BICEP2 Experiment Research Articles

Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, 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 220GHz and BICEP3 observations at 95GHz to the previous 95/150/220 GHz dataset. The Q/U maps now reach depths of 2.8, 2.8, and 8.8 μK_{CMB} arcmin at 95, 150, and 220GHz, respectively, over an effective area of ≈600 square degrees at 95GHz and ≈400 square degrees at 150 and 220GHz. The 220GHz maps now achieve a signal-to-noise ratio on polarized dust emission exceeding that of Planck at 353GHz. We take auto- and cross-spectra between these maps and publicly available WMAP and Planck maps at frequencies from 23 to 353GHz and evaluate the joint likelihood of the spectra versus a multicomponent model of lensed ΛCDM+r+dust+synchrotron+noise. The foreground model has seven parameters, and no longer requires a prior on the frequency spectral index of the dust emission taken from measurements on other regions of the sky. This model is an adequate description of the data at the current noise levels. The likelihood analysis yields the constraint r_{0.05}<0.036 at 95%confidence. Running maximum likelihood search on simulations we obtain unbiased results and find that σ(r)=0.009. These are the strongest constraints to date on primordial gravitational waves.

BICEP2/Keck Array XI: Beam Characterization and Temperature-to-Polarization Leakage in the BK15 Data Set

Abstract 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 220 GHz). Far-field maps of 7360 distinct beam patterns taken from 2010–2015 are used to measure differential beam parameters and predict the contribution of temperature-to-polarization leakage to the BK15 B-mode maps. In the multifrequency, multicomponent likelihood analysis that uses BK15, Planck, and Wilkinson Microwave Anisotropy Probe maps to separate sky components, we find that adding this predicted leakage to simulations induces a bias of Δr = 0.0027 ± 0.0019. Future results using higher-quality beam maps and improved techniques to detect such leakage in CMB data will substantially reduce this uncertainty, enabling the levels of systematics control needed for BICEP Array and other experiments that plan to definitively probe large-field inflation.

BICEP2 / Keck Array IX: New bounds on anisotropies of CMB polarization rotation and implications for axionlike particles and primordial magnetic fields

We present the strongest constraints to date on anisotropies of cosmic microwave background (CMB) polarization rotation derived from 150 GHz data taken by the BICEP2 & Keck Array CMB experiments up to and including the 2014 observing season (BK14). The definition of the polarization angle in BK14 maps has gone through self-calibration in which the overall angle is adjusted to minimize the observed TB and EB power spectra. After this procedure, the QU maps lose sensitivity to a uniform polarization rotation but are still sensitive to anisotropies of polarization rotation. This analysis places constraints on the anisotropies of polarization rotation, which could be generated by CMB photons interacting with axionlike pseudoscalar fields or Faraday rotation induced by primordial magnetic fields. The sensitivity of BK14 maps (∼3 μK−arc min) makes it possible to reconstruct anisotropies of the polarization rotation angle and measure their angular power spectrum much more precisely than previous attempts. Our data are found to be consistent with no polarization rotation anisotropies, improving the upper bound on the amplitude of the rotation angle spectrum by roughly an order of magnitude compared to the previous best constraints. Our results lead to an order of magnitude better constraint on the coupling constant of the Chern-Simons electromagnetic term gaγ≤7.2×10−2/HI (95% confidence) than the constraint derived from the B-mode spectrum, where HI is the inflationary Hubble scale. This constraint leads to a limit on the decay constant of 10−6≲fa/Mpl at mass range of 10−33≤ma≤10−28 eV for r=0.01, assuming gaγ∼α/(2πfa) with α denoting the fine structure constant. The upper bound on the amplitude of the primordial magnetic fields is 30 nG (95% confidence) from the polarization rotation anisotropies.Received 13 May 2017DOI:https://doi.org/10.1103/PhysRevD.96.102003© 2017 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCosmic microwave backgroundPrimordial magnetic fieldsPhysical SystemsAxionsGravitation, Cosmology & AstrophysicsGeneral Physics

