arXiv subjects

J. Richard Gott III

Publications and source records attributed to J. Richard Gott III.

At least 19 recordsLinked to original sources

arXiv2021

Flat Maps that improve on the Winkel Tripel

Goldberg & Gott (2008) developed six error measures to rate flat map projections on their verisimilitude to the sphere: Isotropy, Area, Flexion, Skewness, Distances, and Boundary Cuts. The first two depend on the metric of the projection, the next two on its first derivatives. By these criteria, the Winkel Tripel (used by National Geographic for world maps) was the best scoring of all the known projections with a sum of squares of the six errors of 4.563, normalized relative to the Equirectangular in each error term. We present here a useful Gott-Wagner variant with a slightly better error score of only 4.497. We also present a radically new class of flat double-sided maps (like phonograph records) which have correct topology and vastly improved error scores: 0.881 for the azimuthal equidistant version. We believe it is the most accurate flat map of Earth yet. We also show maps of other solar system objects and sky maps.

astro-ph.IM↗

arXiv2020

A Simple 3D Isometric Embedding of the Flat Square Torus

Start with Gott (2019)'s envelope polyhedron (Squares-4 around a point): a unit cube missing its top and bottom faces. Stretch by a factor of 2 in the vertical direction so its sides become (2x1 unit) rectangles. This has 8 faces (4 exterior, 4 interior), 8 vertices, and 16 edges. F-E+V = 0, implying a (toroidal) genus = 1. It is isometric to a flat square torus. Like any polyhedron it has zero intrinsic Gaussian curvature on its faces and edges. Since 4 right angled rectangles meet at each vertex, there is no angle deficit and zero Gaussian curvature there as well. All meridian and latitudinal circumferences are equal (4 units long).

math.MG↗

arXiv2019

Envelope Polyhedra

This paper presents an additional class of regular polyhedra--envelope polyhedra--made of regular polygons, where the arrangement of polygons (creating a single surface) around each vertex is identical; but dihedral angles between faces need not be identical, and some of the dihedral angles are 0 degrees (i.e., some polygons are placed back to back). For example, squares, 6 around a point, is produced by deleting the triangles from the rhombicuboctahedron, creating a hollow polyhedron of genus 7 with triangular holes connecting 18 interior and 18 exterior square faces. An empty cube missing its top and bottom faces becomes an envelope polyhedron, squares, 4 around a point, with a toroidal topology. This definition leads to many interesting finite and infinite multiply connected regular polygon networks, including one infinite network with squares, 14 around a point, and another with triangles, 18 around a point. These are introduced just over 50 years after my related paper on infinite spongelike pseudopolyhedra in American Mathematical Monthly (Gott, 1967).

math.MG↗

arXiv2017

Reanalysis of the BICEP2, Keck and Planck Data: No Evidence for Gravitational Radiation

A joint analysis of data collected by the Planck and BICEP2+Keck teams has previously given $r = 0.09^{+0.06}_{-0.04}$ for BICEP2 and $r = 0.02^{+0.04}_{-0.02}$ for Keck. Analyzing BICEP2 using its published noise estimate, we had earlier (Colley & Gott 2015) found $r = 0.09 \pm 0.04$, agreeing with the final joint results for BICEP2. With the Keck data now available, we have done something the joint analysis did not: a correlation study of the BICEP2 vs. Keck B-mode maps. Knowing the correlation coefficient between the two and their amplitudes allows us to determine the noise in each map (which we check using the E-modes). We find the noise power in the BICEP2 map to be twice the original BICEP2 published estimate, explaining the anomalously high $r$ value obtained by BICEP2. We now find $r = 0.004 \pm 0.04$ for BICEP2 and $r = -0.01 \pm 0.04$ for Keck. Since $r \ge 0$ by definition, this implies a maximum likelihood value of $r = 0$, or no evidence for gravitational waves. Starobinsky Inflation ($r = 0.0036$) is not ruled out, however. Krauss & Wilzcek (2014) have already argued that "measurement of polarization of the CMB due to a long-wavelength stochastic background of gravitational waves from Inflation in the early Universe would firmly establish the quantization of gravity," and, therefore, the existence of gravitons. We argue it would also constitute a detection of gravitational Hawking radiation (explicitly from the causal horizons due to Inflation).

