Testing gaussianity, homogeneity and isotropy with the cosmic microwave background

We review the basic hypotheses which motivate the statistical framework used to analyze the cosmic microwave background, and how that framework can be enlarged as we relax those hypotheses. In particular, we try to separate as much as possible the questions of gaussianity, homogeneity and isotropy from each other. We focus both on isotropic estimators of non-gaussianity as well as statistically anisotropic estimators of gaussianity, giving particular emphasis on their signatures and the enhanced "cosmic variances" that become increasingly important as our putative Universe becomes less symmetric. After reviewing the formalism behind some simple model-independent tests, we discuss how these tests can be applied to CMB data when searching for large scale "anomalies"Comment: 52 pages, 22 pdf figures. Revised version of the invited review for the special issue "Testing the Gaussianity and Statistical Isotropy of the Universe" for Advances in Astronomy

The Sun, stellar-population models, and the age estimation of high-redshift galaxies

Given sufficiently deep optical spectroscopy, the age estimation of high-redshif t ($z > 1$) galaxies has been claimed to be a relatively robust process (e.g. Dunlop et al. 1996) due to the fact that, for ages $< 5$Gyr, the near-ultraviolet light of a stellar population is expected to be dominated by `well-understood' main-sequence (MS) stars. Recently, however, the reliability of this process has been called into question by Yi et al (2000), who claim to have developed models in which the spectrum produced by the main sequence reddens much more rapidly than in the models of Jimenez et al (2000a), leading to much younger age estimates for the reddest known high-redshift ellipticals. In support of their revised age estimates, Yi et al cite the fact that their models can reproduce the spectrum of the Sun at an age of 5 Gyr, whereas the solar spectrum is not reproduced by the Jimenez et al models until $\simeq 10$ Gyr. Here we confirm this discrepancy, but point out that this is in fact a {\it strength} of the Jimenez et al models and indicative of some flaw in the models of Yi et al (which, in effect, imply that the Sun will turn into a red giant any minute now). We have also explored the models of Worthey (1994) (which are known to differ greatly from those of Jimenez et al in the treatment of post-MS evolution) and find that the main-sequence component of Worthey's models also cannot reproduce the solar spectrum until an age of 9-10 Gyr. We conclude that either the models of Yi et al are not as main-sequence dominated at 4-5 Gyr as claimed, or that the stellar evolutionary timescale in these models is in error by a factor possibly as high as two. (abridged)Comment: Submitted to MNRAS, final versio

Angular-planar CMB power spectrum

Gaussianity and statistical isotropy of the Universe are modern cosmology's minimal set of hypotheses. In this work we introduce a new statistical test to detect observational deviations from this minimal set. By defining the temperature correlation function over the whole celestial sphere, we are able to independently quantify both angular and planar dependence (modulations) of the CMB temperature power spectrum over different slices of this sphere. Given that planar dependence leads to further modulations of the usual angular power spectrum $C_l$, this test can potentially reveal richer structures in the morphology of the primordial temperature field. We have also constructed an unbiased estimator for this angular-planar power spectrum which naturally generalizes the estimator for the usual $C_l$'s. With the help of a chi-square analysis, we have used this estimator to search for observational deviations of statistical isotropy in WMAP's 5 year release data set (ILC5), where we found only slight anomalies on the angular scales $l=7$ and $l=8$. Since this angular-planar statistic is model-independent, it is ideal to employ in searches of statistical anisotropy (e.g., contaminations from the galactic plane) and to characterize non-Gaussianities.Comment: Replaced to match the published version. Journal-ref: Phys.Rev. D80 063525 (2009

CMB in a box: causal structure and the Fourier-Bessel expansion

This paper makes two points. First, we show that the line-of-sight solution to cosmic microwave anisotropies in Fourier space, even though formally defined for arbitrarily large wavelengths, leads to position-space solutions which only depend on the sources of anisotropies inside the past light-cone of the observer. This happens order by order in a series expansion in powers of the visibility $\gamma=e^{-\mu}$, where $\mu$ is the optical depth to Thompson scattering. We show that the CMB anisotropies are regulated by spacetime window functions which have support only inside the past light-cone of the point of observation. Second, we show that the Fourier-Bessel expansion of the physical fields (including the temperature and polarization momenta) is an alternative to the usual Fourier basis as a framework to compute the anisotropies. In that expansion, for each multipole $l$ there is a discrete tower of momenta $k_{i,l}$ (not a continuum) which can affect physical observables, with the smallest momenta being $k_{1,l} ~ l$. The Fourier-Bessel modes take into account precisely the information from the sources of anisotropies that propagates from the initial value surface to the point of observation - no more, no less. We also show that the physical observables (the temperature and polarization maps), and hence the angular power spectra, are unaffected by that choice of basis. This implies that the Fourier-Bessel expansion is the optimal scheme with which one can compute CMB anisotropies. (Abridged)Comment: 23 pages, 7 figure