Bicep2/KECK ARRAY VIII: MEASUREMENT OF GRAVITATIONAL LENSING FROM LARGE-SCALE B-MODE POLARIZATION

ABSTRACT We present measurements of polarization lensing using the 150 GHz maps, which include all data taken by the BICEP2 and Keck Array Cosmic Microwave Background polarization experiments up to and including the 2014 observing season (BK14). Despite their modest angular resolution ( ), the excellent sensitivity (∼3μK-arcmin) of these maps makes it possible to directly reconstruct the lensing potential using only information at larger angular scales ( ). From the auto-spectrum of the reconstructed potential, we measure an amplitude of the spectrum to be (Planck ΛCDM prediction corresponds to ) and reject the no-lensing hypothesis at , which is the highest significance achieved to date using an EB lensing estimator. Taking the cross-spectrum of the reconstructed potential with the Planck 2015 lensing map yields . These direct measurements of are consistent with the ΛCDM cosmology and with that derived from the previously reported BK14 B-mode auto-spectrum ( ). We perform a series of null tests and consistency checks to show that these results are robust against systematics and are insensitive to analysis choices. These results unambiguously demonstrate that the B modes previously reported by BICEP/Keck at intermediate angular scales ( ) are dominated by gravitational lensing. The good agreement between the lensing amplitudes obtained from the lensing reconstruction and B-mode spectrum starts to place constraints on any alternative cosmological sources of B modes at these angular scales.

Perfect fluid and F ( T ) $F(T)$ gravity descriptions of inflationary universe and comparison with observational data

We describe in this paper the observables of inflationary models, in particular the spectrum index of torsion scalar perturbations, the tensor-to-scalar ratio, and the running of the spectral index, in the framework of perfect fluid models and F(T) gravity theories through the reconstruction methods. Then, our results on the perfect fluid and F(T) gravity theories of inflation are compared with recent cosmological observations such as the Planck satellite and BICEP2 experiment. Ours studies prove that the perfect fluid and F(T) gravity models can reproduce the inflationary universe consistent above all with the Planck data. We have reconstructed several models and considered others which give the best fit values compatible with the spectral index of curvature perturbations, the tensor-to-scalar ratio, and the running of the spectral index within the allowed ranges suggested by the Planck and BICEP2 results.

Updated constraints and forecasts on primordial tensor modes

We present new, tight, constraints on the cosmological background of gravitational waves (GWs) using the latest measurements of CMB temperature and polarization anisotropies provided by the Planck, BICEP2 and Keck Array experiments. These constraints are further improved when the GW contribution $N^{\rm GW}_{\rm eff}$ to the effective number of relativistic degrees of freedom $N_{\rm eff}$ is also considered. Parametrizing the tensor spectrum as a power law with tensor-to-scalar ratio $r$, tilt $n_\mathrm{t}$ and pivot $0.01\,\mathrm{Mpc}^{-1}$, and assuming a minimum value of $r=0.001$, we find $r < 0.089$, $n_\mathrm{t} = 1.7^{+2.1}_{-2.0}$ ($95\%\,\mathrm{CL}$, no $N^{\rm GW}_{\rm eff}$) and $r < 0.082$, $n_\mathrm{t} = -0.05^{+0.58}_{-0.87}$ ($95\%\,\mathrm{CL}$, with $N^{\rm GW}_{\rm eff}$). When the recently released $95\,\mathrm{GHz}$ data from Keck Array are added to the analysis, the constraints on $r$ are improved to $r < 0.067$ ($95\%\,\mathrm{CL}$, no $N^{\rm GW}_{\rm eff}$), $r < 0.061$ ($95\%\,\mathrm{CL}$, with $N^{\rm GW}_{\rm eff}$). We discuss the limits coming from direct detection experiments such as LIGO-Virgo, pulsar timing (European Pulsar Timing Array) and CMB spectral distortions (FIRAS). Finally, we show future constraints achievable from a COrE-like mission: if the tensor-to-scalar ratio is of order $10^{-2}$ and the inflationary consistency relation $n_\mathrm{t} = -r/8$ holds, COrE will be able to constrain $n_\mathrm{t}$ with an error of $0.16$ at $95\%\,\mathrm{CL}$. In the case that lensing $B$-modes can be subtracted to $10\%$ of their power, a feasible goal for COrE, these limits will be improved to $0.11$ at $95\%\,\mathrm{CL}$.

