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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, version as accepted by MNRAS

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

We propose a simple model for dark energy useful for comparison with observations. It is based on the idea that dark energy and inflation should be caused by the same physical process. As motivation, we note that Linde's simple chaotic inflation V = 1/2m 2 φ 2 produces values of n s = 0.967 and r = 0.13, which are consistent with the Wilkinson Microwave Anisotropy Probe (WMAP) 1σ error bars. We therefore propose V = 1/2m 2 2 φ 2 2 + 1/2m 2 1 φ 2 1 with m 1 ~ 10 -5 and m 2 ≤ 10 -60 , where c = 1 = ħ and the reduced Planck mass is set to unity. The field φ 1 drives inflation and has damped by now (φ 1.0 = 0), while φ 2 is currently rolling down its potential to produce dark energy. Using this model, we derive the formula δω(z) = w(z) + 1 = δω 0 (H 0 /H(z)) 2 via the slow-roll approximation. Our numerical results from exact and self-consistent solution of the equations of motion for φ 2 and the Friedmann equations support this formula, and it should hold for any slow-roll dark energy. Our potential can be easily realized in N-flation models with many fields, and is easily falsifiable by upcoming experiments - for example, if Linde's chaotic inflation is ruled out. But if r values consistent with Linde's chaotic inflation are detected then one should take this model seriously indeed.

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-\sigma accuracy) 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.

In 2004, we used a very simple, but surprisingly effective, method to successfully predict the outcome of the U.S. Presidential election. Using the median poll in the last month for each state, we correctly predicted the results in all states but one (Hawaii). Just as we had originally hoped, the method made it possible to predict successfully the results in the large close states (Ohio, Pennsylvania, and Florida) where there were a great many polls taken. States with only a few polls were generally not close, and so the median poll also predicted these states successfully. The method appears particularly well adapted to U.S. Presidential elections where the candidates are chosen well in advance, and where outcomes in individual states determine the winner.

We studied the dependence of morphology and luminosity of the SDSS galaxies on the environmental factors. The environmental factors considered include the local density due to the nearest neighbor galaxy ρn, morphology of the nearest neighbor, and the large-scale background density. We found the local environment set up by the nearest neighbor galaxy gives strong effects on the galaxy morphology. The probability for a galaxy to have an early morphological type critically depends on whether or not ρn is above the virialization density. We conclude that the well-known morphology-density relation is basically due to the interactions between galaxy pairs. Dependence of galaxy morphology on the large-scale density is found only because there is a statistical correlation between the average pair separation and the large-scale background density. We also found that galaxy luminosity depends on ρn, and that, when the large-scale density is fixed, more isolated galaxies are more likely to be recent merger products. We propose a scenario that a series of morphology and luminosity transformation occur through a series of distant/close interactions and mergers, which results in the morphology-luminosity-local density relation.

We measure the three-dimensional topology of large-scale structure in the Sloan Digital Sky Survey (SDSS). This allows the genus statistic to be measured with unprecedented statistical accuracy. The sample size is now sufficiently large to allow the topology to be an important tool for testing galaxy formation models. For comparison, we make mock SDSS samples using several state-of-the-art N-body simulations: the Millennium run of Springel et al. (2005)(10 billion particles), Kim & Park (2006) CDM models (1.1 billion particles), and Cen & Ostriker (2006) hydrodynamic code models (8.6 billion cell hydro mesh). Each of these simulations uses a different method for modeling galaxy formation. The SDSS data show a genus curve that is broadly characteristic of that produced by Gaussian random phase initial conditions. Thus the data strongly support the standard model of inflation where Gaussian random phase initial conditions are produced by random quantum fluctuations in the early universe. But on top of this general shape there are measurable differences produced by non-linear gravitational effects (cf. Matsubara 1994), and biasing connected with galaxy formation. The N-body simulations have been tuned to reproduce the power spectrum and multiplicity function but not topology, so topology is an acid test for these models. The data show a ``meatball'' shift (only partly due to the Sloan Great Wall of Galaxies; this shift also appears in a sub-sample not containing the Wall) which differs at the 2.5��level from the results of the Millennium run and the Kim & Park dark halo models, even including the effects of cosmic variance., 13 Apj pages, 7 figures High-resolution stereo graphic available at http://www.astro.princeton.edu/~dclayh/stereo50.eps

