arXiv subjects

Max Tegmark

Publications and source records attributed to Max Tegmark.

At least 127 records · Page 7Linked to original sources

arXiv2011

A Method for 21cm Power Spectrum Estimation in the Presence of Foregrounds

21cm tomography promises to be a powerful tool for estimating cosmological parameters, constraining the epoch of reionization, and probing the so-called dark ages. However, realizing this promise will require the extraction of a cosmological power spectrum from beneath overwhelmingly large sources of foreground contamination. In this paper, we develop a unified matrix-based framework for foreground subtraction and power spectrum estimation, which allows us to quantify the errors and biases that arise in the power spectrum as a result of foreground subtraction. We find that existing line-of-sight foreground subtraction proposals can lead to substantial mode-mixing as well as residual noise and foreground biases, whereas our proposed inverse variance foreground subtraction eliminates noise and foreground biases, gives smaller error bars, and produces less correlated measurements of the power spectrum. We also numerically confirm the intuitive belief in the literature that 21cm foreground subtraction is best done using frequency rather than angular information.

astro-ph.CO↗

arXiv2011

Galaxy Clustering in the Completed SDSS Redshift Survey: The Dependence on Color and Luminosity

We measure the luminosity and color dependence of galaxy clustering in the SDSS DR7 main galaxy sample, focusing on the projected correlation function w_p(r_p) of volume-limited samples. We interpret our measurements using halo occupation distribution (HOD) modeling assuming a Lambda-CDM cosmology. The amplitude of w_p(r_p) grows slowly with luminosity for L < L_* and increases sharply at higher luminosities, with bias factor b(>L)=1.06+0.23(L/L_*)^{1.12}. At fixed luminosity, redder galaxies have a stronger and steeper w_p(r_p), a trend that runs steadily from the bluest galaxies to the reddest galaxies. The individual luminosity trends for the red and blue galaxy populations are strikingly different. Blue galaxies show a slow but steady increase of w_p(r_p) with luminosity, at all scales. The large-scale clustering of red galaxies shows little luminosity dependence until a sharp increase at L > 4L_*, but the lowest luminosity red galaxies (0.04-0.25 L_*) show very strong clustering on scales r_p < 2 Mpc/h. Most of the observed trends can be naturally understood within the LCDM+HOD framework. The growth of w_p(r_p) with luminosity reflects an overall shift in the halo mass scale, in particular an increase in the minimum host halo mass Mmin. The mass at which a halo has, on average, one satellite galaxy brighter than L is M_1 ~ 17 Mmin(L) over most of the luminosity range. The growth and steepening of w_p(r_p) for redder galaxies reflects the increasing fraction of galaxies that are satellite systems in high mass halos instead of central systems in low mass halos, a trend that is especially marked at low luminosities. Our extensive measurements, provided in tabular form, will allow detailed tests of theoretical models of galaxy formation, a firm grounding of semi-empirical models of the galaxy population, and new cosmological tests.

astro-ph.CO↗

arXiv2010

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 δN 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 τNL 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.

astro-ph.CO↗

arXiv2010

Testing Two-Field Inflation

We derive semi-analytic formulae for the power spectra of two-field inflation assuming an arbitrary potential and non-canonical kinetic terms, and we use them both to build phenomenological intuition and to constrain classes of two-field models using WMAP data. Using covariant formalism, we first develop a framework for understanding the background field kinematics and introduce a "slow-turn" approximation. Next, we find covariant expressions for the evolution of the adiabatic/curvature and entropy/isocurvature modes, and we discuss how the mode evolution can be inferred directly from the background kinematics and the geometry of the field manifold. From these expressions, we derive semi-analytic formulae for the curvature, isocurvature, and cross spectra, and the spectral observables, all to second-order in the slow-roll and slow-turn approximations. In tandem, we show how our covariant formalism provides useful intuition into how the characteristics of the inflationary Lagrangian translate into distinct features in the power spectra. In particular, we find that key features of the power spectra can be directly read off of the nature of the roll path, the curve the field vector rolls along with respect to the field manifold. For example, models whose roll path makes a sharp turn 60 e-folds before inflation ends tend to be ruled out because they produce strong departures from scale invariance. Finally, we apply our formalism to confront four classes of two-field models with WMAP data, including doubly quadratic and quartic potentials and non-standard kinetic terms, showing how whether a model is ruled out depends not only on certain features of the inflationary Lagrangian, but also on the initial conditions. Ultimately, models must possess the right balance of kinematical and dynamical behaviors, which we capture in a set of functions that can be reconstructed from spectral observables.