Planckintermediate results

The polarized thermal emission from Galactic dust is the main foreground present in measurements of the polarization of the cosmic microwave background (CMB) at frequencies above 100GHz. We exploit the Planck HFI polarization data from 100 to 353GHz to measure the dust angular power spectra $C_\ell^{EE,BB}$ over the range $40<\ell<600$ well away from the Galactic plane. These will bring new insights into interstellar dust physics and a precise determination of the level of contamination for CMB polarization experiments. We show that statistical properties of the emission can be characterized over large fractions of the sky using $C_\ell$. For the dust, they are well described by power laws in $\ell$ with exponents $\alpha^{EE,BB}=-2.42\pm0.02$. The amplitudes of the polarization $C_\ell$ vary with the average brightness in a way similar to the intensity ones. The dust polarization frequency dependence is consistent with modified blackbody emission with $\beta_d=1.59$ and $T_d=19.6$K. We find a systematic ratio between the amplitudes of the Galactic $B$- and $E$-modes of 0.5. We show that even in the faintest dust-emitting regions there are no "clean" windows where primordial CMB $B$-mode polarization could be measured without subtraction of dust emission. Finally, we investigate the level of dust polarization in the BICEP2 experiment field. Extrapolation of the Planck 353GHz data to 150GHz gives a dust power $\ell(\ell+1)C_\ell^{BB}/(2\pi)$ of $1.32\times10^{-2}\mu$K$_{CMB}^2$ over the $40<\ell<120$ range; the statistical uncertainty is $\pm0.29$ and there is an additional uncertainty (+0.28,-0.24) from the extrapolation, both in the same units. This is the same magnitude as reported by BICEP2 over this $\ell$ range, which highlights the need for assessment of the polarized dust signal even in the cleanest windows of the sky.

Improved Constraints on Cosmology and Foregrounds from BICEP2 and Keck Array Cosmic Microwave Background Data with Inclusion of 95 GHz Band.

We present results from an analysis of all data taken by the BICEP2 and Keck Array cosmic microwave background (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 to 353 GHz. An excess over lensed ΛCDM is detected at modest significance in the 95×150 BB spectrum, and is consistent with the dust contribution expected from our previous work. No significant evidence for synchrotron emission is found in spectra such as 23×95, or for correlation between the dust and synchrotron sky patterns in spectra such as 23×353. We take the likelihood of all the spectra for a multicomponent model including lensed ΛCDM, dust, synchrotron, and a possible contribution from inflationary gravitational waves (as parametrized by the tensor-to-scalar ratio r) using priors on the frequency spectral behaviors of dust and synchrotron emission from previous analyses of WMAP and Planck data in other regions of the sky. This analysis yields an upper limit r_{0.05}<0.09 at 95% confidence, which is robust to variations explored in analysis and priors. Combining these B-mode results with the (more model-dependent) constraints from Planck analysis of CMB temperature plus baryon acoustic oscillations and other data yields a combined limit r_{0.05}<0.07 at 95% confidence. These are the strongest constraints to date on inflationary gravitational waves.

Космологические результаты космической миссии "Планк". Сравнение с данными экспериментов WMAP и BICEP2

Космологические результаты космической миссии &quot;Планк&quot;. Сравнение с данными экспериментов WMAP и BICEP2, Верходанов О.В.

Bicep2. III. INSTRUMENTAL SYSTEMATICS

In a companion paper we have reported a $>5\sigma$ detection of degree scale $B $-mode polarization at 150 GHz by the BICEP2 experiment. Here we provide a detailed study of potential instrumental systematic contamination to that measurement. We focus extensively on spurious polarization that can potentially arise from beam imperfections. We present a heuristic classification of beam imperfections according to their symmetries and uniformities, and discuss how resulting contamination adds or cancels in maps that combine observations made at multiple orientations of the telescope about its boresight axis. We introduce a technique, which we call "deprojection", for filtering the leading order beam-induced contamination from time ordered data, and show that it removes power from BICEP2's $BB$ spectrum consistent with predictions using high signal-to-noise beam shape measurements. We detail the simulation pipeline that we use to directly simulate instrumental systematics and the calibration data used as input to that pipeline. Finally, we present the constraints on $BB$ contamination from individual sources of potential systematics. We find that systematics contribute $BB$ power that is a factor $\sim10\times$ below BICEP2's 3-year statistical uncertainty, and negligible compared to the observed $BB$ signal. The contribution to the best-fit tensor/scalar ratio is at a level equivalent to $r=(3-6)\times10^{-3}$.

