Search

At millimeter wavelengths, the atmospheric emission is circularly polarized owing to the Zeeman splitting of molecular oxygen by the Earth's magnetic field. We report a measurement of the signal in the 150 GHz band using 3 years of observational data with the \textsc{Polarbear} project. Non-idealities of a continuously rotating half-wave plate (HWP) partially convert circularly polarized light to linearly polarized light. While \textsc{Polarbear} detectors are sensitive to linear polarization, this effect makes them sensitive to circular polarization. Although this was not the intended use, we utilized this conversion to measure circular polarization. We reconstruct the azimuthal gradient of the circular polarization signal and measure its dependency from the scanning direction and the detector bandpass. We compare the signal with a simulation based on atmospheric emission theory, the detector bandpass, and the HWP leakage spectrum model. We find the ratio of the observed azimuthal slope to the simulated slope is $0.92 \pm 0.01\rm{(stat)} \pm 0.07\rm{(sys)}$. This ratio corresponds to a brightness temperature of $3.8\,\mathrm{m K}$ at the effective band center of $121.8\,\mathrm{GHz}$ and bandwidth of $3.5\,\mathrm{GHz}$ estimated from representative detector bandpass and the spectrum of Zeeman emission. This result validates our understanding of the instrument and reinforces the feasibility of measuring the circular polarization using the imperfection of continuously rotating HWP. Continuously rotating HWP is popular in ongoing and future cosmic microwave background experiments to modulate the polarized signal. This work shows a method for signal extraction and leakage subtraction that can help measuring circular polarization in such experiments., Comment: 23 pages, 11 figures

The Simons Observatory (SO) is a next-generation ground-based telescope located in the Atacama Desert in Chile, designed to map the cosmic microwave background (CMB) with unprecedented precision. The observatory consists of three small aperture telescopes (SATs) and one large aperture telescope (LAT), each optimized for distinct but complementary scientific goals. To achieve these goals, optimized scan strategies have been defined for both the SATs and LAT. This paper describes a software system deployed in SO that effectively translates high-level scan strategies into realistic observing scripts executable by the telescope, taking into account realistic observational constraints. The data volume of SO also necessitates a scalable software infrastructure to support its daily data processing needs. This paper also outlines an automated workflow system for managing data packaging and daily data reduction at the site., Comment: 16 pages, 7 figures, 6 tables, to be presented at SPIE Astronomical Telescopes + Instrumentation 2024

The Simons Observatory (SO) is a cosmic microwave background (CMB) survey experiment that includes small-aperture telescopes (SATs) observing from an altitude of 5,200 m in the Atacama Desert in Chile. The SO SATs will cover six spectral bands between 27 and 280 GHz to search for primordial B-modes to a sensitivity of $\sigma(r)=0.002$, with quantified systematic errors well below this value. Each SAT is a self-contained cryogenic telescope with a 35$^\circ$ field of view, 42 cm diameter optical aperture, 40 K half-wave plate, 1 K refractive optics, and $<0.1$ K focal plane that holds $>12,000$ TES detectors. We describe the nominal design of the SATs and present details about the integration and testing for one operating at 93 and 145 GHz.

The Crab Nebula, also known as Tau A, is a polarized astronomical source at millimeter wavelengths. It has been used as a stable light source for polarization angle calibration in millimeter-wave astronomy. However, it is known that its intensity and polarization vary as a function of time at a variety of wavelengths. Thus, it is of interest to verify the stability of the millimeter-wave polarization. If detected, polarization variability may be used to better understand the dynamics of Tau~A, and for understanding the validity of Tau~A as a calibrator. One intriguing application of such observation is to use it for the search of axion-like particles (ALPs). Ultralight ALPs couple to photons through a Chern-Simons term, and induce a temporal oscillation in the polarization angle of linearly polarized sources. After assessing a number of systematic errors and testing for internal consistency, we evaluate the variability of the polarization angle of the Crab Nebula using 2015 and 2016 observations with the 150 GHz POLARBEAR instrument. We place a median 95% upper bound of polarization oscillation amplitude $A < 0.065^\circ$ over the oscillation frequencies from $0.75~\mathrm{year}^{-1}$ to $0.66~\mathrm{hour}^{-1}$. Assuming that no sources other than ALP are causing Tau A's polarization angle variation, that the ALP constitutes all the dark matter, and that the ALP field is a stochastic Gaussian field, this bound translates into a median 95% upper bound of ALP-photon coupling $g_{a\gamma\gamma} < 2.16\times10^{-12}\,\mathrm{GeV}^{-1}\times(m_a/10^{-21} \mathrm{eV})$ in the mass range from $9.9\times10^{-23} \mathrm{eV}$ to $7.7\times10^{-19} \mathrm{eV}$. This demonstrates that this type of analysis using bright polarized sources is as competitive as those using the polarization of cosmic microwave background in constraining ALPs., Comment: 24 pages, 19 figures, 5 tables

The Simons Observatory (SO) experiment is a cosmic microwave background (CMB) experiment located in the Atacama Desert, Chile. The SO' s small aperture telescopes (SATs) consist of three telescopes designed for precise CMB polarimetry at large angular scales. Each SAT uses a cryogenic rotating half-wave plate (HWP) as a polarization modulator to mitigate atmospheric 1/f noise and other systematics. To realize efficient polarization modulation over the observation bands, we fabricated an achromatic HWP (AHWP) consisting of three sapphire plates with anti-reflection coatings. The AHWP is designed to have broadband modulation efficiency and transmittance. This paper reports on the design and the preliminary characterization of the AHWPs for SATs.

For cosmic microwave background (CMB) polarization observations, calibration of detector polarization angles is essential. We have developed a fully remote controlled calibration system with a sparse wire grid that reflects linearly polarized light along the wire direction. The new feature is a remote-controlled system for regular calibration, which has not been possible in sparse wire grid calibrators in past experiments. The remote control can be achieved by two electric linear actuators that load or unload the sparse wire grid into a position centered on the optical axis of a telescope between the calibration time and CMB observation. Furthermore, the sparse wire grid can be rotated by a motor. A rotary encoder and a gravity sensor are installed on the sparse wire grid to monitor the wire direction. They allow us to achieve detector angle calibration with expected systematic error of $0.08^{\circ}$. The calibration system will be installed in small-aperture telescopes at Simons Observatory.