astro-ph.CO↗

arXiv2010

Omniscopes: Large Area Telescope Arrays with only N log N Computational Cost

We show that the class of antenna layouts for telescope arrays allowing cheap analysis hardware (with correlator cost scaling as N log N rather than N^2 with the number of antennas N) is encouragingly large, including not only previously discussed rectangular grids but also arbitrary hierarchies of such grids, with arbitrary rotations and shears at each level. We show that all correlations for such a 2D array with an n-level hierarchy can be efficiently computed via a Fast Fourier Transform in not 2 but 2n dimensions. This can allow major correlator cost reductions for science applications requiring exquisite sensitivity at widely separated angular scales, for example 21cm tomography (where short baselines are needed to probe the cosmological signal and long baselines are needed for point source removal), helping enable future 21cm experiments with thousands or millions of cheap dipole-like antennas. Such hierarchical grids combine the angular resolution advantage of traditional array layouts with the cost advantage of a rectangular Fast Fourier Transform Telescope. We also describe an algorithm for how a subclass of hierarchical arrays can efficiently use rotation synthesis to produce global sky maps with minimal noise and a well-characterized synthesized beam.

astro-ph.CO↗

arXiv2010

Solving the Corner-Turning Problem for Large Interferometers

The so-called corner turning problem is a major bottleneck for radio telescopes with large numbers of antennas. The problem is essentially that of rapidly transposing a matrix that is too large to store on one single device; in radio interferometry, it occurs because data from each antenna needs to be routed to an array of processors that will each handle a limited portion of the data (a frequency range, say) but requires input from each antenna. We present a low-cost solution allowing the correlator to transpose its data in real time, without contending for bandwidth, via a butterfly network requiring neither additional RAM memory nor expensive general-purpose switching hardware. We discuss possible implementations of this using FPGA, CMOS, analog logic and optical technology, and conclude that the corner turner cost can be small even for upcoming massive radio arrays.

astro-ph.IM↗

arXiv2010

Precision Calibration of Radio Interferometers Using Redundant Baselines

Growing interest in 21 cm tomography has led to the design and construction of broadband radio interferometers with low noise, moderate angular resolution, high spectral resolution, and wide fields of view. With characteristics somewhat different from traditional radio instruments, these interferometers may require new calibration techniques in order to reach their design sensitivities. Self-calibration or redundant calibration techniques that allow an instrument to be calibrated off complicated sky emission structures are ideal. In particular, the large number of redundant baselines possessed by these new instruments makes redundant calibration an especially attractive option. In this paper, we explore the errors and biases in existing redundant calibration schemes through simulations, and show how statistical biases can be eliminated. We also develop a general calibration formalism that includes both redundant baseline methods and basic point source calibration methods as special cases, and show how slight deviations from perfect redundancy and coplanarity can be taken into account.

astro-ph.IM↗

arXiv2010

Axion Cosmology and the Energy Scale of Inflation

We survey observational constraints on the parameter space of inflation and axions and map out two allowed windows: the classic window and the inflationary anthropic window. The cosmology of the latter is particularly interesting; inflationary axion cosmology predicts the existence of isocurvature fluctuations in the CMB, with an amplitude that grows with both the energy scale of inflation and the fraction of dark matter in axions. Statistical arguments favor a substantial value for the latter, and so current bounds on isocurvature fluctuations imply tight constraints on inflation. For example, an axion Peccei-Quinn scale of 10^16 GeV excludes any inflation model with energy scale > 3.8*10^14 GeV (r > 2*10^(-9)) at 95% confidence, and so implies negligible gravitational waves from inflation, but suggests appreciable isocurvature fluctuations.

