arXiv subjects

Max Tegmark

Publications and source records attributed to Max Tegmark.

At least 271 records · Page 15Linked to original sources

arXiv1996

A high-resolution map of the cosmic microwave background around the north celestial pole

We present a Wiener filtered map of the Cosmic Microwave Background (CMB) fluctuations in a disk with 15 degree diameter, centered at the North Celestial Pole. The map is based on the 1993-1995 data from the Saskatoon (SK) experiment, with an angular resolution around 1 degree in the frequency range 27.6-44.1 GHz. The signal-to-noise ratio in the map is of order two, and some individual hot and cold spots are significant at the 5 sigma level. The spatial features are found to be consistent from year to year, reenforcing the conclusion that the SK results are not dominated by residual atmospheric contamination or other non-celestial signals.

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arXiv1996

Karhunen-Loeve eigenvalue problems in cosmology: how should we tackle large data sets?

Since cosmology is no longer "the data-starved science", the problem of how to best analyze large data sets has recently received considerable attention, and Karhunen-Loeve eigenvalue methods have been applied to both galaxy redshift surveys and Cosmic Microwave Background (CMB) maps. We present a comprehensive discussion of methods for estimating cosmological parameters from large data sets, which includes the previously published techniques as special cases. We show that both the problem of estimating several parameters jointly and the problem of not knowing the parameters a priori can be readily solved by adding an extra singular value decomposition step. It has recently been argued that the information content in a sky map from a next generation CMB satellite is sufficient to measure key cosmological parameters (h, Omega, Lambda, etc) to an accuracy of a few percent or better - in principle. In practice, the data set is so large that both a brute force likelihood analysis and a direct expansion in signal-to-noise eigenmodes will be computationally unfeasible. We argue that it is likely that a Karhunen-Loeve approach can nonetheless measure the parameters with close to maximal accuracy, if preceded by an appropriate form of quadratic "pre-compression". We also discuss practical issues regarding parameter estimation from present and future galaxy redshift surveys, and illustrate this with a generalized eigenmode analysis of the IRAS 1.2 Jy survey optimized for measuring beta=Omega^{0.6}/b using redshift space distortions.

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arXiv1996

An icosahedron-based method for pixelizing the celestial sphere

For power spectrum estimation it's important that the pixelization of a CMB sky map be smooth and regular to high degree. With this criterion in mind the ``COBE sky cube" was defined. This paper has as central theme to further improve on this elegant scheme which uses a cube as projective base -- here an icosahedron is used in its place. Although the sky cube is excellent, a further reduction of 20 percent of the number of pixels can be obtained while the pixel distance is maintained, and without any degradation of accuracy for integration. The pixels are rounder in this scheme, where they are hexagonal rather than square, and the faces are small in this implementation which simplifies area-equalization. The reason distortion is lessened is that the faces are smaller and therefore more flat. To use the method, you can get a FORTRAN code from the Internet.

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arXiv1996

Late reionization by supernova-driven winds

A model is presented in which supernova-driven winds from early galaxies reionize the intergalactic medium by z=5. This scenario can explain the observed absence of a Gunn-Peterson trough in the spectra of high-redshift quasars providing that the bulk of these early galaxies are quite small, no more massive than about 10^8 solar masses. It also predicts that most of the IGM was enriched to at least 10% of current metal content by z=5 and perhaps as early as z=15. The existence of such early mini-galaxies violates no spectral constraints and is consistent with a pure CDM model with b<2. Since the final radius of a typical ionized bubble is only around 100 kpc, the induced modification of the galaxy autocorrelation function is negligible, as is the induced angular smoothing of the CMBR. Some of the gas swept up by shells may be observable as pressure-supported Lyman-alpha forest clouds.

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arXiv1996

On the inevitability of reionization: implications for cosmic microwave background fluctuations

Early photoionization of the intergalactic medium is discussed in a nearly model-independent way, in order to investigate whether early structures corresponding to rare Gaussian peaks in a CDM model can photoionize the intergalactic medium sufficiently early to appreciably smooth out the microwave background fluctuations. We conclude that this is indeed possible for a broad range of CDM normalizations and is almost inevitable for unbiased CDM, provided that the bulk of these early structures are quite small, no more massive than about 10^8 solar masses. Typical parameter values predict that reionization occurs around z=50, thereby suppressing fluctuations on degree scales while leaving the larger angular scales probed by COBE reasonably unaffected. However, for non-standard CDM, incorporating mixed dark matter, vacuum density or a tilted primordial power spectrum, early reionization plays no significant role.

