arXiv subjects

Max Tegmark

Publications and source records attributed to Max Tegmark.

At least 253 records · Page 14Linked to original sources

arXiv1998

Cosmic Complementarity: H_0 and Omega_m from Combining CMB Experiments and Redshift Surveys

We show that upcoming CMB satellite experiments and large redshift surveys can be used together to yield 5% determinations of H_0 and Omega_m, an order of magnitude improvement over CMB data alone. CMB anisotropies provide the sound horizon at recombination as a standard ruler. For reasonable baryon fractions, this scale is imprinted on the galaxy power spectrum as a series of spectral features. Measuring these features in redshift space determines the Hubble constant, which in turn yields Omega_m once combined with CMB data. Since the oscillations in both power spectra are frozen in at recombination, this test is insensitive to low-redshift cosmology.

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arXiv1998

Cosmic complementarity: probing the acceleration of the Universe

We assess the accuracy with which Omega and Lambda can be measured by combining various types of upcoming experiments. Useful expressions for the Fisher information matrix are derived for classical cosmological tests involving luminosity (eg, SN Ia), angular size, age and number counts. These geometric probes are found to be quite complementary both to each other and to inferences from cluster abundance and the cosmic microwave background (CMB). For instance, a joint analysis of SN Ia and CMB reduces the error bars by about an order of magnitude compared to a separate analysis of either data set.

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arXiv1998

Cosmic complementarity: combining CMB and supernova observations

We compute the accuracy with which Omega and Lambda can be measured by combining future SN Ia and CMB experiments, deriving a handy expression for the SN Ia Fisher information matrix. The two data sets are found to be highly complementary: a joint analysis reduces the error bars by more than an order of magnitude compared to a separate analysis of either data set.

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arXiv1998

Removing real-world foregrounds from CMB maps

Most work on foreground removal has treated the case where the frequency dependence of all components is perfectly known and independent of position. In contrast, real-world foregrounds are generally not perfectly correlated between frequencies, with the spectral index varying slightly with position and (in the case of some radio sources) with time. A method incorporating this complication in presented, and illustrated with an application to the upcoming satellite missions MAP and Planck. We find that even spectral index variations as small as 0.1 can have a substantial impact on how channels should be combined and on attainable accuracy.

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arXiv1998

Measuring the galaxy power spectrum with future redshift surveys

Precision measurements of the galaxy power spectrum P(k) require a data analysis pipeline that is both fast enough to be computationally feasible and accurate enough to take full advantage of high-quality data. We present a rigorous discussion of different methods of power spectrum estimation, with emphasis on the traditional Fourier method, the linear (Karhunen-Loeve; KL), and quadratic data compression schemes, showing in what approximations they give the same result. To improve speed, we show how many of the advantages of KL data compression and power spectrum estimation may be achieved with a computationally faster quadratic method. To improve accuracy, we derive analytic expressions for handling the integral constraint, since it is crucial that finite volume effects are accurately corrected for on scales comparable to the depth of the survey. We also show that for the KL and quadratic techniques, multiple constraints can be included via simple matrix operations, thereby rendering the results less sensitive to galactic extinction and mis-estimates of the radial selection function. We present a data analysis pipeline that we argue does justice to the increases in both quality and quantity of data that upcoming redshift surveys will provide. It uses three analysis techniques in conjunction: a traditional Fourier approach on small scales, a pixelized quadratic matrix method on large scales and a pixelized KL eigenmode analysis to probe anisotropic effects such as redshift-space distortions.

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arXiv1997

Measuring cosmological parameters with galaxy surveys

We assess the accuracy with which future galaxy surveys can measure cosmological parameters by deriving a handy approximation that we validate numerically. We find that galaxy surveys are quite complementary to future Cosmic Microwave Background (CMB) experiments. By breaking parameter degeneracies of the Planck CMB satellite in a cold dark matter cosmology, the Sloan Digital Sky Survey might be able to reduce the Planck error bars by about an order of magnitude on the large-scale power normalization and the reionization optical depth, down to percent levels. However, pinpointing attainable accuracies to within better than a factor of a few depends crucially on whether it will be possible to extract useful information from the mildly nonlinear regime.

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arXiv1997

Why is the CMB fluctuation level 10^{-5}?