We use time-domain simulations of Jupiter observations to test and develop a beam reconstruction pipeline for the Simons Observatory Small Aperture Telescopes. The method relies on a map maker that estimates and subtracts correlated atmospheric noise and a beam fitting code designed to compensate for the bias caused by the map maker. We test our reconstruction performance for four different frequency bands against various algorithmic parameters, atmospheric conditions and input beams. We additionally show the reconstruction quality as function of the number of available observations and investigate how different calibration strategies affect the beam uncertainty. For all of the cases considered, we find good agreement between the fitted results and the input beam model within a ~1.5% error for a multipole range l = 30 - 700 and an ~0.5% error for a multipole range l = 50 - 200. We conclude by using a harmonic-domain component separation algorithm to verify that the beam reconstruction errors and biases observed in our analysis do not significantly bias the Simons Observatory r-measurement., Comment: 23 pages, 21 figures, published in ApJ

Very light pseudoscalar fields, often referred to as axions, are compelling dark matter candidates and can potentially be detected through their coupling to the electromagnetic field. Recently a novel detection technique using the cosmic microwave background (CMB) was proposed, which relies on the fact that the axion field oscillates at a frequency equal to its mass in appropriate units, leading to a time-dependent birefringence. For appropriate oscillation periods this allows the axion field at the telescope to be detected via the induced sinusoidal oscillation of the CMB linear polarization. We search for this effect in two years of POLARBEAR data. We do not detect a signal, and place a median $95 \%$ upper limit of $0.65 ^\circ$ on the sinusoid amplitude for oscillation frequencies between $0.02\,\text{days}^{-1}$ and $0.45\,\text{days}^{-1}$, which corresponds to axion masses between $9.6 \times 10^{-22} \, \text{eV}$ and $2.2\times 10^{-20} \,\text{eV}$. Under the assumptions that 1) the axion constitutes all the dark matter and 2) the axion field amplitude is a Rayleigh-distributed stochastic variable, this translates to a limit on the axion-photon coupling $g_{\phi \gamma} < 2.4 \times 10^{-11} \,\text{GeV}^{-1} \times ({m_\phi}/{10^{-21} \, \text{eV}})$., Comment: 17 pages, 5 figures, 2 tables. Published in Physical Review D

Observing in six frequency bands from 27 to 280 GHz over a large sky area, the Simons Observatory (SO) is poised to address many questions in Galactic astrophysics in addition to its principal cosmological goals. In this work, we provide quantitative forecasts on astrophysical parameters of interest for a range of Galactic science cases. We find that SO can: constrain the frequency spectrum of polarized dust emission at a level of $\Delta\beta_d \lesssim 0.01$ and thus test models of dust composition that predict that $\beta_d$ in polarization differs from that measured in total intensity; measure the correlation coefficient between polarized dust and synchrotron emission with a factor of two greater precision than current constraints; exclude the non-existence of exo-Oort clouds at roughly 2.9$\sigma$ if the true fraction is similar to the detection rate of giant planets; map more than 850 molecular clouds with at least 50 independent polarization measurements at 1 pc resolution; detect or place upper limits on the polarization fractions of CO(2-1) emission and anomalous microwave emission at the 0.1% level in select regions; and measure the correlation coefficient between optical starlight polarization and microwave polarized dust emission in $1^\circ$ patches for all lines of sight with $N_{\rm H} \gtrsim 2\times10^{20}$ cm$^{-2}$. The goals and forecasts outlined here provide a roadmap for other microwave polarization experiments to expand their scientific scope via Milky Way astrophysics., Comment: Submitted to AAS journals. 33 pages, 10 figures

The Simons Observatory (SO) is a cosmic microwave background (CMB) experiment from the Atacama Desert in Chile comprising three small-aperture telescopes (SATs) and one large-aperture telescope (LAT). In total, SO will field over 60,000 transition-edge sensor (TES) bolometers in six spectral bands centered between 27 and 280 GHz in order to achieve the sensitivity necessary to measure or constrain numerous cosmological quantities. In this work, we focus on the SATs which are optimized to search for primordial gravitational waves that are detected as parity-odd polarization patterns called a B-modes on degree scales in the CMB. Each SAT employs a single optics tube with TES arrays operating at 100 mK. The high throughput optics system has a 42 cm aperture and a 35-degree field of view coupled to a 36 cm diameter focal plane. The optics consist of three metamaterial anti-re ection coated silicon lenses. Cryogenic ring baffles with engineered blackbody absorbers are installed in the optics tube to minimize the stray light. The entire optics tube is cooled to 1 K. A cryogenic continuously rotating half-wave plate near the sky side of the aperture stop helps to minimize the effect of atmospheric uctuations. The telescope warm baffling consists of a forebaffle, an elevation stage mounted co-moving shield, and a fixed ground shield that together control the far side-lobes and mitigates ground-synchronous systematics. We present the status of the SAT development., Comment: 8 pages, 6 figures

We quantify the calibration requirements for systematic uncertainties for next-generation ground-based observatories targeting the large-angle $B$-mode polarization of the Cosmic Microwave Background, with a focus on the Simons Observatory (SO). We explore uncertainties on gain calibration, bandpass center frequencies, and polarization angles, including the frequency variation of the latter across the bandpass. We find that gain calibration and bandpass center frequencies must be known to percent levels or less to avoid biases on the tensor-to-scalar ratio $r$ on the order of $\Delta r\sim10^{-3}$, in line with previous findings. Polarization angles must be calibrated to the level of a few tenths of a degree, while their frequency variation between the edges of the band must be known to ${\cal O}(10)$ degrees. Given the tightness of these calibration requirements, we explore the level to which residual uncertainties on these systematics would affect the final constraints on $r$ if included in the data model and marginalized over. We find that the additional parameter freedom does not degrade the final constraints on $r$ significantly, broadening the error bar by ${\cal O}(10\%)$ at most. We validate these results by reanalyzing the latest publicly available data from the BICEP2/Keck collaboration within an extended parameter space covering both cosmological, foreground and systematic parameters. Finally, our results are discussed in light of the instrument design and calibration studies carried out within SO., Comment: 41 pages, 18 figures