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arXiv1996

Did the universe recombine? New spectral constraints on reheating

One still cannot conclusively assert that the universe underwent a neutral phase, despite the new COBE FIRAS limit y<0.000025 on Compton y-distortions of the cosmic microwave background. Although scenarios where the very early (z=1000) ionization is thermal, caused by IGM temperatures exceeding 10000K, are clearly ruled out, there is a significant loophole for cosmologies with typical CDM parameters if the dominant ionization mechanism is photoionization. If the ionizing radiation has a typical quasar spectrum, then the y-constraint implies roughly h^{3/2}Ω_b Omega_0^{-1/4}<0.1 for fully ionized models. This means that BDM models with Omega_0 around 0.15 and reionization at about z=1000 are strongly constrained even in this very conservative case, and can survive the y test only if most of the baryons form BDM around the reionization epoch.

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arXiv1996

Reionization in an open cdm universe: implications for cosmic microwave background fluctuations

We generalize previous work on early photoionization to CDM models with Omega<1. Such models have received recent interest because the excess power in the large-scale galaxy distribution is phenomenologically fit if the ``shape parameter" Gamma=h Omega_0 is about 0.25. It has been argued that such models may require early reionization to suppress small-scale anisotropies in order to be consistent with experimental data. We find that if the cosmological constant lambda=0, the extent of this suppression is quite insensitive to Omega_0. Given a sigma_8-normalization today, the loss of small-scale power associated with a lower Omega_0 is partially canceled by higher optical depth from longer lookback times and by structures forming at higher redshifts before the universe becomes curvature-dominated. The maximum angular scale on which fluctuations are suppressed decreases when Omega_0 is lowered, but this effect is also rather weak and unlikely to be measurable in the near future. For flat models, on the other hand, where lambda_0 = 1-Omega_0, the negative effects of lowering Omega_0 dominate, and early reionization is not likely to play a significant role if Omega_0<<1. The same applies to CDM models where the effective Gamma is lowered by increasing the number of relativistic particle species.

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arXiv1996

Real-space cosmic fields from redshift-space distributions: a Green function approach

We present a new method for reconstructing the cosmological density, peculiar velocity and peculiar gravitational potential on large scales from redshift data. We remove the distorting effects of line-of-sight peculiar motions by using the linear theory of gravitational instability, in which the potential is the solution to a linear partial differential equation first derived by Kaiser. We solve this equation by deriving its Green function; the Green functions for the peculiar velocity and the real-space density follow directly. Reconstruction of the cosmic fields is thus reduced to integration over redshift space with the appropriate Green function kernel. Our algorithm has a single input parameter, beta=Omega^0.6/b, where b is the linear bias factor and Omega is the cosmological density parameter. We discuss the virtues of this method for error control, for estimating beta, and for constraining the bias mechanism.

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arXiv1996

A brute force analysis of the COBE DMR data

More than a dozen papers analyzing the COBE data have now appeared. We review the different techniques and compare them to a ``brute force" likelihood analysis where we invert the full 4038 x 4038 Galaxy-cut pixel covariance matrix. This method is optimal in the sense of producing minimal error bars, and is a useful reference point for comparing other analysis techniques. Our maximum-likelihood estimate of the spectral index and normalization are n=1.15 (0.95) and Q=18.2 (21.3) micro-Kelvin including (excluding) the quadrupole. Marginalizing over the normalization C_9, we obtain n=1.10 +/- 0.29 (n=0.90 +/- 0.32). When we compare these results with those of the various techniques that involve a linear ``compression'' of the data, we find that the latter are all consistent with the brute-force analysis and have error bars that are nearly as small as the minimal error bars. We therefore conclude that the data compressions involved in these techniques do indeed retain most of the useful cosmological information.

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arXiv1996

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.

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arXiv1996

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 Δl 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 Δl\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.

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arXiv1996

A method for subtracting foregrounds from multi-frequency CMB sky maps

An improved method for subtracting contaminants from Cosmic Microwave Background (CMB) sky maps is presented, and used to estimate how well future experiments will be able to recover the primordial CMB fluctuations. We find that the naive method of subtracting foregrounds (such as dust emission, synchrotron radiation, free-free-emission, unresolved point sources, etc) on a pixel by pixel basis can be improved by more than an order of magnitude by taking advantage of the correlation of the emission in neighboring pixels. The optimal multi-frequency subtraction method improves on simple pixel-by-pixel subtraction both by taking noise-levels into account, and by exploiting the fact that most contaminants have angular power spectra that differ substantially from that of the CMB. The results are natural to visualize in the two-dimensional plane with axes defined by multipole l and frequency v. We present a brief overview of the geography of this plane, showing the regions probed by various experiments and where we expect contaminants to dominate. We illustrate the method by estimating how well the proposed ESA COBRAS/SAMBA mission will be able to recover the CMB fluctuations against contaminating foregrounds.