astro-ph↗

arXiv2010

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.

quant-ph↗

arXiv2010

Likely values of the Higgs vev

We make an estimate of the likelihood function for the Higgs vacuum expectation value by imposing anthropic constraints on the existence of atoms while allowing the other parameters of the Standard Model to also be variable. We argue that the most important extra ingredients are the Yukawa couplings, and for the intrinsic distribution of Yukawa couplings we use the scale invariant distribution which is favored phenomenologically. The result is successful phenomenologically, favoring values close to the observed vev. We also discuss modifications that could change these conclusions. Our work supports the hypothesis that the anthropic constraints could be the origin of the small value of the Higgs vev.

hep-ph↗

arXiv2009

Baryon Acoustic Oscillations in the Sloan Digital Sky Survey Data Release 7 Galaxy Sample

The spectroscopic Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) galaxy sample represents the final set of galaxies observed using the original SDSS target selection criteria. We analyse the clustering of galaxies within this sample, including both the Luminous Red Galaxy (LRG) and Main samples, and also include the 2-degree Field Galaxy Redshift Survey (2dFGRS) data. Baryon Acoustic Oscillations are observed in power spectra measured for different slices in redshift; this allows us to constrain the distance--redshift relation at multiple epochs. We achieve a distance measure at redshift z=0.275, of r_s(z_d)/D_V(0.275)=0.1390+/-0.0037 (2.7% accuracy), where r_s(z_d) is the comoving sound horizon at the baryon drag epoch, D_V(z)=[(1+z)^2D_A^2cz/H(z)]^(1/3), D_A(z) is the angular diameter distance and H(z) is the Hubble parameter. We find an almost independent constraint on the ratio of distances D_V(0.35)/D_V(0.2)=1.736+/-0.065, which is consistent at the 1.1sigma level with the best fit Lambda-CDM model obtained when combining our z=0.275 distance constraint with the WMAP 5-year data. The offset is similar to that found in previous analyses of the SDSS DR5 sample, but the discrepancy is now of lower significance, a change caused by a revised error analysis and a change in the methodology adopted, as well as the addition of more data. Using WMAP5 constraints on Omega_bh^2 and Omega_ch^2, and combining our BAO distance measurements with those from the Union Supernova sample, places a tight constraint on Omega_m=0.286+/-0.018 and H_0 = 68.2+/-2.2km/s/Mpc that is robust to allowing curvature and non-Lambda dark energy. This result is independent of the behaviour of dark energy at redshifts greater than those probed by the BAO and supernova measurements. (abridged)

astro-ph.CO↗

arXiv2009

Cosmological Constraints from the Clustering of the Sloan Digital Sky Survey DR7 Luminous Red Galaxies

We present the power spectrum of the reconstructed halo density field derived from a sample of Luminous Red Galaxies (LRGs) from the Sloan Digital Sky Survey Seventh Data Release (DR7). The halo power spectrum has a direct connection to the underlying dark matter power for k <= 0.2 h/Mpc, well into the quasi-linear regime. This enables us to use a factor of ~8 more modes in the cosmological analysis than an analysis with kmax = 0.1 h/Mpc, as was adopted in the SDSS team analysis of the DR4 LRG sample (Tegmark et al. 2006). The observed halo power spectrum for 0.02 < k < 0.2 h/Mpc is well-fit by our model: chi^2 = 39.6 for 40 degrees of freedom for the best fit LCDM model. We find Ω_m h^2 * (n_s/0.96)^0.13 = 0.141^{+0.009}_{-0.012} for a power law primordial power spectrum with spectral index n_s and Ω_b h^2 = 0.02265 fixed, consistent with CMB measurements. The halo power spectrum also constrains the ratio of the comoving sound horizon at the baryon-drag epoch to an effective distance to z=0.35: r_s/D_V(0.35) = 0.1097^{+0.0039}_{-0.0042}. Combining the halo power spectrum measurement with the WMAP 5 year results, for the flat LCDM model we find Ω_m = 0.289 +/- 0.019 and H_0 = 69.4 +/- 1.6 km/s/Mpc. Allowing for massive neutrinos in LCDM, we find \sum m_ν < 0.62 eV at the 95% confidence level. If we instead consider the effective number of relativistic species Neff as a free parameter, we find Neff = 4.8^{+1.8}_{-1.7}. Combining also with the Kowalski et al. (2008) supernova sample, we find Ω_{tot} = 1.011 +/- 0.009 and w = -0.99 +/- 0.11 for an open cosmology with constant dark energy equation of state w.