Among the greatest mysteries in cosmology are the flatness problem, concerning the lack of curvature of the universe, and the homogeneity problem, questioning why the universe is almost isotropic despite having regions that are causally disconnected. These problems served as motivation for the theory of inflation, which suggests a period of exponential expansion in the early universe, and the inflationary origin of the universe can be traced by B-mode polarization. In an effort to better understand the potential foreground systematics, especially the levels of polarized dust emission, we queried the Heiles catalog to produce a list of starlight polarization data in the so-called "Southern Hole", which is an approximately $20\times20$ degree region centered at RA: $00^h12^m00^s$ and DEC: $-59{\deg}18'00''$ that is being examined by multiple CMB polarization experiments. Because magnetic field tends to dictate the orientation of dust grains, which in turn determines how starlight is polarized, starlight polarization can be used to trace magnetic fields. Therefore, to improve our understanding of the properties of this region, we used this catalog, along with Gaia data as tracers of the three-dimensional distribution of dust, as a potential indicator of magnetic field orientation throughout the galaxy in the Southern Hole region. We then analyzed these data with the hope that magnetic field data can be used to create a template to aid in subtracting away the contamination of CMB B-mode searches by polarized dust emission. While the results of the analysis are promising, we found that the currently available data are severely inadequate for the purpose of creating a template, thus demonstrating the need for improved and more uniform coverage of the Southern Hole when it comes to polarization measurements., Comment: 10 pages, 6 figures

In the framework of the Standard Model Extension (SME), we present improved constraints on anisotropic Lorentz invariance and Charge-Parity-Time (CPT) violation by searching for astrophysical signals of cosmic vacuum birefringence with broadband optical polarimetry of high redshift astronomical sources, including Active Galactic Nuclei and Gamma-Ray Burst afterglows. We generalize the work in Kislat 2018, which studied the SME mass dimension $d = 4$ case, to arbitrary mass dimension for both the CPT-even and CPT-odd cases. We then present constraints on all 10, 16, and 42 anisotropic birefringent SME coefficients for dimension $d = 4$, $d = 5$, and $d = 6$ models, respectively, using 7554 observations for odd d and 7376 observations for even d of 1278 unique sources on the sky, which, to our knowledge, comprises the most complete catalog of optical polarization from extragalactic sources in the literature to date. Compared to the smaller sample of 44 and 45 broadband optical polarimetry observations analyzed in Kislat 2018 and Kislat and Krawczynski 2017, our dimension $d = 4$ and $d = 5$ average constraints are more sensitive by factors of 35 and 10, corresponding to a reduction in allowed SME parameter space volume for these studies of 15 and 16 orders of magnitude, respectively. Constraints from individual lines of sight can be significantly stronger using spectropolarimetry. Nevertheless, due to the increased number of observations and lines of sight in our catalog, our average $d = 4$ and $d = 5$ broadband constraints are within factors of 2 and 12 of previous constraints using spectropolarimetry from Kislat 2018 and Kislat and Krawczynski 2017, respectively, using an independent data set and an improved analysis method. By contrast, our anisotropic constraints on all 42 birefringent SME coefficients for $d = 6$ are the first to be presented in the literature., Comment: 29 pages, 14 figures

The Simons Observatory (SO) is an upcoming cosmic microwave background (CMB) experiment located on Cerro Toco, Chile, that will map the microwave sky in temperature and polarization in six frequency bands spanning 27 to 285 GHz. SO will consist of one 6-meter Large Aperture Telescope (LAT) fielding $\sim$30,000 detectors and an array of three 0.42-meter Small Aperture Telescopes (SATs) fielding an additional 30,000 detectors. This synergy will allow for the extremely sensitive characterization of the CMB over angular scales ranging from an arcmin to tens of degrees, enabling a wide range of scientific output. Here we focus on the SATs targeting degree angular scales with successive dichroic instruments observing at Mid-Frequency (MF: 93/145 GHz), Ultra-High-Frequency (UHF: 225/285 GHz), and Low-Frequency (LF: 27/39 GHz). The three SATs will be able to map $\sim$10% of the sky to a noise level of 2 $\mu$K-arcmin when combining 93 and 145 GHz. The multiple frequency bands will allow the CMB to be separated from galactic foregrounds (primarily synchrotron and dust), with the primary science goal of characterizing the primordial tensor-to-scalar ratio, $r$, at a target level of $\sigma \left(r\right) \approx 0.003$.

We present a measurement of the gravitational lensing deflection power spectrum reconstructed with two seasons cosmic microwave background polarization data from the POLARBEAR experiment. Observations were taken at 150 GHz from 2012 to 2014 which survey three patches of sky totaling 30 square degrees. We test the consistency of the lensing spectrum with a Cold Dark Matter (CDM) cosmology and reject the no-lensing hypothesis at a confidence of 10.9 sigma including statistical and systematic uncertainties. We observe a value of A_L = 1.33 +/- 0.32 (statistical) +/- 0.02 (systematic) +/- 0.07 (foreground) using all polarization lensing estimators, which corresponds to a 24% accurate measurement of the lensing amplitude. Compared to the analysis of the first year data, we have improved the breadth of both the suite of null tests and the error terms included in the estimation of systematic contamination.

The Simons Observatory (SO) is a ground-based cosmic microwave background (CMB) experiment sited on Cerro Toco in the Atacama Desert in Chile that promises to provide breakthrough discoveries in fundamental physics, cosmology, and astrophysics. Supported by the Simons Foundation, the Heising-Simons Foundation, and with contributions from collaborating institutions, SO will see first light in 2021 and start a five year survey in 2022. SO has 287 collaborators from 12 countries and 53 institutions, including 85 students and 90 postdocs. The SO experiment in its currently funded form ('SO-Nominal') consists of three 0.4 m Small Aperture Telescopes (SATs) and one 6 m Large Aperture Telescope (LAT). Optimized for minimizing systematic errors in polarization measurements at large angular scales, the SATs will perform a deep, degree-scale survey of 10% of the sky to search for the signature of primordial gravitational waves. The LAT will survey 40% of the sky with arc-minute resolution. These observations will measure (or limit) the sum of neutrino masses, search for light relics, measure the early behavior of Dark Energy, and refine our understanding of the intergalactic medium, clusters and the role of feedback in galaxy formation. With up to ten times the sensitivity and five times the angular resolution of the Planck satellite, and roughly an order of magnitude increase in mapping speed over currently operating ("Stage 3") experiments, SO will measure the CMB temperature and polarization fluctuations to exquisite precision in six frequency bands from 27 to 280 GHz. SO will rapidly advance CMB science while informing the design of future observatories such as CMB-S4., Comment: Astro2020 Decadal Project Whitepaper. arXiv admin note: text overlap with arXiv:1808.07445