We explore the qualitative changes that would occur if the amplitude Q ~ 10^{-5} of cosmological density fluctuations were different. If is less than about 10^{-6}, the cosmological objects that form would have so low virial temperatures that they may be unable to cool and form stars, and would be so loosely bound that even if they could produce a supernova explosion, they might be unable to retain the heavy elements necessary for planetary life. If Q is greater than about 10^{-4}, dense supermassive galaxies would form, and biological evolution could be marred by short disruption timescales for planetary orbits. If Q were still larger, most bound systems would collapse directly to supermassive black holes. These constraints on Q can be expressed in terms of fundamental constants alone, and depend only on the electromagnetic and gravitational coupling constants, the electron-proton mass ratio and the matter-to-photon ratio. We discuss the implications for inflation and defect models, and note that the recent anthropic upper bounds on the cosmological constant Lambda would be invalid if both Q and Lambda could vary and there were no anthropic constraints on Q. The same applies to anthropic bounds on the curvature parameter Omega.

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arXiv1997

The Interpretation of Quantum Mechanics: Many Worlds or Many Words?

As cutting-edge experiments display ever more extreme forms of non-classical behavior, the prevailing view on the interpretation of quantum mechanics appears to be gradually changing. A (highly unscientific) poll taken at the 1997 UMBC quantum mechanics workshop gave the once all-dominant Copenhagen interpretation less than half of the votes. The Many Worlds interpretation (MWI) scored second, comfortably ahead of the Consistent Histories and Bohm interpretations. It is argued that since all the above-mentioned approaches to nonrelativistic quantum mechanics give identical cookbook prescriptions for how to calculate things in practice, practical-minded experimentalists, who have traditionally adopted the ``shut-up-and-calculate interpretation'', typically show little interest in whether cozy classical concepts are in fact real in some untestable metaphysical sense or merely the way we subjectively perceive a mathematically simpler world where the Schrodinger equation describes everything - and that they are therefore becoming less bothered by a profusion of worlds than by a profusion of words. Common objections to the MWI are discussed. It is argued that when environment-induced decoherence is taken into account, the experimental predictions of the MWI are identical to those of the Copenhagen interpretation except for an experiment involving a Byzantine form of ``quantum suicide''. This makes the choice between them purely a matter of taste, roughly equivalent to whether one believes mathematical language or human language to be more fundamental.

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arXiv1997

Forecasting Cosmic Parameter Errors from Microwave Background Anisotropy Experiments

Accurate measurements of the cosmic microwave background (CMB) anisotropies with an angular resolution of a few arcminutes can be used to determine fundamental cosmological parameters such as the densities of baryons, cold and hot dark matter, and certain combinations of the cosmological constant and the curvature of the Universe to percent-level precision. Assuming the true theory is a variant of inflationary cold dark matter cosmologies, we calculate the accuracy with which cosmological parameters can be determined by the next generation of CMB satellites, MAP and Planck. We pay special attention to: (a) the accuracy of the computed derivatives of the CMB power spectrum C_L; (b) the number and choices of parameters; (c) the inclusion of prior knowledge of the values of various parameters.

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arXiv1997

Analyzing redshift surveys to measure the power spectrum on large scales

Upcoming large redshift surveys potentially allow precision measurements of the galaxy power spectrum. To accurately measure P(k) on the largest scales, comparable to the depth of the survey, it is crucial that finite volume effects are accurately corrected for in the data analysis. Here we derive analytic expressions for the one such effect that has not previously been worked out exactly: that of the so-called integral constraint. We also show that for data analysis methods based on counts in cells, multiple constraints can be included via simple matrix operations, thereby rendering the results less sensitive to galactic extinction and misestimates of the shape of the radial selection function.

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arXiv1997

CMB mapping experiments: a designer's guide

We apply state-of-the art data analysis methods to a number of fictitious CMB mapping experiments, including 1/f noise, distilling the cosmological information from time-ordered data to maps to power spectrum estimates, and find that in all cases, the resulting error bars can we well approximated by simple and intuitive analytic expressions. Using these approximations, we discuss how to maximize the scientific return of CMB mapping experiments given the practical constraints at hand, and our main conclusions are as follows. (1) For a given resolution and sensitivity, it is best to cover a sky area such that the signal-to-noise ratio per resolution element (pixel) is of order unity. (2) It is best to avoid excessively skinny observing regions, narrower than a few degrees. (3) The minimum-variance mapmaking method can reduce the effects of 1/f noise by a substantial factor, but only if the scan pattern is thoroughly interconnected. (4) 1/f noise produces a 1/l contribution to the angular power spectrum for well connected single-beam scanning, as compared to virtually white noise for a two-beam scan pattern such as that of the MAP satellite.