Precision tests of parity violation over cosmological distances

Recent measurements of the cosmic microwave background (CMB) B-mode polarization power spectrum by the Bicep2 and POLARBEAR experiments have demonstrated new precision tools for probing fundamental physics. Regardless of origin, the detection of sub-μK CMB polarization represents a technological tour de force. Yet more information may be latent in the CMB's polarization pattern. Because of its tensorial nature, CMB polarization may also reveal parity-violating physics via a detection of cosmic polarization rotation. Although current CMB polarimeters are sensitive enough to measure one degree-level polarization rotation with >5σ statistical significance, they lack the ability to differentiate this effect from a systematic instrumental polarization rotation. Here, we motivate the search for cosmic polarization rotation from current CMB data as well as independent radio galaxy and quasar polarization measurements. We argue that an improvement in calibration accuracy would allow the unambiguous measurement of parity- and Lorentz-violating effects. We describe the CalSat space-based polarization calibrator that will provide stringent control of systematic polarization angle calibration uncertainties to 0.05° – an order of magnitude improvement over current CMB polarization calibrators. CalSat-based calibration could be used with current CMB polarimeters searching for B-mode polarization, effectively turning them into probes of cosmic parity violation, ‘for free’ – i.e. without the need to build dedicated instruments.

Primordial gravitational waves measurements and anisotropies of CMB polarization rotation

Searching for the signal of primordial gravitational waves in the B-modes (BB) power spectrum is one of the key scientific aims of the cosmic microwave background (CMB) polarization experiments. However, this could be easily contaminated by several foreground issues, such as the interstellar dust grains and the galactic cyclotron electrons. In this paper we study another mechanism, the cosmic birefringence, which can be introduced by a CPT-violating interaction between CMB photons and an external scalar field. Such kind of interaction could give rise to the rotation of the linear polarization state of CMB photons, and consequently induce the CMB BB power spectrum, which could mimic the signal of primordial gravitational waves at large scales. With the recently released polarization data of BICEP2 and the joint analysis data of BICEP2/Keck Array and Planck, we perform a global fitting analysis on constraining the tensor-to-scalar ratio r by considering the polarization rotation angle [α(nˆ)] which can be separated into a background isotropic part [α¯] and a small anisotropic part [Δα(nˆ)]. Since the data of BICEP2 and Keck Array experiments have already been corrected by using the “self-calibration” method, here we mainly focus on the effects from the anisotropies of CMB polarization rotation angle. We find that including Δα(nˆ) in the analysis could slightly weaken the constraints on the tensor-to-scalar ratio r, when using current CMB polarization measurements. We also simulate the mock CMB data with the BICEP3-like sensitivity. Very interestingly, we find that if the effects of the anisotropic polarization rotation angle could not be taken into account properly in the analysis, the constraints on r will be dramatically biased. This implies that we need to break the degeneracy between the anisotropies of the CMB polarization rotation angle and the CMB primordial tensor perturbations, in order to measure the signal of primordial gravitational waves accurately.

Cosmological evolution of thermal relic particles inf(R)gravity

By considering $f(R)$ gravity models, the cosmic evolution is modified with respect to the standard $\Lambda$CDM scenario. In particular, the thermal history of particles results modified. In this paper, we derive the evolution of relics particles (WIMPs) assuming a reliable $f(R)$ cosmological solution and taking into account observational constraints. The connection to the PAMELA experiment is also discussed. Results are consistent with constraints coming from BICEP2 and PLANCK experiments.

DETECTION OF B-MODE POLARIZATION AT DEGREE SCALES USING BICEP2

In this article, I give a brief description of Bicep2 experiment, and a summary of its result.

BICEP2/KECK ARRAY V: MEASUREMENTS OFB-MODE POLARIZATION AT DEGREE ANGULAR SCALES AND 150 GHz BY THE KECK ARRAY

The Keck Array is a system of cosmic microwave background (CMB) polarimeters, each similar to the BICEP2 experiment. In this paper we report results from the 2012 and 2013 observing seasons, during which the Keck Array consisted of five receivers all operating in the same (150 GHz) frequency band and observing field as BICEP2. We again find an excess of B-mode power over the lensed-$\Lambda$CDM expectation of $> 5 \sigma$ in the range $30 < \ell < 150$ and confirm that this is not due to systematics using jackknife tests and simulations based on detailed calibration measurements. In map difference and spectral difference tests these new data are shown to be consistent with BICEP2. Finally, we combine the maps from the two experiments to produce final Q and U maps which have a depth of 57 nK deg (3.4 $\mu$K arcmin) over an effective area of 400 deg$^2$ for an equivalent survey weight of 250,000 $\mu$K$^{-2}$. The final BB band powers have noise uncertainty a factor of 2.3 times better than the previous results, and a significance of detection of excess power of $> 6\sigma$.