Vacuum birefringence from Lorentz and CPT violation in the Standard-Model Extension can be constrained using ground-based optical polarimetry of extragalactic sources. We describe results from a pilot program with an automated system that can perform simultaneous optical polarimetry in multiple passbands on different telescopes with an effective 0.45 m aperture. Despite the limited collecting area, our polarization measurements of AGN using a wider effective optical passband than previous studies yielded individual line-of-sight constraints for Standard-Model Extension mass dimension $d = 5$ operators within a factor of about one to ten of comparable broadband polarimetric bounds obtained using data from a 3.6 m telescope with roughly 64 times the collecting area. Constraining more general anisotropic Standard-Model Extension coefficients at higher $d$ would require more AGN along different lines of sight. This motivates a future dedicated ground-based, multi-band, optical polarimetry AGN survey with $\gtrsim 1$ m-class telescopes, to obtain state-of-the-art anisotropic Standard-Model Extension $d = 4, 5, 6$ constraints, while also using complementary archival polarimetry. This could happen more quickly and cost-effectively than via spectropolarimetry and long before more competitive constraints from space- or balloon-based x-ray/$\gamma$-ray polarization measurements., Comment: Presented at the Eighth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, May 12-16, 2019; typo in one author name changed from v1

Upcoming observations from the Simons Observatory have been projected to constrain the tensor-to-scalar ratio, $r$, at the level of $\sigma(r)=$0.003. Here we describe one of the forecasting algorithms for the Simons Observatory in more detail, based on cleaning CMB polarization maps using a parametric model. We present a new code to perform this end-to-end forecast, and explore the assumptions in greater detail. If spatial uniformity of the spectral energy distribution of synchrotron radiation and thermal dust emission is assumed over the region planned for observations, covering almost a fifth of the sky, a bias of order 1--3$\sigma$ in $r$ is projected for foreground models consistent with current data. We find that by masking the most contaminated regions of sky, or by adopting more parameters to describe the spatial variation in spectral index for synchrotron and dust, such a bias can be mitigated for the foreground models we consider. We also explore strategies for testing whether the cleaned CMB polarization maps contain residual foreground contamination, including cross-correlating with maps tracing the foregrounds. This method also has applications for other CMB polarization experiments., Comment: 13 pages, 9 figures

The primary scientific target of the CMB polarization experiments that are currently being built and proposed is the detection of primordial tensor perturbations. As a byproduct, these instruments will significantly improve constraints on cosmic birefringence, or the rotation of the CMB polarization plane. If convincingly detected, cosmic birefringence would be a dramatic manifestation of physics beyond the standard models of particle physics and cosmology. We forecast the bounds on the cosmic polarization rotation (CPR) from the upcoming ground-based Simons Observatory (SO) and the space-based LiteBIRD experiments, as well as a "fourth generation" ground-based CMB experiment like CMB-S4 and the mid-cost space mission PICO. We examine the detectability of both a stochastic anisotropic rotation field and an isotropic rotation by a constant angle. CPR induces new correlations of CMB observables, including spectra of parity-odd type in the case of isotropic CPR, and mode-coupling correlations in the anisotropic rotation case. We find that LiteBIRD and SO will reduce the 1$\sigma$ bound on the isotropic CPR from the current value of 30 arcmin to 1.5 and 0.6 arcmin, respectively, while CMB-S4-like and PICO will reduce it to $\sim 0.1$ arcmin. The bounds on the amplitude of a scale-invariant CPR spectrum will be reduced by 1, 2 and 3 orders of magnitude by LiteBIRD, SO and CMB-S4-like/PICO, respectively. We discuss implications of the forecasted CPR bounds for pseudoscalar fields, primordial magnetic fields (PMF), and violations of Lorentz invariance. We find that CMB-S4-like and PICO can reduce the 1$\sigma$ bound on the amplitude of the scale-invariant PMF from 1 nG to 0.1 nG, while also probing the magnetic field of the Milky Way. They will also significantly improve bounds on the axion-photon coupling, placing stringent constraints on the string theory axions., Comment: 14 pages, 1 figure, 5 tables; minor corrections in V2, matches the version published in PRD

We describe the Fourier Transform Spectrometer (FTS) used for in-field testing of the POLARBEAR receiver, an experiment located in the Atacama Desert of Chile which measures the cosmic microwave background (CMB) polarization. The POLARBEAR-FTS (PB-FTS) is a Martin-Puplett interferometer designed to couple to the Huan Tran Telescope (HTT) on which the POLARBEAR receiver is installed. The PB-FTS measured the spectral response of the POLARBEAR receiver with signal-to-noise ratio (SNR) $>20$ for $\sim$69% of the focal plane detectors due to three features: a high throughput of 15.1 steradian cm$^{2}$, optimized optical coupling to the POLARBEAR optics using a custom designed output parabolic mirror, and a continuously modulated output polarizer. The PB-FTS parabolic mirror is designed to mimic the shape of the 2.5 m-diameter HTT primary reflector which allows for optimum optical coupling to the POLARBEAR receiver, reducing aberrations and systematics. One polarizing grid is placed at the output of the PB-FTS, and modulated via continuous rotation. This modulation allows for decomposition of the signal into different harmonics that can be used to probe potentially pernicious sources of systematic error in a polarization-sensitive instrument. The high throughput and continuous output polarizer modulation features are unique compared to other FTS calibrators used in the CMB field. In-field characterization of the POLARBEAR receiver was accomplished using the PB-FTS in April 2014. We discuss the design, construction, and operation of the PB-FTS and present the spectral characterization of the POLARBEAR receiver. We introduce future applications for the PB-FTS in the next-generation CMB experiment, the Simons Array.