Grand Challenges of Traceability: The Next Ten Years

In 2007, the software and systems traceability community met at the first Natural Bridge symposium on the Grand Challenges of Traceability to establish and address research goals for achieving effective, trustworthy, and ubiquitous traceability. Ten years later, in 2017, the community came together to evaluate a decade of progress towards achieving these goals. These proceedings document some of that progress. They include a series of short position papers, representing current work in the community organized across four process axes of traceability practice. The sessions covered topics from Trace Strategizing, Trace Link Creation and Evolution, Trace Link Usage, real-world applications of Traceability, and Traceability Datasets and benchmarks. Two breakout groups focused on the importance of creating and sharing traceability datasets within the research community, and discussed challenges related to the adoption of tracing techniques in industrial practice. Members of the research community are engaged in many active, ongoing, and impactful research projects. Our hope is that ten years from now we will be able to look back at a productive decade of research and claim that we have achieved the overarching Grand Challenge of Traceability, which seeks for traceability to be always present, built into the engineering process, and for it to have "effectively disappeared without a trace". We hope that others will see the potential that traceability has for empowering software and systems engineers to develop higher-quality products at increasing levels of complexity and scale, and that they will join the active community of Software and Systems traceability researchers as we move forward into the next decade of research

Extending the halo mass resolution of NN-body simulations

We present a scheme to extend the halo mass resolution of N-body simulations of the hierarchical clustering of dark matter. The method uses the density field of the simulation to predict the number of sub-resolution dark matter haloes expected in different regions. The technique requires as input the abundance of haloes of a given mass and their average clustering, as expressed through the linear and higher order bias factors. These quantities can be computed analytically or, more accurately, derived from a higher resolution simulation as done here. Our method can recover the abundance and clustering in real- and redshift-space of haloes with mass below $\sim 7.5 \times 10^{13}h^{-1}M_{\odot}$ at $z=0$ to better than 10%. We demonstrate the technique by applying it to an ensemble of 50 low resolution, large-volume $N$-body simulations to compute the correlation function and covariance matrix of luminous red galaxies (LRGs). The limited resolution of the original simulations results in them resolving just two thirds of the LRG population. We extend the resolution of the simulations by a factor of 30 in halo mass in order to recover all LRGs. With existing simulations it is possible to generate a halo catalogue equivalent to that which would be obtained from a $N$-body simulation using more than 20 trillion particles; a direct simulation of this size is likely to remain unachievable for many years. Using our method it is now feasible to build the large numbers of high-resolution large volume mock galaxy catalogues required to compute the covariance matrices necessary to analyse upcoming galaxy surveys designed to probe dark energy.Comment: 11 pages, 7 Figure

Nonreactive solute transport in soil columns: classical and fractional-calculus modeling

Vertical nonreactive solute transport data collected in three laboratory soil columns (made out of sediment samples from the Pampean aquifer located southeast of the Buenos Aires province) are contrasted with the explicit solutions of two model 1D linear PDEs: the classical advection–dispersion equation (ADE), and a fractional advection–dispersion equation (FADE) which has proven to be a useful modeling tool for highly inhomogeneous media exhibiting nontrivial scaling laws. Whereas two of the samples turn out to be quite homogeneous (thus requiring a fractional-derivative order γ → 2), the third one is best described by a FADE with fractional-derivative order γ = 1.68. This example illustrates the FADE’s ability to reveal self-similar geometric structures inside the sample.Fil: Benavente, Micaela Andrea. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Deza, Roberto Raul. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Cs.exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; ArgentinaFil: Grondona, Sebastian. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Geología de Costas y del Cuaternario. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto de Geología de Costas y del Cuaternario; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Mascioli, S.. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Geología de Costas y del Cuaternario. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto de Geología de Costas y del Cuaternario; ArgentinaFil: Martinez, Daniel Emilio. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Geología de Costas y del Cuaternario. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto de Geología de Costas y del Cuaternario; Argentin