How to make maps from CMB data without losing information

The next generation of CMB experiments can measure cosmological parameters with unprecedented accuracy - in principle. To achieve this in practice when faced with such gigantic data sets, elaborate data analysis methods are needed to make it computationally feasible. An important step in the data pipeline is to make a map, which typically reduces the size of the data set my orders of magnitude. We compare ten map-making methods, and find that for the Gaussian case, both the method used by the COBE DMR team and various variants of Wiener filtering are optimal in the sense that the map retains all cosmological information that was present in the time-ordered data (TOD). Specifically, one obtains just as small error bars on cosmological parameters when estimating them from the map as one could have obtained by estimating them directly from the TOD. The method of simply averaging the observations of each pixel (for total-power detectors), on the contrary, is found to generally destroy information, as does the maximum entropy method and most other non-linear map-making techniques. Since it is also numerically feasible, the COBE method is the natural choice for large data sets. Other lossless (e.g. Wiener-filtered) maps can then be computed directly from the COBE method map.Comment: Minor revisions to match published version. 12 pages, with 1 figure included. Color figure and links at http://www.sns.ias.edu/~max/mapmaking.html (faster from the US), from http://www.mpa-garching.mpg.de/~max/mapmaking.html (faster from Europe) or from [email protected]

Removing point sources from CMB maps

For high-precision cosmic microwave background (CMB) experiments, contamination from extragalactic point sources is a major concern. It is therefore useful to be able to detect and discard point source contaminated pixels using the map itself. We show that the sensitivity with which this can be done can often be greatly improved (by factors between 2.5 and 18 for the upcoming Planck mission) by a customized hi-pass filtering that suppresses fluctuations due to CMB and diffuse galactic foregrounds. This means that point source contamination will not severely degrade the cleanest Planck channels unless current source count estimates are off by more than an order of magnitude. A catalog of around 40,000 far infra-red sources at 857 GHz may be a useful by-product of Planck.Comment: 4 pages, with 2 figures included. Minor revisions to match accepted version. Color figure and links at http://www.sns.ias.edu/~max/cleaning.html (faster from the US), from http://www.mpa-garching.mpg.de/~max/cleaning.html (faster from Europe) or from [email protected], and Angelica's foreground links at http://www.sns.ias.edu/~angelica/foreground.htm

Cosmic Microwave Background Anisotropy Observing Strategy Assessment

I develop a method for assessing the ability of an instrument, coupled with an observing strategy, to measure the angular power spectrum of the cosmic microwave background (CMB). It allows for efficient calculation of expected parameter uncertainties. Related to this method is a means of graphically presenting, via the ``eigenmode window function'', the sensitivity of an observation to different regions of the spectrum, which is a generalization of the traditional practice of presenting the trace of the window function. I apply these techniques to a balloon-borne bolometric instrument to be flown this summer (MSAM2). I find that a smoothly scanning secondary is better than a chopping one and that, in this case, a very simple analytic formula provides a good (40\% or better) approximation to expected power spectrum uncertainties.Comment: Substantial revisions, LaTeX 15 pages including 3 figure

Non-Gaussianity in Two-Field Inflation

We derive semi-analytic formulae for the local bispectrum and trispectrum in general two-field inflation and provide a simple geometric recipe for building observationally allowed models with observable non-Gaussianity. We use the \delta N formalism and the transfer function formalism to express the bispectrum almost entirely in terms of model-independent physical quantities. Similarly, we calculate the trispectrum and show that the trispectrum parameter \tau NL can be expressed entirely in terms of spectral observables, which provides a new consistency relation unique to two-field inflation. We show that in order to generate observably large non-Gaussianity during inflation, the sourcing of curvature modes by isocurvature modes must be extremely sensitive to the initial conditions, and that the amount of sourcing must be moderate in order to avoid excessive fine-tuning. Under some minimal assumptions, we argue that the first condition is satisfied only when neighboring trajectories through the two-dimensional field space diverge during inflation. Geometrically, this means that the inflaton must roll along a ridge in the potential V for some time during inflation and that its trajectory must turn slightly (but not too sharply) in field space. Therefore, it follows that two-field scenarios with attractor solutions necessarily produce small non-Gaussianity. This explains why it has been so difficult to achieve large non-Gaussianity in two-field inflation, and why it has only been achieved in a narrow class of models like hybrid inflation and certain product potentials where the potential and/or the initial conditions are fine-tuned. Some of our conclusions generalize qualitatively to general multi-field inflation.Comment: Discussion improved, gNL formula and extra figure included, typos corrected, references added. 18 pages, 2 figure

The angular power spectrum of the 4 year COBE data

The angular power spectrum C_l is extracted from the 4 year COBE DMR data with a 20 degree galactic cut, using the narrowest window functions possible. The average power in eight multipole bands is also computed, and plotted together with a compilation of power spectrum measurements from other experiments. The COBE results are found to be consistent with an n=1 power spectrum with the normalization Qrmsps=18 microkelvin reported by the COBE DMR team. Certain non-standard cosmologies, such as "small universe" models with nontrivial spatial topology, predict power spectra which are not smooth functions. Rather, they contain bumps and wiggles that may not have been detected by other data analysis techniques such as the Hauser-Peebles method (Wright etal 1996), the band-power method (Hinshaw etal 1996) and orthogonalized spherical harmonics (Gorski etal 1996), since these methods all give broader window functions that can smear such features out beyond recognition. On the large angular scales probed by COBE, the Universe thus appears to be kind to us, presenting a power spectrum that is a simple smooth function.Comment: Final accepted version, incl. plots with new Saskatoon data. 14 pages, with 4 figures included. Postscript. Latest version at http://www.sns.ias.edu/~max/cobepow.html (faster from the US), from http://www.mpa-garching.mpg.de/~max/cobepow.html (faster from Europe) or from [email protected]

Experimental neutrino physics

The current experimental status of neutrino physics is reviewed. It contains the evidences for a non-vanishing neutrino rest mass from neutrino oscillation searches. In addition an outlook is given on determining the various mixing matrix elements and mass differences more precisely with new experiments. Of special interest is the value of the mixing angle \theta_{13} determining the possibility of detecting leptonic CP violation in the future. The prospect for absolute mass measurements using beta and double beta decay as well as cosmological observations is presented.Comment: 11 pages, 11 figures, Inv. talk presented at the DPF 2004 meeting of the APS, Riverside, Aug. 200

Learning from observations of the microwave background at small angular scales

In this paper, we focus our attention on the following question: How well can we recover the power spectrum of the cosmic microwave background from the maps of a given experiment?. Each experiment is described by a a pixelization scale, a beam size, a noise level and a sky coverage. We use accurate numerical simulations of the microwave sky and a cold dark matter model for structure formation in the universe. Angular scales smaller than those of previous simulations are included. The spectrum obtained from the simulated maps is appropriately compared with the theoretical one. Relative deviations between these spectra are estimated. Various contributions to these deviations are analyzed. The method used for spectra comparisons is discussed.Comment: 15 pages (LATEX), 2 postcript figures, accepted in Ap