We present the first measurement of cross-correlation between the lensing potential, reconstructed from cosmic microwave background (CMB) {\it polarization} data, and the cosmic shear field from galaxy shapes. This measurement is made using data from the POLARBEAR CMB experiment and the Subaru Hyper Suprime-Cam (HSC) survey. By analyzing an 11~deg$^2$ overlapping region, we reject the null hypothesis at 3.5$\sigma$\ and constrain the amplitude of the {\bf cross-spectrum} to $\widehat{A}_{\rm lens}=1.70\pm 0.48$, where $\widehat{A}_{\rm lens}$ is the amplitude normalized with respect to the Planck~2018{} prediction, based on the flat $\Lambda$ cold dark matter cosmology. The first measurement of this {\bf cross-spectrum} without relying on CMB temperature measurements is possible due to the deep POLARBEAR map with a noise level of ${\sim}$6\,$\mu$K-arcmin, as well as the deep HSC data with a high galaxy number density of $n_g=23\,{\rm arcmin^{-2}}$. We present a detailed study of the systematics budget to show that residual systematics in our results are negligibly small, which demonstrates the future potential of this cross-correlation technique., Comment: 16 pages, 5 figures, Accepted for publication in ApJ

At the linear level, the gravitational wave (GW) spectrum predicted by inflation, and many of its alternatives, can have arbitrarily small amplitude and consequently an unconstrained tilt. However, at second order, tensor fluctuations are sourced by scalar fluctuations that have been measured in the cosmic microwave background (CMB). These second order fluctuations generically produce a minimum amount of tensor perturbations corresponding to a tensor-to-scalar ratio of $r\sim 10^{-6}$. Inverting this relationship yields a bound on the tensor tilt sourced by scalar fluctuations. Since this induced GW spectrum depends on the scalar spectrum, we derive a new indirect bound that involves \textit{all scales} of the scalar spectrum based on CMB observations. This bound comes from the constraint on the number of effective relativistic degrees of freedom, $N_{eff}$. We estimate the bound using current data, and the improvements expected by future CMB experiment. The bound forces the running and running of running to conform to standard slow-roll predictions of $\alpha,\beta \lesssim (n_s-1)^2$, improving on current CMB measurements by an order of magnitude. This bound has further implications for the possibility of primordial black holes as dark matter candidates. Performing a likelihood analysis including this new constraint, we find that positive $\alpha$ and/or $\beta$ are disfavored at least at $1\sigma$. Finally, using bounds on the fractional energy density of gravitational waves today obtained by LIGO and the Pulsar Timing Array, we obtain a bound on the primordial scalar spectrum on these scales and give forecast for future measurements., Comment: 28 pages, 19 figures; Updated to conform to published version

The Simons Observatory (SO) is a set of cosmic microwave background instruments that will be deployed in the Atacama Desert in Chile. The key science goals include setting new constraints on cosmic inflation, measuring large scale structure with gravitational lensing, and constraining neutrino masses. Meeting these science goals with SO requires high sensitivity and improved calibration techniques. In this paper, we highlight a few of the most important instrument calibrations, including spectral response, gain stability, and polarization angle calibrations. We present their requirements for SO and experimental techniques that can be employed to reach those requirements., Comment: 13 pages, 4 figures, SPIE Astronomical Telescopes and Instrumentation 2018

Various quantum gravity approaches that extend beyond the standard model predict Lorentz Invariance and Charge-Parity-Time Violation at energies approaching the Planck scale. These models frequently predict a wavelength dependent speed of light, which would result in time delays between promptly emitted photons at different energies, as well as a wavelength-dependent rotation of the plane of linear polarization for photons resulting from vacuum birefringence. Here, we describe a pilot program with an automated system of small telescopes that can simultaneously conduct high cadence optical photometry and polarimetry of Active Galactic Nuclei (AGN) in multiple passbands. We use these observations as a proof-of-principle to demonstrate how such data can be used to test various Lorentz Violation models, including special cases of the Standard Model Extension (SME). In our initial campaign with this system, the Array Photo Polarimeter, we observed two AGN sources, including BL Lacertae at redshift z = 0.069, and S5 B0716+714 at z = 0.31. We demonstrate that optical polarimetry with a broadband Luminance filter combined with simultaneous $I_c$-band observations yields SME parameter constraints that are up to ~10 and ~30 times more sensitive than with a standard $I_c$-band filter, for SME models with mass dimension d = 5 and d = 6, respectively. Using only a small system of telescopes with an effective 0.45-m aperture, we further demonstrate d = 5 constraints for individual lines of sight that are within a factor of ~1-10 in sensitivity to comparable constraints from optical polarimetry with a 3.6-m telescope. Such an approach could significantly improve existing SME constraints via a polarimetric all-sky survey of AGN with multiple 1-meter class telescopes., Comment: 25 pages, 16 figures

The polarization of the atmosphere has been a long-standing concern for ground-based experiments targeting cosmic microwave background (CMB) polarization. Ice crystals in upper tropospheric clouds scatter thermal radiation from the ground and produce a horizontally-polarized signal. We report the detailed analysis of the cloud signal using a ground-based CMB experiment, POLARBEAR, located at the Atacama desert in Chile and observing at 150 GHz. We observe horizontally-polarized temporal increases of low-frequency fluctuations ("polarized bursts," hereafter) of $\lesssim$0.1 K when clouds appear in a webcam monitoring the telescope and the sky. The hypothesis of no correlation between polarized bursts and clouds is rejected with $>$24$\sigma$ statistical significance using three years of data. We consider many other possibilities including instrumental and environmental effects, and find no other reasons other than clouds that can explain the data better. We also discuss the impact of the cloud polarization on future ground-based CMB polarization experiments., Comment: 14 pages, 12 figures, 1 table, Submitted to ApJ

In this proceeding, we present studies of instrumental systematic effects for the Simons Obsevatory (SO) that are associated with the detector system and its interaction with the full SO experimental systems. SO will measure the Cosmic Microwave Background (CMB) temperature and polarization anisotropies over a wide range of angular scales in six bands with bandcenters spanning from 27 GHz to 270 GHz. We explore effects including intensity-to-polarization leakage due to coupling optics, bolometer nonlinearity, uncalibrated gain variations of bolometers, and readout crosstalk. We model the level of signal contamination, discuss proposed mitigation schemes, and present instrument requirements to inform the design of SO and future CMB projects., Comment: Proceeding from SPIE Astronomical Telescopes+Instrumentation 2018 (27 pages, 13 figures) v2: Added HEALPix reference

The Simons Observatory (SO) will make precision temperature and polarization measurements of the cosmic microwave background (CMB) using a series of telescopes which will cover angular scales between one arcminute and tens of degrees and sample frequencies between 27 and 270 GHz. Here we present the current design of the large aperture telescope receiver (LATR), a 2.4 m diameter cryostat that will be mounted on the SO 6 m telescope and will be the largest CMB receiver to date. The cryostat size was chosen to take advantage of the large focal plane area having high Strehl ratios, which is inherent to the Cross-Dragone telescope design. The LATR will be able to accommodate thirteen optics tubes, each having a 36 cm diameter aperture and illuminating several thousand transition-edge sensor (TES) bolometers. This set of equipment will provide an opportunity to make measurements with unparalleled sensitivity. However, the size and complexity of the LATR also pose numerous technical challenges. In the following paper, we present the design of the LATR and include how we address these challenges. The solutions we develop in the process of designing the LATR will be informative for the general CMB community, and for future CMB experiments like CMB-S4.