The renormalizable three-term polynomial inflation with large tensor-to-scalar ratio

We systematically study the renormalizable three-term polynomial inflation in the supersymmetric and non-supersymmetric models. The supersymmetric inflaton potentials can be realized in supergravity theory, and only have two independent parameters. We show that the general renormalizable supergravity model is equivalent to one kind of our supersymmetric models. We find that the spectral index and tensor-to-scalar ratio can be consistent with the Planck and BICEP2 results, but the running of spectral index is always out of the $2\sigma$ range. If we do not consider the BICEP2 experiment, these inflationary models can be highly consistent with the Planck observations and saturate its upper bound on the tensor-to-scalar ratio ($r \le 0.11$). Thus, our models can be tested at the future Planck and QUBIC experiments.

Beginning of Universe through large field hybrid inflation

Recent detection of B-mode polarization induced from tensor perturbations by the BICEP2 experiment implies the so-called large field inflation, where an inflaton field takes super-Planckian expectation value during inflation, at a high energy scale. We show however, if another inflation follows hybrid inflation, the hybrid inflation can generate a large tensor perturbation with not super-Planckian but Planckian field value. This scenario would relax the tension between BICEP2 and Planck concerning the tensor-to-scalar ratio, because a negative large running can also be obtained for a certain number of e-fold of the hybrid inflation. A natural interpretation of a large gravitational wave mode with or without the scalar spectral running might be multiple inflation in the early Universe.

Inflation that runs naturally: Gravitational waves and suppression of power at large and small scales

We point out three correlated predictions of the axion monodromy inflation model: the large amplitude of gravitational waves, the suppression of power on horizon scales and on scales relevant for the formation of dwarf galaxies. While these predictions are likely generic to models with oscillations in the inflaton potential, the axion monodromy model naturally accommodates the required running spectral index through Planck-scale corrections to the inflaton potential. Applying this model to a combined data set of Planck, ACT, SPT, and WMAP low-$\ensuremath{\ell}$ polarization cosmic microwave background (CMB) data, we find a best-fit tensor-to-scalar ratio ${r}_{0.05}={0.07}_{\ensuremath{-}0.04}^{+0.05}$ due to gravitational waves, which may have been observed by the BICEP2 experiment. Despite the contribution of gravitational waves, the total power on large scales (CMB power spectrum at low multipoles) is lower than the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmology with a power-law spectrum of initial perturbations and no gravitational waves, thus mitigating some of the tension on large scales. There is also a reduction in the matter power spectrum of 20--30% at scales corresponding to $k=10\text{ }\text{ }{\text{Mpc}}^{\ensuremath{-}1}$, which are relevant for dwarf galaxy formation. This will alleviate some of the unsolved small-scale structure problems in the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmology. The inferred matter power spectrum is also found to be consistent with recent Lyman-$\ensuremath{\alpha}$ forest data, which is in tension with the Planck-favored $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model with a power-law primordial power spectrum.

Two-field axion-monodromy hybrid inflation model: Dante’s Waterfall

We describe a hybrid axion-monodromy inflation model motivated by the Dante's Inferno scenario. In Dante's Inferno, a two-field potential features a stable trench along which a linear combination of the two fields slowly rolls, rendering the dynamics essentially identical to that of single-field chaotic inflation. A shift symmetry allows for the Lyth bound to be effectively evaded as in other axion-monodromy models. In our proposal, the potential is concave downward near the origin and the inflaton trajectory is a gradual downward spiral, ending at a point where the trench becomes unstable. There, the fields begin falling rapidly towards the minimum of the potential and inflation terminates as in a hybrid model. We find parameter choices that reproduce observed features of the cosmic microwave background, and discuss our model in light of recent results from the BICEP2 and Planck experiments.

Chaotic inflation in no-scale supergravity with string inspired moduli stabilization

The simple chaotic inflation is highly consistent with the BICEP2 experiment, and no-scale supergravity can be realized naturally in various string compactifications. Thus, we construct a chaotic inflation model in no-scale supergravity inspired from Type IIB string compactification with an anomalous U(1)_X gauged symmetry. We introduce two moduli T_1 and T_2 which transform non-trivially under U(1)_X, and some pairs of fundamental quarks charged under the SU(N) x U(1)_X gauge group. The non-trivial transformations of moduli under U(1)_X lead to a moduli-dependent Fayet-Iliopoulos (FI) term. The modulus T_2 and the real component of T_1 are stabilized by the non-perturbative effect from quark condensation and the U(1)_X D-term. In particular, the stabilization from the anomalous U(1)_X D-term with moduli-dependent FI term is crucial for inflation since it gives heavy mass to the real component of the modulus T_1 while keeping its axionic part light. Choosing the proper parameters, we obtain a global Minkowski vacuum where the imaginary part of T_1 has a quadratic potential for chaotic inflation.