astro-ph.CO↗

arXiv2015

Cosmological implications of baryon acoustic oscillation (BAO) measurements

We derive constraints on cosmological parameters and tests of dark energy models from the combination of baryon acoustic oscillation (BAO) measurements with cosmic microwave background (CMB) and Type Ia supernova (SN) data. We take advantage of high-precision BAO measurements from galaxy clustering and the Ly-alpha forest (LyaF) in the BOSS survey of SDSS-III. BAO data alone yield a high confidence detection of dark energy, and in combination with the CMB angular acoustic scale they further imply a nearly flat universe. Combining BAO and SN data into an "inverse distance ladder" yields a 1.7% measurement of $H_0=67.3 \pm1.1$ km/s/Mpc. This measurement assumes standard pre-recombination physics but is insensitive to assumptions about dark energy or space curvature, so agreement with CMB-based estimates that assume a flat LCDM cosmology is an important corroboration of this minimal cosmological model. For open LCDM, our BAO+SN+CMB combination yields $Ω_m=0.301 \pm 0.008$ and curvature $Ω_k=-0.003 \pm 0.003$. When we allow more general forms of evolving dark energy, the BAO+SN+CMB parameter constraints remain consistent with flat LCDM. While the overall $χ^2$ of model fits is satisfactory, the LyaF BAO measurements are in moderate (2-2.5 sigma) tension with model predictions. Models with early dark energy that tracks the dominant energy component at high redshifts remain consistent with our constraints. Expansion history alone yields an upper limit of 0.56 eV on the summed mass of neutrino species, improving to 0.26 eV if we include Planck CMB lensing. Standard dark energy models constrained by our data predict a level of matter clustering that is high compared to most, but not all, observational estimates. (Abridged)

astro-ph.CO↗

arXiv2014

Genus Topology and Cross-Correlation of BICEP2 and Planck 353 GHz B-Modes: Further Evidence Favoring Gravity Wave Detection

We have analyzed the genus topology of the BICEP2 B-modes and find them to be Gaussian random phase as expected if they have a cosmological origin. These BICEP2 B-modes can be produced by gravity waves in the early universe, but some question has arisen as to whether these B-modes (for 50 < l < 120) may instead be produced by foreground polarized dust emission. The dust emission at 150 GHz observed by BICEP2 should be less in magnitude but have similar structure to that at 353 GHz. We have therefore calculated and mapped the B-modes in the BICEP2 region from the publicly available Q and U 353 GHz preliminary Planck polarization maps. These have a genus curve that is different from that seen in the BICEP2 observations, with features at different locations from those in the BICEP2 map. The two maps show a positive correlation coefficient of 15.2% +/- 3.9% (1-sigma). This requires the amplitude of the Planck (50 < l <120) dust modes to be low in the BICEP2 region, and the majority of the Planck 353 GHz signal in the BICEP2 region in these modes to be noise. We can explain the observed correlation coefficient of 15.2% with a BICEP2 gravity wave signal with an rms amplitude equal to 54% of the total BICEP2 rms amplitude. The gravity wave signal corresponds to a tensor-to-scalar ratio r = 0.11 +/- 0.04 (1-sigma). This is consistent with a gravity wave signal having been detected, at a 2.5-sigma level. The Planck and BICEP2 teams have recently engaged in joint analysis of their combined data|it will be interesting to see if that collaboration reaches similar conclusions.

astro-ph.CO↗

arXiv2014

The Tenth Data Release of the Sloan Digital Sky Survey: First Spectroscopic Data from the SDSS-III Apache Point Observatory Galactic Evolution Experiment