Tissot indicatrices have provided visual measures of local area and isotropy distortions. Here we show how large-scale distortions of flexion (bending) and skewness (lopsidedness) can be measured. Area and isotropy distortions depend on the map-projection metric; flexion and skewness, which manifest themselves on continental scales, depend on the first derivatives of the metric. We introduce new indicatrices that show not only area and isotropy distortions but flexion and skewness as well. We present a table showing error measures for area, isotropy, flexion, skewness, distances, and boundary cuts, allowing us to compare different world-map projections. We find that the Winkel-Tripel projection (already adopted for world maps by National Geographic) has low distortion on most measures and excellent quality overall.

We have produced a cleaned map of the WMAP three-year data using an improved version of an internal linear combination (ILC) method to subtract the Galactic foreground emission. We divide the whole sky into hundreds of pixel groups with similar foreground spectral indices over a range of WMAP frequencies, apply the ILC for each group, and obtain a CMB map with foreground emission effectively reduced. With the resulting foreground-reduced ILC map, we have investigated the known anomalies in CMB maps at large scales, and confirmed that the quadrupole power is low and the quadrupole and the octopole are strongly aligned and are planar. Although our estimates are consistent with the previous measurements, ILC simulation implies that the observed low quadrupole power and the alignment between the quadrupole and the octopole are marginally statistically significant, and the observed planarity is not statistically significant.

We have produced a cleaned CMB temperature fluctuation map of the Wilkinson Microwave Anisotropy Probe (WMAP) 3 year data using an improved internal linear combination (ILC) method as a Galactic foreground subtraction technique. We divide the whole sky into hundreds of pixel groups with similar foreground spectral indices over a range of WMAP frequencies, apply the ILC for each group, and obtain a CMB map with foreground emission effectively reduced. With the resulting ILC map, we have investigated the known anomalies in CMB maps at large scales, namely, the low quadrupole (l = 2) power, and the strong alignment and planarity of the quadrupole and the octopole (l = 3). Our estimates are consistent with the previous measurements. The quadrupole and the octopole powers measured from our ILC map are δT = 276 μK2 and δT = 952 μK2, respectively. The 68% confidence limits are estimated from the ILC simulations and include the cosmic variance. The measured quadrupole power is lower than the value expected in the concordance ΛCDM model (1250 μK2), in which the probability of finding a quadrupole power lower than the measured value is p = 5.7%. We have confirmed that the quadrupole and the octopole are strongly aligned with angle θ23 = 11.8° and are planar with high planarity parameters t = 0.98 ± 0.02 for l = 2 and t = 0.91 for l = 3. The observed angular separation θ23 is marginally significant with p = 4.3%. However, the observed planarity is not statistically significant. The probability of observing such a planarity as high as the measured t-values is over 18%. The ILC simulations show that the residual foreground emission in the ILC map does not affect the estimated values significantly.

We have produced a new conformal map of the universe illustrating recent discoveries, ranging from Kuiper belt objects in the Solar system, to the galaxies and quasars from the Sloan Digital Sky Survey. This map projection, based on the logarithm map of the complex plane, preserves shapes locally, and yet is able to display the entire range of astronomical scales from the Earth's neighborhood to the cosmic microwave background. The conformal nature of the projection, preserving shapes locally, may be of particular use for analyzing large scale structure. Prominent in the map is a Sloan Great Wall of galaxies 1.37 billion light years long, 80% longer than the Great Wall discovered by Geller and Huchra and therefore the largest observed structure in the universe., Comment: Figure 8, and additional material accessible on the web at: http://www.astro.princeton.edu/~mjuric/universe/

We construct the error distribution of Hubble constant ($H_0$) measurements from Huchra's compilation of 461 measurements of $H_0$ and the WMAP experiment central value $H_0$ = 71 km s$^{-1}$ Mpc$^{-1}$. This error distribution is non-Gaussian, with significantly larger probability in the tails of the distribution than predicted by a Gaussian distribution. The 95.4 % confidence limits are 7.0 $\sigma$ in terms of the quoted errors. It is remarkably well described by either a widened $n = 2$ Student's $t$ distribution or a widened double exponential distribution. These conclusions are unchanged if we use instead the central value $H_0$ = 67 km s$^{-1}$ Mpc$^{-1}$ found from a median statistics analysis of a major subset of $H_0$ measurements used here., Comment: 12 pages, 8 figures

