On the signature of z∼0.6z\sim 0.6 superclusters and voids in the Integrated Sachs-Wolfe effect

Through a large ensemble of Gaussian realisations and a suite of large-volume N-body simulations, we show that in a standard LCDM scenario, supervoids and superclusters in the redshift range $z\in[0.4,0.7]$ should leave a {\em small} signature on the ISW effect of the order $\sim 2 \mu$K. We perform aperture photometry on WMAP data, centred on such superstructures identified from SDSS LRGs, and find amplitudes at the level of 8 -- 11$\mu$K -- thus confirming the earlier work of Granett et al 2008. If we focus on apertures of the size \sim3.6\degr, then our realisations indicate that LCDM is discrepant at the level of $\sim4 \sigma$. If we combine all aperture scales considered, ranging from 1\degr--20\degr, then the discrepancy becomes $\sim2\sigma$, and it further lowers to $\sim 0.6 \sigma$ if only 30 superstructures are considered in the analysis (being compatible with no ISW signatures at $1.3\sigma$ in this case). Full-sky ISW maps generated from our N-body simulations show that this discrepancy cannot be alleviated by appealing to Rees-Sciama mechanisms, since their impact on the scales probed by our filters is negligible. We perform a series of tests on the WMAP data for systematics. We check for foreground contaminants and show that the signal does not display the correct dependence on the aperture size expected for a residual foreground tracing the density field. The signal also proves robust against rotation tests of the CMB maps, and seems to be spatially associated to the angular positions of the supervoids and superclusters. We explore whether the signal can be explained by the presence of primordial non-Gaussianities of the local type. We show that for models with \FNL=\pm100, whilst there is a change in the pattern of temperature anisotropies, all amplitude shifts are well below $<1\mu$K.Comment: 14 pages, 9 figures, matches accepted version in MNRA

Uniform Approximation of Abhyankar Valuation Ideals in Smooth Function Fields

In this paper we use the theory of multiplier ideals to show that the valuation ideals of a rank one Abhyankar valuation centered at a smooth point of a complex algebraic variety are approximated, in a quite strong sense, by sequences of powers of fixed ideals. Fix a rank one valuation v centered at a smooth point x on an algebraic variety over a field of characteristic zero. Assume that v is Abhyankar, that is, that its rational rank plus its transcendence degree equal the dimension of the variety. Let a_m denote the ideal of elements in the local ring of x whose valuations are at least m. Our main theorem is that there exists e>0 such that a_{mn} is contained in (a_{m-e})^n for all m and n. This can be viewed as a greatly strengthened form of Izumi's Theorem for Abhyankar valuations centered on smooth complex varieties.Comment: 27 pages, late

Halo Mass Function and the Free Streaming Scale

The nature of structure formation around the particle free streaming scale is still far from understood. Many attempts to simulate hot, warm, and cold dark matter cosmologies with a free streaming cutoff have been performed with cosmological particle-based simulations, but they all suffer from spurious structure formation at scales below their respective free streaming scales -- i.e. where the physics of halo formation is most affected by free streaming. We perform a series of high resolution numerical simulations of different WDM models, and develop an approximate method to subtract artificial structures in the measured halo mass function. The corrected measurements are then used to construct and calibrate an extended Press-Schechter (EPS) model with sharp-$k$ window function and adequate mass assignment. The EPS model gives accurate predictions for the low redshift halo mass function of CDM and WDM models, but it significantly under-predicts the halo abundance at high redshifts. By taking into account the ellipticity of the initial patches and connecting the characteristic filter scale to the smallest ellipsoidal axis, we are able to eliminate this inconsistency and obtain an accurate mass function over all redshifts and all dark matter particle masses covered by the simulations. As an additional application we use our model to predict the microhalo abundance of the standard neutralino-CDM scenario and we give the first quantitative prediction of the mass function over the full range of scales of CDM structure formation.Comment: 16 pages, 10 figures, published in MNRA