The Sloan Digital Sky Survey (SDSS) has been in operation since 2000 April. This paper presents the tenth public data release (DR10) from its current incarnation, SDSS-III. This data release includes the first spectroscopic data from the Apache Point Observatory Galaxy Evolution Experiment (APOGEE), along with spectroscopic data from the Baryon Oscillation Spectroscopic Survey (BOSS) taken through 2012 July. The APOGEE instrument is a near-infrared R~22,500 300-fiber spectrograph covering 1.514--1.696 microns. The APOGEE survey is studying the chemical abundances and radial velocities of roughly 100,000 red giant star candidates in the bulge, bar, disk, and halo of the Milky Way. DR10 includes 178,397 spectra of 57,454 stars, each typically observed three or more times, from APOGEE. Derived quantities from these spectra (radial velocities, effective temperatures, surface gravities, and metallicities) are also included.DR10 also roughly doubles the number of BOSS spectra over those included in the ninth data release. DR10 includes a total of 1,507,954 BOSS spectra, comprising 927,844 galaxy spectra; 182,009 quasar spectra; and 159,327 stellar spectra, selected over 6373.2 square degrees.

astro-ph.IM↗

arXiv2014

A one-parameter formula for testing slow-roll dark energy: observational prospects

Numerous upcoming observations, such as WFIRST, BOSS, BigBOSS, LSST, Euclid, and Planck, will constrain dark energy (DE)'s equation of state with great precision. They may well find the ratio of pressure to energy density, $w$, is -1, meaning DE is equivalent to a cosmological constant. However, many time-varying DE models have also been proposed. A single parametrization to test a broad class of them and that is itself motivated by a physical picture is therefore desirable. We suggest the simplest model of DE has the same mechanism as inflation, likely a scalar field slowly rolling down its potential. If this is so, DE will have a generic equation of state and the Universe will have a generic dependence of the Hubble constant on redshift independent of the potential's starting value and shape. This equation of state and expression for the Hubble constant offer the desired model-independent but physically motivated parametrization, because they will hold for most of the standard scalar-field models of DE such as quintessence and phantom DE. Up until now two-parameter descriptions of $w$ have been available, but this work finds an additional approximation that leads to a single-parameter model. Using it, we conduct a $χ^2$ analysis and find that experiments in the next seven years should be able to distinguish any of these time-varying DE models on the one hand from a cosmological constant on the other to 73% confidence if $w$ today differs from -1 by 3.5%. In the limit of perfectly accurate measurements of $Ω_m$ and $H_0$, this confidence would rise to 96%. We also include discussion of the current status of DE experiment, a table compiling the techniques each will use, and tables of the precisions of the experiments for which this information was available at the time of publication.

astro-ph.CO↗

arXiv2012

The Challenge of the Largest Structures in the Universe to Cosmology

Large galaxy redshift surveys have long been used to constrain cosmological models and structure formation scenarios. In particular, the largest structures discovered observationally are thought to carry critical information on the amplitude of large-scale density fluctuations or homogeneity of the universe, and have often challenged the standard cosmological framework. The Sloan Great Wall (SGW) recently found in the Sloan Digital Sky Survey (SDSS) region casts doubt on the concordance cosmological model with a cosmological constant (i.e. the flat LCDM model). Here we show that the existence of the SGW is perfectly consistent with the LCDM model, a result that only our very large cosmological N-body simulation (the Horizon Run 2, HR2) could supply. In addition, we report on the discovery of a void complex in the SDSS much larger than the SGW, and show that such size of the largest void is also predicted in the LCDM paradigm. Our results demonstrate that an initially homogeneous isotropic universe with primordial Gaussian random phase density fluctuations growing in accordance with the General Relativity, can explain the richness and size of the observed large-scale structures in the SDSS. Using the HR2 simulation we predict that a future galaxy redshift survey about four times deeper or with 3 magnitude fainter limit than the SDSS should reveal a largest structure of bright galaxies about twice as big as the SGW.

astro-ph.CO↗

arXiv2012

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological implications of the large-scale two-point correlation function

