Supernova Constraints on Models of Neutrino Dark Energy

In this paper we use the recently released Type Ia Supernova (SNIa) data to constrain the interactions between the neutrinos and the dark energy scalar fields. In the analysis we take the dark energy scalars to be either Quintessence-like or Phantom-like. Our results show the data mildly favor a model where the neutrinos couple to a phantom-like dark energy scalar, which implies the equation of state of the coupled system behaves like Quintom scenario in the sense of parameter degeneracy. We find future observations like SNAP are potentially promising to measure the couplings between neutrino and dark energy.Comment: Typos fixed and references updated. Version pressed in PR

Photometric properties and luminosity function of nearby massive early-type galaxies

We perform photometric analyses for a bright early-type galaxy (ETG) sample with 2949 galaxies ($M_{\rm r}<-22.5$ mag) in the redshift range of 0.05 to 0.15, drawn from the SDSS DR7 with morphological classification from Galaxy Zoo 1. We measure the Petrosian and isophotal magnitudes, as well as the corresponding half-light radius for each galaxy. We find that for brightest galaxies ($M_{\rm r}<-23$ mag), our Petrosian magnitudes, and isophotal magnitudes to 25 ${\rm mag/arcsec^2}$ and 1\% of the sky brightness are on average 0.16 mag, 0.20 mag, and 0.26 mag brighter than the SDSS Petrosian values, respectively. In the first case the underestimations are caused by overestimations in the sky background by the SDSS PHOTO algorithm, while the latter two are also due to deeper photometry. Similarly, the typical half-light radii ($r_{50}$) measured by the SDSS algorithm are smaller than our measurements. As a result, the bright-end of the $r$-band luminosity function is found to decline more slowly than previous works. Our measured luminosity densities at the bright end are more than one order of magnitude higher than those of Blanton et al. (2003), and the stellar mass densities at $M_{\ast}\sim 5\times10^{11} M_{\odot}$ and $M_{\ast}\sim 10^{12} M_{\odot}$ are a few tenths and a factor of few higher than those of Bernardi et al. (2010). These results may significantly alleviate the tension in the assembly of massive galaxies between observations and predictions of the hierarchical structure formation model.Comment: 43 pages, 14 figures, version accepted for publication in the Astrophysical Journa

Dominant Eigenvalue-Eigenvector Pair Estimation via Graph Infection

We present a novel method to estimate the dominant eigenvalue and eigenvector pair of any non-negative real matrix via graph infection. The key idea in our technique lies in approximating the solution to the first-order matrix ordinary differential equation (ODE) with the Euler method. Graphs, which can be weighted, directed, and with loops, are first converted to its adjacency matrix A. Then by a naive infection model for graphs, we establish the corresponding first-order matrix ODE, through which A's dominant eigenvalue is revealed by the fastest growing term. When there are multiple dominant eigenvalues of the same magnitude, the classical power iteration method can fail. In contrast, our method can converge to the dominant eigenvalue even when same-magnitude counterparts exist, be it complex or opposite in sign. We conduct several experiments comparing the convergence between our method and power iteration. Our results show clear advantages over power iteration for tree graphs, bipartite graphs, directed graphs with periods, and Markov chains with spider-traps. To our knowledge, this is the first work that estimates dominant eigenvalue and eigenvector pair from the perspective of a dynamical system and matrix ODE. We believe our method can be adopted as an alternative to power iteration, especially for graphs.Comment: 13 pages, 8 figures, 3 table

High-Redshift Cosmography

We constrain the parameters describing the kinematical state of the universe using a cosmographic approach, which is fundamental in that it requires a very minimal set of assumptions (namely to specify a metric) and does not rely on the dynamical equations for gravity. On the data side, we consider the most recent compilations of Supernovae and Gamma Ray Bursts catalogues. This allows to further extend the cosmographic fit up to $z = 6.6$, i.e. up to redshift for which one could start to resolve the low z degeneracy among competing cosmological models. In order to reliably control the cosmographic approach at high redshifts, we adopt the expansion in the improved parameter $y = z/(1+z)$. This series has the great advantage to hold also for $z > 1$ and hence it is the appropriate tool for handling data including non-nearby distance indicators. We find that Gamma Ray Bursts, probing higher redshifts than Supernovae, have constraining power and do require (and statistically allow) a cosmographic expansion at higher order than Supernovae alone. Exploiting the set of data from Union and GRBs catalogues, we show (for the first time in a purely cosmographic approach parametrized by deceleration $q_0$, jerk $j_0$, snap $s_0$) a definitively negative deceleration parameter $q_0$ up to the 3$\sigma$ confidence level. We present also forecasts for realistic data sets that are likely to be obtained in the next few years.Comment: 16 pages, 6 figures, 3 tables. Improved version matching the published one, additional comments and reference