The World is Either Algorithmic or Mostly Random

I will propose the notion that the universe is digital, not as a claim about what the universe is made of but rather about the way it unfolds. Central to the argument will be the concepts of symmetry breaking and algorithmic probability, which will be used as tools to compare the way patterns are distributed in our world to the way patterns are distributed in a simulated digital one. These concepts will provide a framework for a discussion of the informational nature of reality. I will argue that if the universe were analog, then the world would likely be random, making it largely incomprehensible. The digital model has, however, an inherent beauty in its imposition of an upper limit and in the convergence in computational power to a maximal level of sophistication. Even if deterministic, that it is digital doesn't mean that the world is trivial or predictable, but rather that it is built up from operations that at the lowest scale are very simple but that at a higher scale look complex and even random, though only in appearance.Comment: Third Prize Winning Essay -- 2011 Foundational Questions Institute (FQXi) Contest "Is Reality Digital or Analog?

SNLS3: Constraints on Dark Energy Combining the Supernova Legacy Survey Three Year Data with Other Probes

We present observational constraints on the nature of dark energy using the Supernova Legacy Survey three year sample (SNLS3) of Guy et al. (2010) and Conley et al. (2011). We use the 472 SNe Ia in this sample, accounting for recently discovered correlations between SN Ia luminosity and host galaxy properties, and include the effects of all identified systematic uncertainties directly in the cosmological fits. Combining the SNLS3 data with the full WMAP7 power spectrum, the Sloan Digital Sky Survey luminous red galaxy power spectrum, and a prior on the Hubble constant H0 from SHOES, in a flat universe we find omega_m=0.269+/-0.015 and w=-1.061+0.069-0.068 -- a 6.5% measure of the dark energy equation-of-state parameter w. The statistical and systematic uncertainties are approximately equal, with the systematic uncertainties dominated by the photometric calibration of the SN Ia fluxes -- without these calibration effects, systematics contribute only a ~2% error in w. When relaxing the assumption of flatness, we find omega_m=0.271+/-0.015, omega_k=-0.002+/-0.006, and w=-1.069+0.091-0.092. Parameterizing the time evolution of w as w(a)=w_0+w_a(1-a), gives w_0=-0.905+/-0.196, w_a=-0.984+1.094-1.097 in a flat universe. All of our results are consistent with a flat, w=-1 universe. The size of the SNLS3 sample allows various tests to be performed with the SNe segregated according to their light curve and host galaxy properties. We find that the cosmological constraints derived from these different sub-samples are consistent. There is evidence that the coefficient, beta, relating SN Ia luminosity and color, varies with host parameters at >4sigma significance (in addition to the known SN luminosity--host relation); however this has only a small effect on the cosmological results and is currently a sub-dominant systematic.Comment: Accepted for publication in ApJ. Data available from https://tspace.library.utoronto.ca/snl

Evidence for dust reddening in DLAs identified through CaII H&K absorption

We present a new sample of 31 CaII(H&K) 3935,3970 absorption line systems with 0.84<z_abs<1.3 discovered in the spectra of Sloan Digital Sky Survey (SDSS) Data Release 3 quasars, together with an analysis of their dust content. The presence of Calcium absorption together with measurements of the MgII 2796, FeII 2600 and MgI 2853 lines lead to the conclusion that the majority of our systems are Damped Ly-alpha (DLA) absorbers. The composite spectrum in the rest frame of the absorber shows clear evidence for reddening. Large and Small Magellanic Cloud extinction curves provide satisfactory fits, with a best-fit E(B-V) of 0.06, while the Galactic dust extinction curve provides a poor fit due to the lack of a strong 2175A feature. A trend of increasing dust content with equivalent width of CaII is present. Monte Carlo techniques demonstrate that the detection of reddening is significant at >99.99% confidence. The discovery of significant amounts of dust in a subsample of DLAs has direct implications for studies of the metallicity evolution of the universe and the nature of DLAs in relation to high redshift galaxies. The gas:dust ratio is discussed. Our results suggest that at least ~40% of the CaII absorption systems are excluded from the magnitude-limited SDSS quasar sample as a result of the associated extinction, a fraction similar to the upper limit deduced at higher redshifts from radio-selected surveys.Comment: 5 pages, 2 figures, accepted MNRAS Letter

The distribution of stellar mass in the low-redshift Universe

We use a complete and uniform sample of almost half a million galaxies from the Sloan Digital Sky Survey to characterise the distribution of stellar mass in the low-redshift Universe. Galaxy abundances are well determined over almost four orders of magnitude in stellar mass, and are reasonably but not perfectly fit by a Schechter function with characteristic stellar mass m* = 6.7 x 10^10 M_sun and with faint-end slope \alpha = -1.155. For a standard cosmology and a standard stellar Initial Mass Function, only 3.5% of the baryons in the low-redshift Universe are locked up in stars. The projected autocorrelation function of stellar mass is robustly and precisely determined for r_p < 30 Mpc/h. Over the range 10 kpc/kpc < r_p < 10 Mpc/h it is extremely well represented by a power law. The corresponding three-dimensional autocorrelation function is \xi*(r) = (r/6.1 Mpc/h)^{-1.84}. Relative to the dark matter, the bias of the stellar mass distribution is approximately constant on large scales, but varies by a factor of five for r_p < 1 Mpc/h. This behaviour is approximately but not perfectly reproduced by current models for galaxy formation in the concordance LCDM cosmology. Detailed comparison suggests that a fluctuation amplitude \sigma_8 ~ 0.8 is preferred to the somewhat larger value adopted in the Millennium Simulation models with which we compare our data. This comparison also suggests that observations of stellar mass autocorrelations as a function of redshift might provide a powerful test for the nature of Dark Energy.Comment: 12 pages, 11 figures, accepted for publication in Monthly Notices, two appendices added to explore possible systematic biases due to the stellar mass definition and surface density limit

Observing Long Cosmic Strings Through Gravitational Lensing

We consider the gravitational lensing produced by long cosmic strings formed in a GUT scale phase transition. We derive a formula for the deflection of photons which pass near the strings that reduces to an integral over the light cone projection of the string configuration plus constant terms which are not important for lensing. Our strings are produced by performing numerical simulations of cosmic string networks in flat, Minkowski space ignoring the effects of cosmological expansion. These strings have more small scale structure than those from an expanding universe simulation - fractal dimension 1.3 for Minkowski versus 1.1 for expanding - but share the same qualitative features. Lensing simulations show that for both point-like and extended objects, strings produce patterns unlike more traditional lenses, and, in particluar, the kinks in strings tend to generate demagnified images which reside close to the string. Thus lensing acts as a probe of the small scale structure of a string. Estimates of lensing probablity suggest that for string energy densities consistant with string seeded structure formation, on the order of tens of string lenses should be observed in the Sloan Digital Sky Survey quasar catalog. We propose a search strategy in which string lenses would be identified in the SDSS quasar survey, and the string nature of the lens can be confirmed by the observation of nearby high redshift galaxies which are also be lensed by the string.Comment: 24 pages revtex with 12 postscript firgure