We obtain constraints on cosmological parameters from the spherically averaged redshift-space correlation function of the CMASS Data Release 9 (DR9) sample of the Baryonic Oscillation Spectroscopic Survey (BOSS). We combine this information with additional data from recent CMB, SN and BAO measurements. Our results show no significant evidence of deviations from the standard flat-Lambda CDM model, whose basic parameters can be specified by Omega_m = 0.285 +- 0.009, 100 Omega_b = 4.59 +- 0.09, n_s = 0.96 +- 0.009, H_0 = 69.4 +- 0.8 km/s/Mpc and sigma_8 = 0.80 +- 0.02. The CMB+CMASS combination sets tight constraints on the curvature of the Universe, with Omega_k = -0.0043 +- 0.0049, and the tensor-to-scalar amplitude ratio, for which we find r < 0.16 at the 95 per cent confidence level (CL). These data show a clear signature of a deviation from scale-invariance also in the presence of tensor modes, with n_s <1 at the 99.7 per cent CL. We derive constraints on the fraction of massive neutrinos of f_nu < 0.049 (95 per cent CL), implying a limit of sum m_nu < 0.51 eV. We find no signature of a deviation from a cosmological constant from the combination of all datasets, with a constraint of w_DE = -1.033 +- 0.073 when this parameter is assumed time-independent, and no evidence of a departure from this value when it is allowed to evolve as w_DE(a) = w_0 + w_a (1 - a). The achieved accuracy on our cosmological constraints is a clear demonstration of the constraining power of current cosmological observations.

astro-ph.CO↗

arXiv2012

The New Horizon Run Cosmological N-Body Simulations

We present two large cosmological N-body simulations, called Horizon Run 2 (HR2) and Horizon Run 3 (HR3), made using 6000^3 = 216 billions and 7210^3 = 374 billion particles, spanning a volume of (7.200 Gpc/h)^3 and (10.815 Gpc/h)^3, respectively. These simulations improve on our previous Horizon Run 1 (HR1) up to a factor of 4.4 in volume, and range from 2600 to over 8800 times the volume of the Millennium Run. In addition, they achieve a considerably finer mass resolution, down to 1.25x10^11 M_sun/h, allowing to resolve galaxy-size halos with mean particle separations of 1.2 Mpc/h and 1.5 Mpc/h, respectively. We have measured the power spectrum, correlation function, mass function and basic halo properties with percent level accuracy, and verified that they correctly reproduce the LCDM theoretical expectations, in excellent agreement with linear perturbation theory. Our unprecedentedly large-volume N-body simulations can be used for a variety of studies in cosmology and astrophysics, ranging from large-scale structure topology, baryon acoustic oscillations, dark energy and the characterization of the expansion history of the Universe, till galaxy formation science - in connection with the new SDSS-III. To this end, we made a total of 35 all-sky mock surveys along the past light cone out to z=0.7 (8 from the HR2 and 27 from the HR3), to simulate the BOSS geometry. The simulations and mock surveys are already publicly available at http://astro.kias.re.kr/Horizon-Run23/.

astro-ph.CO↗

arXiv2010

Galaxy Clustering Topology in the Sloan Digital Sky Survey Main Galaxy Sample: a Test for Galaxy Formation Models

We measure the topology of the main galaxy distribution using the Seventh Data Release of the Sloan Digital Sky Survey, examining the dependence of galaxy clustering topology on galaxy properties. The observational results are used to test galaxy formation models. A volume-limited sample defined by $M_r<-20.19$ enables us to measure the genus curve with amplitude of $G=378$ at $6h^{-1}$Mpc smoothing scale, with 4.8\% uncertainty including all systematics and cosmic variance. The clustering topology over the smoothing length interval from 6 to $10 h^{-1}$Mpc reveals a mild scale-dependence for the shift ($Δν$) and void abundance ($A_V$) parameters of the genus curve. We find substantial bias in the topology of galaxy clustering with respect to the predicted topology of the matter distribution, which varies with luminosity, morphology, color, and the smoothing scale of the density field. The distribution of relatively brighter galaxies shows a greater prevalence of isolated clusters and more percolated voids. Even though early (late)-type galaxies show topology similar to that of red (blue) galaxies, the morphology dependence of topology is not identical to the color dependence. In particular, the void abundance parameter $A_V$ depends on morphology more strongly than on color. We test five galaxy assignment schemes applied to cosmological N-body simulations of a $Λ$CDM universe to generate mock galaxies: the Halo-Galaxy one-to-one Correspondence model, the Halo Occupation Distribution model, and three implementations of Semi-Analytic Models (SAMs). None of the models reproduces all aspects of the observed clustering topology; the deviations vary from one model to another but include statistically significant discrepancies in the abundance of isolated voids or isolated clusters and the amplitude and overall shift of the genus curve. (Abridged)

