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 history after inflation, and using this, for considered potential, we show compatible regions for the $n_s$, $r$ within the recent BICEP/Keck results.
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.
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…
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 …
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]"
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…
BICEP/Keck XX: Component-separated maps of polarized CMB and thermal dust emission using Planck and BICEP/Keck Observations through the 2018 Observing Season
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…
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…
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…
Natural Inflation with non-minimal coupling (NMC) to gravity, embodied by a Lagrangian term $ξϕ^2 R $, is investigated in the context of an extended gravity of the form $R+ αR^2$. The treatment is performed in the Palatini formalism. We discuss various limits of the model ``$α\gg 1$'' and ``$α\ll 1$'' in light of two scenarios of inflation: a ``Slow roll'' and a ``Constant roll'' scenario. By analyzing the observational consequences of the model, our results show a significant improvement regarding compatibility between the theoretical results of this model and the observational constraints fr…
BICEP2/Keck and SPIDER are cosmic microwave background (CMB) polarimeters targeting the B-mode polarization induced by primordial gravitational waves from inflation. They will be using planar arrays of polarization sensitive antenna-coupled TES bolometers, operating at frequencies between 90 GHz and 220 GHz. At 150 GHz each array consists of 64 polarimeters and four of these arrays are assembled together to make a focal plane, for a total of 256 dual-polarization elements (512 TES sensors). The detector arrays are integrated with a time-domain SQUID multiplexer developed at NIST and read out u…
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…
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 …
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 …
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…
We discuss the impact of the preheating stage in radiative corrections due to interaction of the inflaton to fermions to $ϕ^4$ inflation with non-minimal coupling in Palatini formulation. In Palatini inflation with large non-minimal coupling the field is allow to return to the plateau region during the reheating stage, so the average equation of state per oscillations is closer to $-1$ than to $1/3$. The incursion in the plateau leads, however, to a highly efficient tachyonic instability able to reheat the Universe in less than one e-fold. By taking into account prescription II discussed in th…
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…
We present measurements of polarization lensing using the 150 GHz maps which include all data taken by the BICEP2 & Keck Array CMB polarization experiments up to and including the 2014 observing season (BK14). Despite their modest angular resolution ($\sim 0.5^\circ$), the excellent sensitivity ($\sim 3μ$K-arcmin) of these maps makes it possible to directly reconstruct the lensing potential using only information at larger angular scales ($\ell\leq 700$). From the auto-spectrum of the reconstructed potential we measure an amplitude of the spectrum to be $A^{ϕϕ}_{\rm L}=1.15\pm 0.36$ (Planck $Λ…
We study Quadratic Inflation with the inflaton field $ϕ$ coupled non-minimally to the curvature scalar $R$, so that the potential during inflation is of the form $V\propto m^2ϕ^2+ξRϕ^2$. We show that with a suitable choice of the non-minimal coupling strength, $ξ=\mathcal{O}(10^{-3})$, one can resurrect the success of the scenario when compared against the Planck and BICEP2/Keck Array data, and that in the region of the parameter space which is still allowed the model predicts values of the tensor-to-scalar ratio in the range $0.01\leq r < 0.12$, making it possible to either confirm the scenar…
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 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 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…
Single field inflationary models are investigated within Palatini quadratic gravity represented by $R+αR^2$ along with a non-minimal coupling of the form $f(ϕ) R$ between the inflaton field $ϕ$ and the gravity. The treatment is performed in the Einstein frame, where the minimal coupling to gravity is recovered through conformal transformation. We consider various limits of the model with different inflationary scenarios characterized as canonical slow-roll inflation in the limit $α\dotϕ^2\ll (1+f(ϕ)) $, constant-roll k-inflation for $α\ll 1$, and slow-roll K-inflation for$ α\gg 1$ . A cosine a…
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…
In this paper my prime objective is to analyze the constraints on a sub-Planckian excursion of a single inflaton field within Effective Field Theory framework in a model independent fashion. For a generic single field inflationary potential, using the various parameterization of the primordial power spectrum I have derived the most general expression for the field excursion in terms of various inflationary observables, applying the observational constraints obtained from recent Planck 2015 and Planck 2015 +BICEP2/Keck Array data. By explicit computation I have reconstructed the structural form…
We present constraints on the tensor-to-scalar ratio r using a combination of BICEP/Keck 2018 and Planck PR4 data allowing us to fit for r consistently with the six parameters of the $Λ$CDM model without fixing any of them. In particular, we are able to derive a constraint on the reionization optical depth $τ$ and thus propagate its uncertainty onto the posterior distribution for r. While Planck sensitivity to r is no longer comparable with ground-based measurements, combining Planck with BK18 and BAO gives results consistent with r = 0 and tightens the constraint to r < 0.032.