The cosmological information of shear peaks: beyond the abundance

We study the cosmological information of weak lensing (WL) peaks, focusing on two other statistics besides their abundance: the stacked tangential-shear profiles and the peak-peak correlation function. We use a large ensemble of simulated WL maps with survey specifications relevant to future missions like Euclid and LSST, to explore the three peak probes. We find that the correlation function of peaks with high signal-to-noise (S/N) measured from fields of size 144 sq. deg. has a maximum of ~0.3 at an angular scale ~10 arcmin. For peaks with smaller S/N, the amplitude of the correlation function decreases, and its maximum occurs on smaller angular scales. We compare the peak observables measured with and without shape noise and find that for S/N~3 only ~5% of the peaks are due to large-scale structures, the rest being generated by shape noise. The covariance matrix of the probes is examined: the correlation function is only weakly covariant on scales < 30 arcmin, and slightly more on larger scales; the shear profiles are very correlated for theta > 2 arcmin, with a correlation coefficient as high as 0.7. Using the Fisher-matrix formalism, we compute the cosmological constraints for {Om_m, sig_8, w, n_s} considering each probe separately, as well as in combination. We find that the correlation function of peaks and shear profiles yield marginalized errors which are larger by a factor of 2-4 for {Om_m, sig_8} than the errors yielded by the peak abundance alone, while the errors for {w, n_s} are similar. By combining the three probes, the marginalized constraints are tightened by a factor of ~2 compared to the peak abundance alone, the least contributor to the error reduction being the correlation function. This work therefore recommends that future WL surveys use shear peaks beyond their abundance in order to constrain the cosmological model.Comment: 15 pages, 10 figures, submitted to MNRA

Covariance of cross-correlations: towards efficient measures for large-scale structure

We study the covariance of the cross-power spectrum of different tracers for the large-scale structure. We develop the counts-in-cells framework for the multitracer approach, and use this to derive expressions for the full non-Gaussian covariance matrix. We show that for the usual autopower statistic, besides the off-diagonal covariance generated through gravitational mode-coupling, the discreteness of the tracers and their associated sampling distribution can generate strong off-diagonal covariance, and that this becomes the dominant source of covariance as spatial frequencies become larger than the fundamental mode of the survey volume. On comparison with the derived expressions for the cross-power covariance, we show that the off-diagonal terms can be suppressed, if one cross-correlates a high tracer-density sample with a low one. Taking the effective estimator efficiency to be proportional to the signal-to-noise ratio (S/N), we show that, to probe clustering as a function of physical properties of the sample, i.e. cluster mass or galaxy luminosity, the cross-power approach can outperform the autopower one by factors of a few. We confront the theory with measurements of the mass-mass, halo-mass and halo-halo power spectra from a large ensemble of N-body simulations. We show that there is a significant S/N advantage to be gained from using the cross-power approach when studying the bias of rare haloes. The analysis is repeated in configuration space and again S/N improvement is found. We estimate the covariance matrix for these samples, and find strong off-diagonal contributions. The covariance depends on halo mass, with higher mass samples having stronger covariance. In agreement with theory, we show that the covariance is suppressed for the cross-power. This work points the way towards improved estimators for studying the clustering of tracers as a function of their physical propertie

Using a Primordial Gravitational Wave Background to Illuminate New Physics

A primordial spectrum of gravitational waves serves as a backlight to the relativistic degrees of freedom of the cosmological fluid. Any change in the particle physics content, due to a change of phase or freeze-out of a species, will leave a characteristic imprint on an otherwise featureless primordial spectrum of gravitational waves and indicate its early-Universe provenance. We show that a gravitational wave detector such as the Laser Interferometer Space Antenna would be sensitive to physics near 100 TeV in the presence of a sufficiently strong primordial spectrum. Such a detection could complement searches at newly proposed 100 km circumference accelerators such as the Future Circular Collider at CERN and the Super Proton-Proton Collider in China, thereby providing insight into a host of beyond Standard Model issues, including the hierarchy problem, dark matter, and baryogenesis.Comment: 7 pages, 3 figures; added reference

The classical capacity of quantum thermal noise channels to within 1.45 bits

We find a tight upper bound for the classical capacity of quantum thermal noise channels that is within $1/\ln 2$ bits of Holevo's lower bound. This lower bound is achievable using unentangled, classical signal states, namely displaced coherent states. Thus, we find that while quantum tricks might offer benefits, when it comes to classical communication they can only help a bit.Comment: Two pages plus a bi