astro-ph.CO↗

arXiv2009

An Improved Method for 21cm Foreground Removal

21 cm tomography is expected to be difficult in part because of serious foreground contamination. Previous studies have found that line-of-sight approaches are capable of cleaning foregrounds to an acceptable level on large spatial scales, but not on small spatial scales. In this paper, we introduce a Fourier-space formalism for describing the line-of-sight methods, and use it to introduce an improved new method for 21 cm foreground cleaning. Heuristically, this method involves fitting foregrounds in Fourier space using weighted polynomial fits, with each pixel weighted according to its information content. We show that the new method reproduces the old one on large angular scales, and gives marked improvements on small scales at essentially no extra computational cost.

astro-ph.CO↗

arXiv2009

Relativity Revisited

Was Einstein wrong? This paper provides a detailed technical review of Einstein's special and general relativity from an astrophysical perspective, including the historical development of the theories, experimental tests, modern applications to black holes, cosmology and parallel universes, and last but not least, novel ways of expressing their seven most important equations.

astro-ph↗

arXiv2009

The Multiverse Hierarchy

I survey physics theories involving parallel universes, arguing that they form a natural four-level hierarchy of multiverses allowing progressively greater diversity. Level I: A generic prediction of inflation is an infinite ergodic universe, which contains Hubble volumes realizing all initial conditions -- including an identical copy of you about 10^(10^29)m away. Level II: In chaotic inflation, other thermalized regions may have different physical constants, dimensionality and particle content. Level III: In unitary quantum mechanics, other branches of the wavefunction add nothing qualitatively new, which is ironic given that this level has historically been the most controversial. Level IV: Other mathematical structures give different fundamental equations of physics. The key question is not whether parallel universes exist (Level I is the uncontroversial cosmological concordance model), but how many levels there are. I discuss how multiverse models can be falsified and argue that there is a severe "measure problem" that must be solved to make testable predictions at levels II-IV.

physics.pop-ph↗

arXiv2009

The Second Law and Cosmology

I use cosmology examples to illustrate that the second law of thermodynamics is not old and tired, but alive and kicking, continuing to stimulate interesting research on really big puzzles. The question "Why is the entropy so low?" (despite the second law) suggests that our observable universe is merely a small and rather uniform patch in a vastly larger space stretched out by cosmological inflation. The question "Why is the entropy so high" (compared to the complexity required to describe many candidate "theories of everything") independently suggests that physical reality is much larger than the part we can observe.

physics.pop-ph↗

arXiv2009

The Fast Fourier Transform Telescope

We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of Fast Fourier Transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moore's law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an N-element array scales as N log N rather than N^2) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large Fast Fourier Transform Telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.

astro-ph↗

arXiv2009

Cosmology from the Highly-Redshifted 21 cm Line

One of the next decade's most exciting prospects is to explore the cosmic "dark ages," during which the first stars in the Universe formed, with the 21 cm line of neutral hydrogen. At z>6, this light redshifts into the low-frequency radio regime and can be observed with new generations of wide-field arrays. These experiments have the potential to observe enormous volumes and to improve both cosmological and astrophysical constraints dramatically. In this white paper, we describe how the next decade will see the first steps toward unlocking this potential, allowing us to answer two key questions about the fundamental physics of our Universe and the intergalactic medium: Does the standard cosmological model describe the Universe during the "dark ages?" How did the intergalactic medium evolve during this important time, ending with the reionization of hydrogen?

astro-ph.CO↗