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arXiv1996

Measuring quantum states: an experimental setup for measuring the spatial density matrix

To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wavefunction, but the entire density matrix, whose phases carry information about momentum and how pure the state is. An experimental setup is presented which can measure the density matrix (or equivalently, the Wigner function) of a beam of identically prepared charged particles to an arbitrary accuracy, limited only by count statistics and detector resolution. The particles enter into an electric field causing simple harmonic oscillation in the transverse direction. This corresponds to rotating the Wigner function in phase space. With a slidable detector, the marginal distribution of the Wigner function can be measured from all angles. Thus the phase-space tomography formalism can be used to recover the Wigner function by the standard inversion of the Radon transform. By applying this technique to for instance double-slit experiments with various degrees of environment-induced decoherence, it should be possible to make our understanding of decoherence and apparent wave-function collapse less qualitative and more quantitative.

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arXiv1996

Does the universe in fact contain almost no information?

At first sight, an accurate description of the state of the universe appears to require a mind-bogglingly large and perhaps even infinite amount of information, even if we restrict our attention to a small subsystem such as a rabbit. In this paper, it is suggested that most of this information is merely apparent, as seen from our subjective viewpoints, and that the algorithmic information content of the universe as a whole is close to zero. It is argued that if the Schrödinger equation is universally valid, then decoherence together with the standard chaotic behavior of certain non-linear systems will make the universe appear extremely complex to any self-aware subsets that happen to inhabit it now, even if it was in a quite simple state shortly after the big bang. For instance, gravitational instability would amplify the microscopic primordial density fluctuations that are required by the Heisenberg uncertainty principle into quite macroscopic inhomogeneities, forcing the current wavefunction of the universe to contain such Byzantine superpositions as our planet being in many macroscopically different places at once. Since decoherence bars us from experiencing more than one macroscopic reality, we would see seemingly complex constellations of stars etc, even if the initial wavefunction of the universe was perfectly homogeneous and isotropic.

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arXiv1996

Apparent wave function collapse caused by scattering

Some experimental implications of the recent progress on wave function collapse are calculated. Exact results are derived for the center-of-mass wave function collapse caused by random scatterings and applied to a range of specific examples. The results show that recently proposed experiments to measure the GRW effect are likely to fail, since the effect of naturally occurring scatterings is of the same form as the GRW effect but generally much stronger. The same goes for attempts to measure the collapse caused by quantum gravity as suggested by Hawking and others. The results also indicate that macroscopic systems tend to be found in states with (Delta-x)(Delta-p) = hbar/sqrt(2), but microscopic systems in highly tiltedly squeezed states with (Delta-x)(Delta-p) >> hbar.

gr-qc↗

arXiv1996

Steady states of harmonic oscillator chains and shortcomings of harmonic heat baths

We study properties of steady states (states with time-independent density operators) of systems of coupled harmonic oscillators. Formulas are derived showing how adiabatic change of the Hamiltonian transforms one steady state into another. It is shown that for infinite systems, sudden change of the Hamiltonian also tends to produce steady states, after a transition period of oscillations. These naturally arising steady states are compared to the maximum-entropy state (the thermal state) and are seen not to coincide in general. The approach to equilibrium of subsystems consisting of n coupled harmonic oscillators has been widely studied, but only in the simple case where n=1. The power of our results is that they can be applied to more complex subsustems, where n>1. It is shown that the use of coupled harmonic oscillators as heat baths models is fraught with some problems that do not appear in the simple n=1 case. Specifically, the thermal states that are though to be achievable through hard-sphere collisions with heat-bath particles can generally NOT be achieved with harmonic coupling to the heat-bath particles, except approximately when the coupling is weak.

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arXiv1996

Decoherence produces coherent states: an explicit proof for harmonic chains

We study the behavior of infinite systems of coupled harmonic oscillators as t->infinity, and generalize the Central Limit Theorem (CLT) to show that their reduced Wigner distributions become Gaussian under quite general conditions. This shows that generalized coherent states tend to be produced naturally. A sufficient condition for this to happen is shown to be that the spectral function is analytic and nonlinear. For a rectangular lattice of coupled oscillators, the nonlinearity requirement means that waves must be dispersive, so that localized wave-packets become suppressed. Virtually all harmonic heat-bath models in the literature satisfy this constraint, and we have good reason to believe that coherent states and their generalizations are not merely a useful analytical tool, but that nature is indeed full of them. Standard proofs of the CLT rely heavily on the fact that probability densities are non-negative. Although the CLT generally fails if the probability densities are allowed to take negative values, we show that a CLT does indeed hold for a special class of such functions. We find that, intriguingly, nature has arranged things so that all Wigner functions belong to this class.

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arXiv1996

Spherical Harmonic Analysis of the Angular Distribution of Gamma-Ray Bursts

We compute the angular power spectrum C_l of the BATSE 3B catalog, and find no evidence for clustering on any scale. These constraints bridge the entire range from small scales, probing source clustering and repetition, to large scales constraining possible Galactic anisotropies, or those from nearby cosmological large scale structures.

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