experiments and can be adapted for other datasets. As a first demonstration, we process data from the 2012 observing season to set upper limits on the axio…
We exploit the complementarity among supersymmetry, inflation, axions, Big Bang Nucleosynthesis (BBN) and Cosmic Microwave Background Radiation (CMB) to constrain supersymmetric axion models in the light of the recent Planck and BICEP results. In particular, we derive BBN bounds coming from altering the light element abundances by taking into account hadronic and electromagnetic energy injection, and CMB constraints from black-body spectrum distortion. Lastly, we outline the viable versus excluded region of these supersymetric models that might account for the mild dark radiation observed.
The recent BICEP2 measurements of B-modes indicate a large tensor-to-scalar ratio in inflationary cosmology, which points towards trans-Planckian evolution of the inflaton. We propose possible string-theory realizations thereof. Schemes for natural and axion monodromy inflation are presented in the framework of the type IIB large volume scenario. The inflaton in both cases is given by the universal axion and its potential is generated at subleading order by F-terms. Our models are shown to feature a natural mechanism for inflaton decay into predominantly Standard Model particles.
We present an improved search for axion-like polarization oscillations in the cosmic microwave background (CMB) with observations from the Keck Array. An all-sky, temporally sinusoidal rotation of CMB polarization, equivalent to a time-variable cosmic birefringence, is an observable manifestation of a local axion field and potentially allows a CMB polarimeter to detect axion-like dark matter directly. We describe improvements to the method presented in previous work, and we demonstrate the updated method with an expanded dataset consisting of the 2012-2015 observing seasons. We set limits on t…
Precision measurements of cosmic microwave background (CMB) polarization require extreme control of instrumental systematics. In a companion paper we have presented cosmological constraints from observations with the BICEP2 and Keck Array experiments up to and including the 2015 observing season (BK15), resulting in the deepest CMB polarization maps to date and a statistical sensitivity to the tensor-to-scalar ratio of $σ(r) = 0.020$. In this work we characterize the beams and constrain potential systematic contamination from main beam shape mismatch at the three BK15 frequencies (95, 150, and…
BICEP/Keck XXI: Constraints on Early-Universe Parity Violation from Multipole-Dependent Birefringence
Cardiff University（卡迪夫大学）；Kavli Institute for Particle Astrophysics and Cosmology, Stanford University（斯坦福大学卡弗里粒子天体物理与宇宙学研究所）；SLAC National Accelerator Laboratory（斯坦福直线加速器中心）；University of British Columbia（不列颠哥伦比亚大学）；Center for Astrophysics, Harvard & Smithsonian（哈佛史密松尼天体物理中心）；California Institute of Technology（加州理工学院）；University of Cincinnati（辛辛那提大学）；Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）；Kavli Institute for Cosmological Physics, University of Chicago（芝加哥大学卡弗里宇宙物理学研究所）
We present a two-field inflation model where inflaton field has a non-canonical kinetic term due to the presence of a dilaton field. It is a two-parameter generalization of one-parameter Brans-Dicke gravity in the Einstein frame. We show that in such an inflation model the quartic and quadratic inflaton potentials, which are otherwise ruled out by the present Planck-{\it Keck}/BICEP2 data, yield scalar spectral index and tensor-to-scalar ratio in accordance with the present data. Such a model yield tensor-to-scalar ratio of the order of $10^{-2}$ which is within the reach of $B-$mode experimen…
The BICEP2 experiment determined the Hubble parameter during inflation to be about $10^{14}$ GeV. Such high inflation scale is in tension with the QCD axion dark matter if the Peccei-Quinn (PQ) symmetry remains broken during and after inflation, because too large axion isocurvature perturbations would be generated. The axion isocurvature perturbations can be suppressed if the axion acquires a sufficiently heavy mass during inflation. We show that this is realized if the PQ symmetry is explicitly broken down to a discrete symmetry and if the breaking is enhanced during inflation. We also show t…
We propose a landscape of many axions, where the axion potential receives various contributions from shift symmetry breaking effects. We show that the existence of the axion with a super-Planckian decay constant is very common in the axion landscape for a wide range of numbers of axions and shift symmetry breaking terms, because of the accidental alignment of axions. The effective inflation model is either natural or multi-natural inflation in the axion landscape, depending on the number of axions and the shift symmetry breaking terms. The tension between BICEP2 and Planck could be due to smal…
Bicep Array is a cosmic microwave background (CMB) polarization experiment that will begin observing at the South Pole in early 2019. This experiment replaces the five Bicep2 style receivers that compose the Keck Array with four larger Bicep3 style receivers observing at six frequencies from 30 to 270GHz. The 95GHz and 150GHz receivers will continue to push the already deep Bicep/Keck CMB maps while the 30/40GHz and 220/270GHz receivers will constrain the synchrotron and galactic dust foregrounds respectively. Here we report on the design and performance of the Bicep Array instruments focusing…
We propose the natural inflation from the heterotic string theory on "Swiss-Cheese" Calabi-Yau manifold with multiple $U(1)$ magnetic fluxes. Such multiple $U(1)$ magnetic fluxes stabilize the same number of the linear combination of the universal axion and Kähler axions and one of the Kähler axions is identified as the inflaton. This axion decay constant can be determined by the size of one-loop corrections to the gauge kinetic function of the hidden gauge groups, which leads effectively to the trans-Planckian axion decay constant consistent with the WMAP, Planck and/or BICEP2 data. During th…
We propose a natural inflation model driven by an imaginary or axionic component of a Kähler modulus in string-inspired supergravity. The shift symmetry of the axion is gauged under an anomalous $U(1)_X$ symmetry, which leads to a modulus-dependent Fayet-Iliopoulos (FI) term. The matter fields are stabilized by F-terms, and the real component of the modulus is stabilized by the $U(1)_X$ D-term, while its axion remains light. Therefore, the masses of real and imaginary components of the modulus are separated at different scales. The scalar potential for natural inflation is realized by the supe…
The large tensor spectrum recently observed by the BICEP2 Collaboration requires a super-Planckian field variation of the inflaton in the single-field inflationary scenario. The required slow-roll parameter ε\approx 0.01 would restrict the e-folding number to around 7 in (sub-)Planckian inflationary models. To overcome such problems, we consider a two-field scenario based on the natural assisted supersymmetric (SUSY) hybrid model ("natural SUSY hybrid inflation" [1]), which combines the SUSY hybrid and the natural inflation models. The axionic inflaton field from the natural inflation sector c…
