We report results from the BICEP2 experiment, a cosmic microwave background (CMB) polarimeter specifically designed to search for the signal of inflationary gravitational waves in the B-mode power spectrum around l ∼ 80. The telescope comprised a 26 cm aperture all-cold refracting optical system equipped with a focal plane of 512 antenna coupled transition edge sensor 150 GHz bolometers each with temperature sensitivity of ≈300 μK CMB ffiffi s p . BICEP2 observed from the South Pole for three seasons from 2010 to 2012. A low-foreground region of sky with an effective area of 380 square deg was observed to a depth of 87 nK deg in Stokes Q and U. In this paper we describe the observations, data reduction, maps, simulations, and results. We find an excess of B-mode power over the base lensed-ΛCDM expectation in the range 30 < l < 150, inconsistent with the null hypothesis at a significance of > 5σ. Through jackknife tests and simulations based on detailed calibration measurements we show that systematic contamination is much smaller than the observed excess. Cross correlating against WMAP 23 GHz maps we find that Galactic synchrotron makes a negligible contribution to the observed signal. We also examine a number of available models of polarized dust emission and find that at their default parameter values they predict power ∼ð5-10Þ× smaller than the observed excess signal (with no significant cross-correlation with our maps). However, these models are not sufficiently constrained by external public data to exclude the possibility of dust emission bright enough to explain the entire excess signal. Cross correlating BICEP2 against 100 GHz maps from the BICEP1 experiment, the excess signal is confirmed with 3σ significance and its spectral index is found to be consistent with that of the CMB, disfavoring dust at 1.7σ. The observed B-mode power spectrum is well fit by a lensed-ΛCDM þ tensor theoretical model with −0.05 , with r ¼ 0 disfavored at 7.0σ. Accounting for the contribution of foreground, dust will shift this value downward by an amount which will be better constrained with upcoming data sets.

We report the results of a joint analysis of data from BICEP2/Keck Array and Planck. BICEP2 and Keck Array have observed the same approximately 400 deg 2 patch of sky centered on RA 0 h, Dec. −57.5°. The combined maps reach a depth of 57 nK deg in Stokes Q and U in a band centered at 150 GHz. Planck has observed the full sky in polarization at seven frequencies from 30 to 353 GHz, but much less deeply in any given region (1.2 μK deg in Q and U at 143 GHz). We detect 150 × 353 cross-correlation in B modes at high significance. We fit the single-and cross-frequency power spectra at frequencies ≥ 150 GHz to a lensed-ΛCDM model that includes dust and a possible contribution from inflationary gravitational waves (as parametrized by the tensor-to-scalar ratio r), using a prior on the frequency spectral behavior of polarized dust emission from previous Planck analysis of other regions of the sky. We find strong evidence for dust and no statistically significant evidence for tensor modes. We probe various model variations and extensions, including adding a synchrotron component in combination with lower frequency data, and find that these make little difference to the r constraint. Finally, we present an alternative analysis which is similar to a map-based cleaning of the dust contribution, and show that this gives similar constraints. The final result is expressed as a likelihood curve for r, and yields an upper limit r 0.05 < 0.12 at 95% confidence. Marginalizing over dust and r, lensing B modes are detected at 7.0σ significance.

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. DOI: 10.1103/PhysRevLett.116.031302 PRL 116, 031302 (2016) P H Y S I C A L R E V I E W L E T T E R S week ending 22 JANUARY 20160031-9007=16=116(3)=031302 (9) 031302-1 © 2016 American Physical SocietyIntroduction.-Measurements of the cosmic microwave background (CMB) [1] are one of the observational pillars of the standard cosmological model (ΛCDM) and constrain its parameters to high precision (see most recently Ref. [2]). This model extrapolates the Universe back to very high temperatures (≫10 12 K) and early times (≪ 1 s). Observations indicate that conditions at these early times are described by an almost uniform plasma with a nearly scale invariant spectrum of adiabatic density perturbations. However, ΛCDM itself offers no explanation for how these conditions occurred. The theory of inflation is an extension to the standard model, which postulates a phase of exponential expansion at a still earlier epoch (∼10 −35 s) that precedes ΛCDM and produces the required initial conditions (see Ref.[3] for a recent review and citations to the original literature).There is widespread support for the claim that existing observations already indicate that some version of inflation probably did occur, but there are also skeptics [4,5]. As well as the specific form of the initial density perturbations, there is an additional relic which inflation predicts, and which one can attempt to detect....