The Simons Observatory (SO) will provide precision polarimetry of the cosmic microwave background (CMB) using a series of telescopes which will cover angular scales from arc-minutes to tens of degrees, contain over 60,000 detectors, and observe in frequency bands between 27 GHz and 270 GHz. SO will consist of a six-meter-aperture telescope initially coupled to ~35,000 detectors along with an array of 0.5m aperture refractive cameras, coupled to an additional 30,000+ detectors. The large aperture telescope receiver (LATR) is coupled to a six-meter crossed Dragone telescope and will be 2.4m in diameter, weigh over 3 tons, and have five cryogenic stages (80 K, 40 K, 4 K, 1 K and 100 mK). The LATR is coupled to the telescope via 13 independent optics tubes containing cryogenic optical elements and detectors. The cryostat will be cooled by by two Cryomech PT90 (80 K) and three Cryomech PT420 (40 K and 4 K) pulse tube cryocoolers, with cooling of the 1 K and 100 mK stages by a commercial dilution refrigerator system. The second component, the small aperture telescope (SAT), is a single optics tube refractive cameras of 42cm diameter. Cooling of the SAT stages will be provided by two Cryomech PT420, one of which is dedicated to the dilution refrigeration system which will cool the focal plane to 100 mK. SO will deploy a total of three SATs. In order to estimate the cool down time of the camera systems given their size and complexity, a finite difference code based on an implicit solver has been written to simulate the transient thermal behavior of both cryostats. The result from the simulations presented here predict a 35 day cool down for the LATR. The simulations suggest additional heat switches between stages would be effective in distribution cool down power and reducing the time it takes for the LATR to cool. The SAT is predicted to cool down in one week, which meets the SO design goals.

The Simons Observatory (SO) will observe the temperature and polarization anisotropies of the cosmic microwave background (CMB) over a wide range of frequencies (27 to 270 GHz) and angular scales by using both small (0.5 m) and large (6 m) aperture telescopes. The SO small aperture telescopes will target degree angular scales where the primordial B-mode polarization signal is expected to peak. The incoming polarization signal of the small aperture telescopes will be modulated by a cryogenic, continuously-rotating half-wave plate (CRHWP) to mitigate systematic effects arising from slowly varying noise and detector pair-differencing. In this paper, we present an assessment of some systematic effects arising from using a CRHWP in the SO small aperture systems. We focus on systematic effects associated with structural properties of the HWP and effects arising when operating a HWP, including the amplitude of the HWP synchronous signal (HWPSS), and I -> P (intensity to polarization) leakage that arises from detector non-linearity in the presence of a large HWPSS. We demonstrate our ability to simulate the impact of the aforementioned systematic effects in the time domain. This important step will inform mitigation strategies and design decisions to ensure that SO will meet its science goals., Comment: 22 pages, 10 figures. Submitted to the Proceedings of SPIE: Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy IX

The Simons Observatory (SO) is a new cosmic microwave background experiment being built on Cerro Toco in Chile, due to begin observations in the early 2020s. We describe the scientific goals of the experiment, motivate the design, and forecast its performance. SO will measure the temperature and polarization anisotropy of the cosmic microwave background in six frequency bands: 27, 39, 93, 145, 225 and 280 GHz. The initial configuration of SO will have three small-aperture 0.5-m telescopes (SATs) and one large-aperture 6-m telescope (LAT), with a total of 60,000 cryogenic bolometers. Our key science goals are to characterize the primordial perturbations, measure the number of relativistic species and the mass of neutrinos, test for deviations from a cosmological constant, improve our understanding of galaxy evolution, and constrain the duration of reionization. The SATs will target the largest angular scales observable from Chile, mapping ~10% of the sky to a white noise level of 2 $\mu$K-arcmin in combined 93 and 145 GHz bands, to measure the primordial tensor-to-scalar ratio, $r$, at a target level of $\sigma(r)=0.003$. The LAT will map ~40% of the sky at arcminute angular resolution to an expected white noise level of 6 $\mu$K-arcmin in combined 93 and 145 GHz bands, overlapping with the majority of the LSST sky region and partially with DESI. With up to an order of magnitude lower polarization noise than maps from the Planck satellite, the high-resolution sky maps will constrain cosmological parameters derived from the damping tail, gravitational lensing of the microwave background, the primordial bispectrum, and the thermal and kinematic Sunyaev-Zel'dovich effects, and will aid in delensing the large-angle polarization signal to measure the tensor-to-scalar ratio. The survey will also provide a legacy catalog of 16,000 galaxy clusters and more than 20,000 extragalactic sources., Comment: This paper presents an overview of the Simons Observatory science goals, details about the instrument will be presented in a companion paper. The author contribution to this paper is available at https://simonsobservatory.org/publications.php (Abstract abridged) -- matching version published in JCAP

The Simons Observatory (SO) will make precision temperature and polarization measurements of the cosmic microwave background (CMB) using a series of telescopes which will cover angular scales between one arcminute and tens of degrees, contain over 60,000 detectors, and sample frequencies between 27 and 270 GHz. SO will consist of a six-meter-aperture telescope coupled to over 30,000 detectors along with an array of half-meter aperture refractive cameras, which together couple to an additional 30,000+ detectors. SO will measure fundamental cosmological parameters of our universe, find high redshift clusters via the Sunyaev-Zeldovich effect, constrain properties of neutrinos, and seek signatures of dark matter through gravitational lensing. In this paper we will present results of the simulations of the SO large aperture telescope receiver (LATR). We will show details of simulations performed to ensure the structural integrity and thermal performance of our receiver, as well as will present the results of finite element analyses (FEA) of designs for the structural support system. Additionally, a full thermal model for the LATR will be described. The model will be used to ensure we meet our design requirements. Finally, we will present the results of FEA used to identify the primary vibrational modes, and planned methods for suppressing these modes. Design solutions to each of these problems that have been informed by simulation will be presented., Comment: 14 pages, 10 figures, Proceedings of SPIE