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arXiv1997

Cosmological Parameter Estimation from the CMB

We discuss the problems of applying Maximum Likelihood methods to the CMB and how one can make it both efficient and optimal. The solution is a generalised eigenvalue problem that allows virtually no loss of information about the parameter being estimated, but can allow a substantial compression of the data set. We discuss the more difficult question of simultaneous estimation of many parameters, and propose solutions. A much fuller account of most of this work is available (Tegmark, Taylor & Heavens 1997)

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arXiv1997

On the dimensionality of spacetime

Some superstring theories have more than one effective low-energy limit, corresponding to classical spacetimes with different dimensionalities. We argue that all but the 3+1-dimensional one might correspond to ``dead worlds'', devoid of observers, in which case all such ensemble theories would actually predict that we should find ourselves inhabiting a 3+1-dimensional spacetime. With more or less than one time-dimension, the partial differential equations of nature would lack the hyperbolicity property that enables observers to make predictions. In a space with more than three dimensions, there can be no traditional atoms and perhaps no stable structures. A space with less than three dimensions allows no gravitational force and may be too simple and barren to contain observers.

gr-qc↗

arXiv1997

Is lensing of point sources a problem for future CMB experiments?

Weak gravitational lensing from large-scale structure enhances and reduces the fluxes from extragalactic point sources with an rms amplitude of order 15%. In cosmic microwave background (CMB) experiments, sources exceeding some flux threshold are removed, which means that lensing will modulate the brightness map of the remaining unresolved sources. Since this mean brightness is of order 100 micro-Kelvin at 30 GHz for a reasonable flux cut, one might be concerned that this modulation could cause substantial problems for future CMB experiments. We present a detailed calculation of this effect and, fortunately, find that its power spectrum is always smaller than the normal point source power spectrum. Thus although this effect should be taken into account when analysing future high-precision CMB measurements, it will not substantially reduce the accuracy with which cosmological parameters can be measured.

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arXiv1997

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.

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arXiv1997

How to measure CMB power spectra without losing information

A new method for estimating the angular power spectrum C_l from cosmic microwave background (CMB) maps is presented, which has the following desirable properties: (1) It is unbeatable in the sense that no other method can measure C_l with smaller error bars. (2) It is quadratic, which makes the statistical properties of the measurements easy to compute and use for estimation of cosmological parameters. (3) It is computationally faster than rival high-precision methods such as the nonlinear maximum-likelihood technique, with the crucial steps scaling as n^2 rather than n^3, where n is the number of map pixels. (4) It is applicable to any survey geometry whatsoever, with arbitraty regions masked out and arbitrary noise behaviour. (5) It is not a "black-box" method, but quite simple to understand intuitively: it corresponds to a high-pass filtering and edge softening of the original map followed by a straight expansion in truncated spherical-harmonics. It is argued that this method is computationally feasible even for futute high-resolution CMB experiments with n=10^6-10^7. It is also shown that C_l computed with this method is useful not merely for graphical presentation purposes, but also as an intermediate (and arguably necessary) step in the data analysis pipeline, reducing the data set to a more manageable size before the final step of constraining Gaussian cosmological models and parameters - while retaining all the cosmological information that was present in the original map.

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arXiv1997

Uncorrelated measurements of the CMB power spectrum

We describe how to compute estimates of the power spectrum C_l from Cosmic Microwave Background (CMB) maps that not only retain all the cosmological information, but also have uncorrelated error bars and well-behaved window functions. We apply this technique to the 4-year COBE/DMR data, and tabulate eight uncorrelated band-powers.

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arXiv1997

How small were the first cosmological objects?

The minimum mass that a virialized gas cloud must have in order to be able to cool in a Hubble time is computed, using a detailed treatment of the chemistry of molecular hydrogen. With a simple model for halo profiles, we reduce the problem to that of numerically integrating a system of chemical equations. The results agree well with numerically expensive 3D simulations, and our approach has the advantage of rapidly being able to explore large regions of parameter space. The minimum baryonic mass M_b is found to be strongly redshift dependent, dropping from 10^6 solar masses at z=15 to 5000 solar masses at z=100 as molecular cooling becomes effective. For z>>100, M_b rises again, as CMB photons inhibit H_2-formation through the H^- channel. Finally, for z>>200, the H_2^+ channel for H_2-formation becomes effective, driving M_b down towards 10^3 solar masses. With a standard CDM power spectrum with sigma_8=0.7, this implies that a fraction 10^{-3} of all baryons may have formed luminous objects by z=30, which could be sufficient to reheat the universe.

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