astro-ph.CO↗

arXiv2010

The Sloan Digital Sky Survey Quasar Lens Search. IV. Statistical Lens Sample from the Fifth Data Release

We present the second report of our systematic search for strongly lensed quasars from the data of the Sloan Digital Sky Survey (SDSS). From extensive follow-up observations of 136 candidate objects, we find 36 lenses in the full sample of 77,429 spectroscopically confirmed quasars in the SDSS Data Release 5. We then define a complete sample of 19 lenses, including 11 from our previous search in the SDSS Data Release 3, from the sample of 36,287 quasars with i<19.1 in the redshift range 0.6<z<2.2, where we require the lenses to have image separations of 1"<θ<20" and i-band magnitude differences between the two images smaller than 1.25 mag. Among the 19 lensed quasars, 3 have quadruple-image configurations, while the remaining 16 show double images. This lens sample constrains the cosmological constant to be Ω_Λ=0.84^{+0.06}_{-0.08}(stat.)^{+0.09}_{-0.07}(syst.) assuming a flat universe, which is in good agreement with other cosmological observations. We also report the discoveries of 7 binary quasars with separations ranging from 1.1" to 16.6", which are identified in the course of our lens survey. This study concludes the construction of our statistical lens sample in the full SDSS-I data set.

astro-ph.CO↗

arXiv2010

Using the Topology of Large Scale Structure to constrain Dark Energy

The use of standard rulers, such as the scale of the Baryonic Acoustic oscillations (BAO), has become one of the more powerful techniques employed in cosmology to probe the entity driving the accelerating expansion of the Universe. In this paper, the topology of large scale structure (LSS) is used as one such standard ruler to study this mysterious `dark energy'. By following the redshift evolution of the clustering of luminous red galaxies (LRGs) as measured by their 3D topology (counting structures in the cosmic web), we can chart the expansion rate and extract information about the equation of state of dark energy. Using the technique first introduced in (Park & Kim, 2009), we evaluate the constraints that can be achieved using 3D topology measurements from next-generation LSS surveys such as the Baryonic Oscillation Spectroscopic Survey (BOSS). In conjunction with the information that will be available from the Planck satellite, we find a single topology measurement on 3 different scales is capable of constraining a single dark energy parameter to within 5% and 10% when dynamics are permitted. This offers an alternative use of the data available from redshift surveys and serves as a cross-check for BAO studies.

astro-ph.CO↗

arXiv2009

The Horizon Run N-body Simulation: Baryon Acoustic Oscillations and Topology of Large Scale Structure of the Universe

In support of the new Sloan III survey, which will measure the baryon oscillation scale using the luminous red galaxies (LRGs), we have run the largest N-body simulation to date using $4120^3 = 69.9$ billion particles, and covering a volume of $(6.592 h^{-1} {\rm Gpc})^3$. This is over 2000 times the volume of the Millennium Run, and corner-to-corner stretches all the way to the horizon of the visible universe. LRG galaxies are selected by finding the most massive gravitationally bound, cold dark matter subhalos, not subject to tidal disruption, a technique that correctly reproduces the 3D topology of the LRG galaxies in the Sloan Survey.We have measured the covariance function, power spectrum, and the 3D topology of the LRG galaxy distribution in our simulation and made 32 mock surveys along the past lightcone to simulate the Sloan III survey. Our large N-body simulation is used to accurately measure the non-linear systematic effects such as gravitational evolution, redshift space distortion, past light cone space gradient, and galaxy biasing, and to calibrate the baryon oscillation scale and the genus topology. For example, we predict from our mock surveys that the baryon acoustic oscillation peak scale can be measured with the cosmic variance-dominated uncertainty of about 5% when the SDSS-III sample is divided into three equal volume shells, or about 2.6% when a thicker shell with $0.4<z<0.6$ is used. We find that one needs to correct the scale for the systematic effects amounting up to 5.2% to use it to constrain the linear theories. And the uncertainty in the amplitude of the genus curve is expected to be about 1% at 15 $h^{-1}$Mpc scale. We are making the simulation and mock surveys publicly available.

