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]

A method for extracting maximum resolution power spectra from microwave sky maps

A method for extracting maximal resolution power spectra from microwave sky maps is presented and applied to the 2 year COBE data, yielding a power spectrum that is consistent with a standard n=1, Q=20 micro-Kelvin model. By using weight functions that fall off smoothly near the galactic cut, it is found that the spectral resolution \Delta l can be more than doubled at l=15 and more than tripled at l=20 compared to simply using galaxy-cut spherical harmonics. For a future high-resolution experiment with reasonable sky coverage, the resolution around the CDM Doppler peaks would be enhanced by a factor of about 100, down to \Delta l\approx 1, thus allowing spectral features such as the locations of the peaks to be determined with great accuracy. The reason that the improvement is so large is basically that functions with a sharp edge at the galaxy cut exhibit considerable "ringing" in the Fourier domain, whereas smooth functions do not. The method presented here is applicable to any survey geometry, chopping strategy and exposure pattern whatsoever. The so called signal-to-noise eigenfunction technique is found to be a special case, corresponding to ignoring the width of the window functions.Comment: 25 pages, including 4 figures. Postscript. Substantially revised, more than twice original length, matches accepted version. Latest version available from http://www.sns.ias.edu/~max/window.html (faster from the US), from http://www.mpa-garching.mpg.de/~max/window.html (faster from Europe) or from [email protected]

Many Worlds in Context

Everett's Many-Worlds Interpretation of quantum mechanics is discussed in the context of other physics disputes and other proposed kinds of parallel universes. We find that only a small fraction of the usual objections to Everett's theory are specific to quantum mechanics, and that all of the most controversial issues crop up also in settings that have nothing to do with quantum mechanics.Comment: Replaced to match published version. 16 pages, 2 figs, 1 quantum poll. In "Many Worlds? Everett, Quantum Theory and Reality", S. Saunders, J. Barrett, A. Kent & D. Wallace (eds), Oxford Univ. Press (2010

Many lives in many worlds

I argue that accepting quantum mechanics to be universally true means that you should also believe in parallel universes. I give my assessment of Everett's theory as it celebrates its 50th anniversary.Comment: Nature version with better graphics at http://www.nature.com/nature/journal/v448/n7149/full/448023a.html Everett bio and other links at http://space.mit.edu/home/tegmark/quantum.htm

New CMB constraints on the cosmic matter budget: trouble for nucleosynthesis?

We compute the joint constraints on ten cosmological parameters from the latest CMB measurements. The lack of a significant second acoustic peak in the latest Boomerang and Maxima data favors models with more baryons than Big Bang nucleosynthesis predicts, almost independently of what prior information is included. The simplest flat inflation models with purely scalar scale-invariant fluctuations prefer a baryon density 0.022 <h^2 Omega_b < 0.040 and a total nonbaryonic (hot + cold) dark matter density 0.14 < h^2 Omega_dm < 0.32 at 95% confidence, and allow reionization no earlier than z~30.Comment: Replaced to match accepted PRL version. Joint Boom+Maxima analysis, fig 2 fixed. Movies and more figs at http://www.hep.upenn.edu/~max/boompa_frames.html or from [email protected]

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