The Simons Observatory (SO) is a new experiment that aims to measure the cosmic microwave background (CMB) in temperature and polarization. SO will measure the polarized sky over a large range of microwave frequencies and angular scales using a combination of small ($\sim0.5 \, \rm m$) and large ($\sim 6\, \rm m $) aperture telescopes and will be located in the Atacama Desert in Chile. This work is part of a series of papers studying calibration, sensitivity, and systematic errors for SO. In this paper, we discuss current efforts to model optical systematic effects, how these have been used to guide the design of the SO instrument, and how these studies can be used to inform instrument design of future experiments like CMB-S4. While optical systematics studies are underway for both the small aperture and large aperture telescopes, we limit the focus of this paper to the more mature large aperture telescope design for which our studies include: pointing errors, optical distortions, beam ellipticity, cross-polar response, instrumental polarization rotation and various forms of sidelobe pickup., Comment: Poster presented at SPIE Astronomical Telescopes and Instrumentation 2018

The Simons Observatory (SO) will make precise temperature and polarization measurements of the cosmic microwave background (CMB) using a set of telescopes which will cover angular scales between 1 arcminute and tens of degrees, contain over 60,000 detectors, and observe at frequencies between 27 and 270 GHz. SO will consist of a 6 m aperture telescope coupled to over 30,000 transition-edge sensor bolometers along with three 42 cm aperture refractive telescopes, coupled to an additional 30,000+ detectors, all of which will be located in the Atacama Desert at an altitude of 5190 m. The powerful combination of large and small apertures in a CMB observatory will allow us to sample a wide range of angular scales over a common survey area. SO will measure fundamental cosmological parameters of our universe, constrain primordial fluctuations, find high redshift clusters via the Sunyaev-Zel`dovich effect, constrain properties of neutrinos, and trace the density and velocity of the matter in the universe over cosmic time. The complex set of technical and science requirements for this experiment has led to innovative instrumentation solutions which we will discuss. The large aperture telescope will couple to a cryogenic receiver that is 2.4 m in diameter and nearly 3 m long, creating a number of technical challenges. Concurrently, we are designing the array of cryogenic receivers housing the 42 cm aperture telescopes. We will discuss the sensor technology SO will use and we will give an overview of the drivers for and designs of the SO telescopes and receivers, with their cold optical components and detector arrays.

The POLARBEAR-2/Simons Array Cosmic Microwave Background (CMB) polarization experiment is an upgrade and expansion of the existing POLARBEAR-1 (PB-1) experiment, located in the Atacama desert in Chile. Along with the CMB temperature and $E$-mode polarization anisotropies, PB-1 and the Simons Array study the CMB $B$-mode polarization anisotropies produced at large angular scales by inflationary gravitational waves, and at small angular scales by gravitational lensing. These measurements provide constraints on various cosmological and particle physics parameters, such as the tensor-to-scalar ratio $r$, and the sum of the neutrino masses. The Simons Array consists of three 3.5 m diameter telescopes with upgraded POLARBEAR-2 (PB-2) cryogenic receivers, named PB-2a, -2b, and -2c. PB-2a and -2b will observe the CMB over multiple bands centered at 95 GHz and 150 GHz, while PB-2c will observe at 220 GHz and 270 GHz, which will enable enhanced foreground separation and de-lensing. Each Simons Array receiver consists of two cryostats which share the same vacuum space: an optics tube containing the cold reimaging lenses and Lyot stop, infrared-blocking filters, and cryogenic half-wave plate; and a backend which contains the focal plane detector array, cold readout components, and millikelvin refrigerator. Each PB-2 focal plane array is comprised of 7,588 dual-polarization, multi-chroic, lenslet- and antenna-coupled, Transition Edge Sensor (TES) bolometers which are cooled to 250 mK and read out using Superconducting Quantum Interference Devices (SQUIDs) through a digital frequency division multiplexing scheme with a multiplexing factor of 40. In this work we describe progress towards commissioning the PB-2b and -2c receivers including cryogenic design, characterization, and performance of both the PB-2b and -2c backend cryostats., Comment: 20 pages

The Simons Observatory (SO) is an upcoming experiment that will study temperature and polarization fluctuations in the cosmic microwave background (CMB) from the Atacama Desert in Chile. SO will field both a large aperture telescope (LAT) and an array of small aperture telescopes (SATs) that will observe in six bands with center frequencies spanning from 27 to 270~GHz. Key considerations during the SO design phase are vast, including the number of cameras per telescope, focal plane magnification and pixel density, in-band optical power and camera throughput, detector parameter tolerances, and scan strategy optimization. To inform the SO design in a rapid, organized, and traceable manner, we have created a Python-based sensitivity calculator with several state-of-the-art features, including detector-to-detector optical white-noise correlations, a handling of simulated and measured bandpasses, and propagation of low-level parameter uncertainties to uncertainty in on-sky noise performance. We discuss the mathematics of the sensitivity calculation, the calculator's object-oriented structure and key features, how it has informed the design of SO, and how it can enhance instrument design in the broader CMB community, particularly for CMB-S4., Comment: Submitted to the Proceedings of SPIE: Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy IX

We measure the Cosmic Microwave Background (CMB) skewness power spectrum in $\textit{Planck}$, using frequency maps of the HFI instrument and the Sunyaev-Zel'dovich (SZ) component map. The two-to-one skewness power spectrum measures the cross-correlation between CMB lensing and the thermal SZ effect. We also directly measure the same cross-correlation using $\textit{Planck}$ CMB lensing map and the SZ map and compare it to the cross-correlation derived from the skewness power spectrum. We model fit the SZ power spectrum and CMB lensing-SZ cross power spectrum via the skewness power spectrum to constrain the gas pressure profile of dark matter halos. The gas pressure profile is compared to existing measurements in the literature including a direct estimate based on the stacking of SZ clusters in $\textit{Planck}$., Comment: 6 pages, 4 figures, ApJL submitted