We consider a generic model of quadratic gravity coupled to a single scalar and investigate the effects of gravitational degrees of freedom on inflationary parameters. We find that quantum corrections arising from the massive spin-2 ghost generate significant contributions to the effective inflationary potential and allow for a realization of the spontaneous breakdown of global scale invariance without the need for additional scalar fields. We compute inflationary parameters, compare the resulting predictions to well-known inflationary models, and find that they fit well within the Planck and …
We provide the latest constraints on the power spectra of both scalar and tensor perturbations from the CMB data (including \textit{Planck}~2015, BICEP2 \& \textit{Keck Array} experiments) and the new BAO scales from SDSS-III BOSS observation. We find that the inflation model with a convex potential is not favored and both the inflation model with a monomial potential and the natural inflation model are marginally disfavored at around $95\%$ confidence level. But both the Brane inflation model and the Starobinsky inflation model fit the data quite well.
BICEP/Keck XXII: Analysis of the South Pole Atmosphere for CMB Observations
Cardiff University（卡迪夫大学）；Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；University of British Columbia（不列颠哥伦比亚大学）；Center for Astrophysics, Harvard & Smithsonian（哈佛与史密森尼天体物理中心）；University of New Mexico（新墨西哥大学）；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）；University of Chicago（芝加哥大学）
We consider Supersymmetric (SUSY) and non-SUSY models of chaotic inflation based on the simplest power-law potential with exponents n=2 and 4. We propose a convenient non-minimal coupling to gravity and a non-minimal kinetic term which ensure, mainly for n=4, inflationary observables favored by the BICEP2/Keck Array and Planck results. Inflation can be attained for subplanckian inflaton values with the corresponding effective theories retaining the perturbative unitarity up to the Planck scale.
We show that the Planck 2015 and BICEP2/KECK measurements of the Cosmic Microwave Background (CMB) anisotropies provide together an information gain of 0.82 +- 0.13 bits on the reheating history over all slow-roll single-field models of inflation. This corresponds to a 40% improvement compared to the Planck 2013 constraints on the reheating. Our method relies on an exhaustive CMB data analysis performed over nearly 200 models of inflation to derive the Kullback-Leibler entropy between the prior and the fully marginalized posterior of the reheating parameter. This number is a weighted average b…
We examine the impact of a non-minimal coupling of the inflaton to the Ricci scalar, $\frac12 ξRϕ^2$, on the inflationary predictions. Such a non-minimal coupling is expected to be present in the inflaton Lagrangian on fairly general grounds. As a case study, we focus on the simplest inflationary model governed by the potential $V\propto ϕ^2$, using the latest combined 2015 analysis of Planck and BICEP2/Keck Array. We find that the presence of a coupling $ξ$ is favoured at a significance of $99\%$ CL, assuming that nature has chosen the potential $V\propto ϕ^2$ to generate the primordial pertu…
We have studied the paradigm of cosmic inflation using the simplest model based on the idea of supersymmetric hybrid inflation with non-minimal coupling to gravity, specially under the slow-roll approximation following the superconformal approach to supergravity. It is found that within a range of values of the non-minimal coupling parameter $ξ$, the model can accommodate the inflation data reported by the Planck ($n_s$ and upper limit of $r$) and BICEP2/Keck (upper limit of $r$) collaborations. The study shows that the most probable value of $ξ$ should be $\sim 0.0134\pm0.0005$. That is coupl…
