[Paper Review] A New Upper Limit on the Polarization of the Cosmic Microwave Background Radiation

C. O’Dell|ArXiv.org|Jan 15, 2002

Cosmology and Gravitation Theories68 references3 citations

TL;DR

This paper presents a new upper limit on large-scale cosmic microwave background (CMB) polarization using a ground-based experiment at the University of Wisconsin-Madison. Despite using older technology and a suboptimal site, the study achieved a 95% confidence upper limit of 10 μK for both E- and B-mode polarization, and 8 μK if B-mode is assumed zero, setting the tightest constraints to date before future high-sensitivity missions began.

ABSTRACT

The Cosmic Microwave Background Radiation (CMB) is an invaluable probe of the conditions of the early universe. Recent measurements of its spatial anisotropy have allowed accurate determinations of several fundamental cosmological parameters, such as the curvature of the universe, the shape of the spectrum of primordial density fluctuations, and the contribution of baryons, dark matter, and dark energy to the overall energy density of the universe. In addition to being spatially non-uniform, the CMB is theorized to be slightly polarized. Measurements of this polarization, particularly at large angular scales, have the potential to provide information on primordial gravitational waves, theories of inflation, and the ionization history of the universe, as well as help further constrain cosmological parameters. Polarization has not yet been detected in the CMB. This thesis describes a recent search for CMB polarization at large angular scales, conducted in the spring of 2000 at the University of Wisconsin-Madison. After a general introduction on both CMB polarization and general microwave polarimetry, details of the experiment itself are given, as well as a full description of the data selection and analysis techniques. Using these techniques, our data lead to a new upper limit on CMB polarization at large angular scales of 10 $μ$K in both E- and B-type polarization at 95% confidence. If B-polarization is assumed to be zero, the limit for E-type polarization is lowered to 8 $μ$K. This experiment is the first of a new breed of highly-sensitive instruments that will one day map out this interesting property of the Cosmic Microwave Background Radiation.

Motivation & Objective

• To set a new upper limit on large-scale cosmic microwave background (CMB) polarization using a ground-based microwave polarimeter.
• To improve constraints on cosmological parameters through polarization measurements, particularly those related to primordial gravitational waves and inflation.
• To demonstrate the feasibility of high-sensitivity CMB polarization measurements using a single-receiver system with optimized data analysis.
• To lay the groundwork for future multi-pixel, multi-band experiments by validating data selection and analysis techniques on real-world data.
• To explore the potential of temperature-polarization cross-correlations for setting even tighter limits, despite low expected signal amplitudes.

Proposed method

• Conducted a ground-based CMB polarization survey in spring 2000 at the University of Wisconsin-Madison using a single-dish polarimeter (POLAR) with a 2.6 m primary dish.
• Employed a cryogenically cooled HEMT receiver operating at Ka-band (27–35 GHz) to minimize system temperature and enhance sensitivity.
• Applied a full data selection and analysis pipeline, including calibration, flagging of bad data, and noise characterization using time-ordered data.
• Used Cholesky decomposition to efficiently compute the likelihood function and invert the covariance matrix, reducing numerical errors and improving computational speed.
• Performed a likelihood analysis using the radiometer equation and full noise covariance modeling to derive confidence intervals on polarization amplitudes.
• Evaluated both E-mode and B-mode polarization power spectra independently, assuming isotropy and Gaussian noise, to derive upper limits at 95% confidence.

Experimental results

Research questions

• RQ1 What is the tightest upper limit on large-scale CMB E-mode and B-mode polarization achievable with a single-receiver ground-based experiment?
• RQ2 How do data selection and noise modeling techniques affect the sensitivity and reliability of CMB polarization upper limits?
• RQ3 Can temperature-polarization cross-correlations be used to set more stringent limits on CMB polarization, even when the expected signal is below 1 μK?
• RQ4 What improvements in sensitivity are possible by relocating such experiments to high-altitude, low-noise sites like White Mountain or the Atacama Desert?
• RQ5 To what extent can future multi-pixel, multi-band systems improve on the current upper limits, especially for B-mode detection?

Key findings

• The experiment established a new 95% confidence upper limit of 10 μK on large-scale CMB polarization for both E-mode and B-mode components.
• Assuming zero B-mode polarization, the upper limit for E-mode polarization was reduced to 8 μK, reflecting improved sensitivity under a simplified model.
• The study demonstrated that even with outdated technology and a non-ideal observing site, a well-designed data analysis pipeline could achieve state-of-the-art limits.
• The use of Cholesky decomposition for likelihood evaluation significantly improved numerical stability and computational efficiency in covariance matrix inversion.
• The results suggest that future experiments using similar techniques at high-altitude sites could achieve sensitivity down to ~0.5 μK, a factor of 20 improvement over this work.
• The authors anticipate that future multi-pixel, multi-band systems—such as the upgraded POLAR-COMPASS project—will have a strong potential to detect CMB polarization.