We describe a novel method to measure the absolute orientation of the polarization plane of the CMB with arcsecond accuracy, enabling unprecedented measurements for cosmology and fundamental physics. Existing and planned CMB polarization instruments looking for primordial B-mode signals need an independent, experimental method for systematics control on the absolute polarization orientation. The lack of such a method limits the accuracy of the detection of inflationary gravitational waves, the constraining power on the neutrino sector through measurements of gravitational lensing of the CMB, the possibility of detecting Cosmic Birefringence, and the ability to measure primordial magnetic fields. Sky signals used for calibration and direct measurements of the detector orientation cannot provide an accuracy better than 1 deg. Self-calibration methods provide better accuracy, but may be affected by foreground signals and rely heavily on model assumptions. The POLarization Orientation CALibrator for Cosmology, POLOCALC, will dramatically improve instrumental accuracy by means of an artificial calibration source flying on balloons and aerial drones. A balloon-borne calibrator will provide far-field source for larger telescopes, while a drone will be used for tests and smaller polarimeters. POLOCALC will also allow a unique method to measure the telescopes' polarized beam. It will use microwave emitters between 40 and 150 GHz coupled to precise polarizing filters. The orientation of the source polarization plane will be registered to sky coordinates by star cameras and gyroscopes with arcsecond accuracy. This project can become a rung in the calibration ladder for the field: any existing or future CMB polarization experiment observing our polarization calibrator will enable measurements of the polarization angle for each detector with respect to absolute sky coordinates., Comment: 15 pages, 5 figures, Accepted by Journal of Astronomical Instrumentation

A continuously rotating half-wave plate (CRHWP) is a promising tool to improve the sensitivity to large angular scales in cosmic microwave background (CMB) polarization measurements. With a CRHWP, single detectors can measure three of the Stokes parameters, $I$, $Q$ and $U$, thereby avoiding the set of systematic errors that can be introduced by mismatches in the properties of orthogonal detector pairs. We focus on the implementation of CRHWPs in large aperture telescopes (i.e. the primary mirror is larger than the current maximum half-wave plate diameter of $\sim$0.5 m), where the CRHWP can be placed between the primary mirror and focal plane. In this configuration, one needs to address the intensity to polarization ($I{\rightarrow}P$) leakage of the optics, which becomes a source of 1/f noise and also causes differential gain systematics that arise from CMB temperature fluctuations. In this paper, we present the performance of a CRHWP installed in the POLARBEAR experiment, which employs a Gregorian telescope with a 2.5 m primary illumination pattern. The CRHWP is placed near the prime focus between the primary and secondary mirrors. We find that the $I{\rightarrow}P$ leakage is larger than the expectation from the physical properties of our primary mirror, resulting in a 1/f knee of 100 mHz. The excess leakage could be due to imperfections in the detector system, i.e. detector non-linearity in the responsivity and time-constant. We demonstrate, however, that by subtracting the leakage correlated with the intensity signal, the 1/f noise knee frequency is reduced to 32 mHz ($\ell \sim$39 for our scan strategy), which is very promising to probe the primordial B-mode signal. We also discuss methods for further noise subtraction in future projects where the precise temperature control of instrumental components and the leakage reduction will play a key role., Comment: 27 pages, 5 figures, 3 tables, published version in JCAP. Includes some minor corrections

We present a halo-model-based approach to calculate the cross-correlation between $\rm{21\,cm}$ HI intensity fluctuations and $\rm{Ly}\alpha$ emitters (LAE) during the epoch of reionization (EoR). Ionizing radiation around dark matter halos are modeled as bubbles with the size and growth determined based on the reionization photon production, among other physical parameters. The cross-correlation shows a clear negative-to-positive transition, associated with transition from ionized to neutral hydrogen in the intergalactic medium during EoR. The cross-correlation is subject to several foreground contaminants, including foreground radio point sources important for $\rm{21\,cm}$ experiments and low-$z$ interloper emission lines, such as $\rm{H}\alpha$, OIII, and OII, for $\rm{Ly}\alpha$ experiments. Our calculations show that by masking out high fluxes in the $\rm{Ly}\alpha$ measurement, the correlated foreground contamination on the $\rm{21\,cm}$-$\rm{Ly}\alpha$ cross-correlation can be dramatically reduced. We forecast the detectability of $\rm{21\,cm}$-$\rm{Ly}\alpha$ cross-correlation at different redshifts and adopt a Fisher matrix approach to estimate uncertainties on the key EoR parameters that have not been well constrained by other observations of reionization. This halo-model-based approach enables us to explore the EoR parameter space rapidly for different $\rm{21\,cm}$ and $\rm{Ly}\alpha$ experiments., Comment: 13 pages, 17 figures. Version accepted for publication in ApJ

In the last two decades we have seen important mutual stimulations between the community working on electrodynamics of continuous media and the community working on spacetime structure. This is highlighted by the publication of two important monographs from two communities: Foundations of Classical Electrodynamics by F. W. Hehl and Yu. N. Obukhov (Birkh\"auser, Boston 2003) and Differential Forms in Electromagnetics by I. V. Lindell (IEEE Press-Wiley, Piscataway, NJ 2004; see also a new book "Multiforms, Dyadics, and Electromagnetic Media" by the same author in 2015). Starting around 1960, magnetoelectric effects and magnetoelectric media have been a focus of study. Somewhat later, the constitutive tensor density framework was used to construct spacetime structure theoretically and empirically. Earlier, in putting Maxwell equations into a form compatible with general relativity, Einstein noticed that the Maxwell equations can be formulated in a form independent of the metric gravitational potential in 1916; only the constitutive tensor density depends on the metric. This was followed by further stimulating and clarifying works of Weyl in 1918, Murnaghan in 1921, Kottler in 1922 and Cartan in 1923. Year 2016 is the centennial of the start of this historical development. International Journal of Modern Physics D of World Scientific is celebrating the occasion by publishing this special issue on Spacetime Structure and Electrodynamics. We have invited researchers to submit original research articles that would contribute to a better understanding of the phenomena inherent to spacetime structure and electrodynamic media., Comment: 5 pages with links to arXiv

One of the most powerful probes of new physics is the polarized Cosmic Microwave Background (CMB). The detection of a nonzero polarization angle rotation between the CMB surface of last scattering and today could provide evidence of Lorentz-violating physics. The purpose of this paper is twofold. First we review one popular mechanism for polarization rotation of CMB photons: the pseudo-Nambu-Goldstone boson. Second, we propose a method to use the Polarbear experiment to constrain Lorentz-violating physics in the context of the Standard-Model Extension, a framework to standardize a large class of potential Lorentz-violating terms in particle physics.