astro-ph↗

arXiv2009

3D Genus Topology of Luminous Red Galaxies

We measure the 3D genus topology of large scale structure using Luminous Red Galaxies (LRGs) in the Sloan Digital Sky Survey and find it consistent with the Gaussian random phase initial conditions expected from the simplest scenarios of inflation. This studies 3D topology on the largest scales ever obtained. The topology is sponge-like. We measure topology in two volume-limited samples: a dense shallow sample studied with smoothing length of 21h^{-1}Mpc, and a sparse deep sample studied with a smoothing length of 34h^{-1}Mpc. The amplitude of the genus curve is measured with 4% uncertainty. Small distortions in the genus curve expected from non-linear biasing and gravitational effects are well explained (to about 1-σaccuracy) by N-body simulations using a subhalo-finding technique to locate LRGs. This suggests the formation of LRGs is a clean problem that can be modeled well without any free fitting parameters. This bodes well for using LRGs to measure the characteristic scales such as the baryon oscillation scale in future deep redshift surveys.

astro-ph↗

arXiv2008

Boltzmann Brains--I'd Rather See Than Be One

A perceived problem with the standard flat-lambda model is that in the far future spacetime becomes an exponentially expanding de Sitter space, filled with Gibbons-Hawking thermal radiation, and given infinite time there will appear an infinite number of Boltzmann Brains (BB's) per finite co-moving volume today. If BB's outnumber ordinary observers by an infinite factor, why am I not one? This Gibbons-Hawking thermal radiation is observer dependent--due to observer dependent event horizons. Different observers moving relative to each other will see different photons, and different BB's. I will argue that the only particles that are real are the particles dredged out of the quantum vacuum state by particular real material detectors. (In much the same way, accelerated detectors dredge thermal Unruh radiation out of the Minkowski vacuum due to their observer dependent event horizons.) Thus, I may see a thermal BB, but cannot be one. Observer independent BB's can be created by quantum tunneling events, but the rate at which ordinary observers are being added to the universe by tunneling events to inflating regions exceeds the rate for producing BB's by tunneling by an infinite factor. I also argue that BB's do not really pass the Turing test for intelligent observers. Thus, the standard flat-lambda model is safe.

gr-qc↗

arXiv2007

The Topology of Cosmological Reionization

Using the largest cosmological reionization simulation to-date (~24 billion particles), we use the genus curve to quantify the topology of neutral hydrogen distribution on scales > 1 Mpc as it evolves during cosmological reionization. We find that the reionization process proceeds primarily in an inside-out fashion, where higher density regions become ionized earlier than lower density regions. There are four distinct topological phases: (1) Pre-reionization at z ~ 15, when the genus curve is consistent with a Gaussian density distribution. (2) Pre-overlap at 10 < z < 15, during which the number of HII bubbles increases gradually with time, until percolation of HII bubbles starts to take effect, characterized by a very flat genus curve at high volume fractions. (3) Overlap at 8 < z < 10, when large HII bubbles rapidly merge, manifested by a precipitous drop in the amplitude of the genus curve. (4) Post-overlap at 6 < z < 8, when HII bubbles have mostly overlapped and the genus curve is consistent with a diminishing number of isolated neutral islands. After the end of reionization (z < 6), the genus of neutral hydrogen is consistent with Gaussian random phase, in agreement with observations.

astro-ph↗