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 µKcmb arcmin at 95, 150 and 220 GHz respectively over an effective area of ≈ 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 available WMAP and Planck maps at frequencies from 23 to 353 GHz. We 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 we impose priors on some of these using external information from Planck and WMAP derived from larger regions of sky. The model is shown to be an adequate description of the data at the current noise levels. The likelihood analysis yields the constraint r0.05 < 0.07 at 95% confidence, which tightens to r0.05 < 0.06 in conjunction with Planck temperature measurements and other data. The lensing signal is detected at 8.8σ significance. Running maximum likelihood search on simulations we obtain unbiased results and find that σ(r) = 0.020. These are the strongest constraints to date on primordial gravitational waves.

A linear polarization field on the sphere can be uniquely decomposed into an E-mode and a B-mode component. These two components are analytically defined in terms of spin-2 spherical harmonics. Maps that contain filtered modes on a partial sky can also be decomposed into E-mode and B-mode components. However, the lack of full sky information prevents orthogonally separating these components using spherical harmonics. In this paper, we present a technique for decomposing an incomplete map into E and B-mode components using E and B eigenmodes of the pixel covariance in the observed map. This method is found to orthogonally define E and B in the presence of both partial sky coverage and spatial filtering. This method has been applied to the Bicep2 and the Keck Array maps and results in reducing E to B leakage from ΛCDM E-modes to a level corresponding to a tensor-to-scalar ratio of .

Executive SummaryPrecision cosmological measurements push the boundaries of our understanding of the fundamental physics that governs our universe. In the coming years, cosmologists will be in a position to make major breakthroughs in our understanding of the physics of the very early universe and be able to probe particle physics and gravity at the highest energy scales yet accessed. A major leap forward in the sensitivity of cosmological experiments is within our technological reach, leveraging past and current experience to tackle some of the most interesting fundamental physics questions.Cosmic inflation, the theory that the universe underwent a violent, exponential expansion during the first moments of time, is the leading theoretical paradigm for the earliest history of the universe and for the origin of the structure in the universe. Current measurements of the cosmic microwave background (CMB) and observations of the large-scale distributions of dark matter and galaxies in the universe are in stunning agreement with the concept of inflation. The next generations of experiments in observational cosmology are poised to decide central questions about the mechanism behind inflation. In this short document, we highlight the importance of experimentally determining the nature of inflation in the early universe and the unique opportunity these experiments provide to explore the physics of space, time, and matter at the highest energies possible: those found at the birth of the universe.

We report on the design and performance of the Bicep2 instrument and on its three-year data set. Bicep2 was designed to measure the polarization of the cosmic microwave background (CMB) on angular scales of 1 •-5 • (= 40-200), near the expected peak of the B-mode polarization signature of primordial gravitational waves from cosmic inflation. Measuring B-modes requires dramatic improvements in sensitivity combined with exquisite control of systematics. The Bicep2 telescope observed from the South Pole with a 26 cm aperture and cold, on-axis, refractive optics. Bicep2 also adopted a new detector design in which beam-defining slot antenna arrays couple to transition-edge sensor (TES) bolometers, all fabricated on a common substrate. The antenna-coupled TES detectors supported scalable fabrication and multiplexed readout that allowed Bicep2 to achieve a high detector count of 500 bolometers at 150 GHz, giving unprecedented sensitivity to B-modes at degree angular scales. After optimization of detector and readout parameters, Bicep2 achieved an instrument noise-equivalent temperature of 15.8 μK √ s. The full data set reached Stokes Q and U map depths of 87.2 nK in square-degree pixels (5. 2 μK) over an effective area of 384 deg 2 within a 1000 deg 2 field. These are the deepest CMB polarization maps at degree angular scales to date. The power spectrum analysis presented in a companion paper has resulted in a significant detection of B-mode polarization at degree scales.

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. * Corresponding author. toshiyan@stanford.edu PHYSICAL REVIEW D 96, 102003 (2017) 2470-0010=2017=96(10)=102003 (7) 102003-1 © 2017 American Physical SocietyOur results lead to an order of magnitude better constraint on the coupling constant of the Chern-Simons electromagnetic term g aγ ≤ 7.2 × 10 −2 =H I (95% confidence) than the constraint derived from the B-mode spectrum, where H I is the inflationary Hubble scale. This constraint leads to a limit on the decay constant of 10 −6 ≲ f a =M pl at mass range of 10 −33 ≤ m a ≤ 10 −28 eV for r ¼ 0.01, assuming g aγ ∼ α=ð2πf a Þ 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.