We have independently measured the genus topology of the temperature fluctuations in the cosmic microwave background seen by the Wilkinson Microwave Anisotropy Probe (WMAP). A genus analysis of the WMAP data indicates consistency with Gaussian random-phase initial conditions, as predicted by standard inflation., Comment: PDF: http://www.astro.virginia.edu/~wnc5c/WMAPtopology.pdf

We present the first analysis of three-dimensional genus statistics for the SDSS EDR galaxy sample. Due to the complicated survey volume and the selection function, analytic predictions of the genus statistics for this sample are not feasible, therefore we construct extensive mock catalogs from N-body simulations in order to compare the observed data with model predictions. This comparison allows us to evaluate the effects of a variety of observational systematics on the estimated genus for the SDSS sample, including the shape of the survey volume, the redshift distortion effect, and the radial selection function due to the magnitude limit. The observed genus for the SDSS EDR galaxy sample is consistent with that predicted by simulations of a $\Lambda$-dominated spatially-flat cold dark matter model. Standard ($\Omega_0=1$) cold dark matter model predictions do not match the observations. We discuss how future SDSS galaxy samples will yield improved estimates of the genus., Comment: 20 pages, 10 figures, accepted for publication in PASJ (Vol.54, No.5, 2002)

We study the topology of the publicly available data released by the 2dFGRS. The 2dFGRS data contains over 100,000 galaxy redshifts with a magnitude limit of b_J=19.45 and is the largest such survey to date. The data lie over a wide range of right ascension (75 degree strips) but only within a narrow range of declination (10 degree and 15 degree strips). This allows measurements of the two-dimensional genus to be made. The NGP displays a slight meatball shift topology, whereas the SGP displays a bubble like topology. The current SGP data also have a slightly higher genus amplitude. In both cases, a slight excess of overdense regions are found over underdense regions. We assess the significance of these features using mock catalogs drawn from the Virgo Consortium's Hubble Volume LCDM z=0 simulation. We find that differences between the NGP and SGP genus curves are only significant at the 1 sigma level. The average genus curve of the 2dFGRS agrees well with that extracted from the LCDM mock catalogs. We compare the amplitude of the 2dFGRS genus curve to the amplitude of a Gaussian random field with the same power spectrum as the 2dFGRS and find, contradictory to results for the 3D genus of other samples, that the amplitude of the GRF genus curve is slightly lower than that of the 2dFGRS. This could be due to a a feature in the current data set or the 2D genus may not be as sensitive as the 3D genus to non-linear clustering due to the averaging over the thickness of the slice in 2D. (Abridged)

We have simulated cosmic microwave background (CMB) anisotropy maps for several COBE-DMR-normalized cold dark matter (CDM) cosmogonies, to make predictions for the upcoming MAP experiment. We have studied the sensitivity of the simulated MAP data to cosmology, sky coverage, and instrumental noise. With accurate knowledge of instrumental noise, MAP data will discriminate among the cosmogonies considered, and determine the topology of the initial fluctuations. A correlation function analysis of the simulated MAP data results in a very accurate measurement of the acoustic Hubble radius at decoupling. A low-density open CDM model with Omega_0=0.4 can be distinguished from the Omega_0=1 fiducial CDM model or a Lambda CDM model with > 99% confidence from the location of the acoustic "valley" in the correlation function. A genus analysis of the simulated MAP data indicates that in cosmogonies with Gaussian random-phase initial conditions, a shift of the zero-crossing point of the genus curve near the mean temperature threshold level nu=0 should not exceed |Delta nu| = 0.01 (0.04) when the total effective FWHM smoothing is 0.3 deg (1.0 deg). The asymmetry of the genus curve at the positive and negative threshold levels should not exceed |Delta g/g(nu=1,-1)| = 0.8% (4%) at 0.3 deg (1.0 deg) FWHM smoothing. Deviations of the observed MAP data in excess of these small values will be evidence for non-Gaussian behavior. The amplitude of the genus curve is a measure of the shape of the power spectrum at the smoothing scale. Even with the expected amount of instrumental noise and partial sky coverage (due to the Galaxy), the MAP data should allow discrimination amongst the cosmogonies considered at more than 99% confidence solely from a genus amplitude analysis.