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These lecture notes intend to form a short pedagogical introduction to the use of typical type Ia-Supernovae (hereafter SNIa) as standard candles to determine the energy density of the universe. Problems of principle for taking SNIa as cosmological probes are pointed out, and new attempts at solving them are indicated including the empirical width-luminosity relation and its possible explanations. Finally, the observations of SNIa at high redshift carried out by two major teams are briefly reviewed and their interpretation as evidence for an accelerating universe is also rapidly discussed.
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The proper usage of Type Ia supernovae (SNe Ia) as distance indicators has revolutionized cosmology, and added a new dominant component to the energy density of the Universe, dark energy. Following the discovery and confirmation era, the currently ongoing SNe Ia surveys aim to determine the properties of the dark energy. ESSENCE is a five year ground-based supernova survey aimed at finding and characterizing 200 SNe Ia in the redshift domain z=[0.2-0.8]. The goal of the project is to put constraints on the equation of state parameter, w, of the dark energy with an accuracy of <10%. This paper presents these ongoing efforts in the context of the current developments in observational cosmology.
Supernova cosmology without spectroscopic confirmation is an exciting new frontier which we address here with the Bayesian Estimation Applied to Multiple Species (BEAMS) algorithm and the full three years of data from the Sloan Digital Sky Survey II Supernova Survey (SDSS-II SN). BEAMS is a Bayesian framework for using data from multiple species in statistical inference when one has the probability that each data point belongs to a given species, corresponding in this context to different types of supernovae with their probabilities derived from their multi-band lightcurves. We run the BEAMS algorithm on both Gaussian and more realistic SNANA simulations with of order 10^4 supernovae, testing the algorithm against various pitfalls one might expect in the new and somewhat uncharted territory of photometric supernova cosmology. We compare the performance of BEAMS to that of both mock spectroscopic surveys and photometric samples which have been cut using typical selection criteria. The latter typically are either biased due to contamination or have significantly larger contours in the cosmological parameters due to small data-sets. We then apply BEAMS to the 792 SDSS-II photometric supernovae with host spectroscopic redshifts. In this case, BEAMS reduces the area of the (Omega_m,Omega_Lambda) contours by a factor of three relative to the case where only spectroscopically confirmed data are used (297 supernovae). In the case of flatness, the constraints obtained on the matter density applying BEAMS to the photometric SDSS-II data are Omega_m(BEAMS)=0.194pm0.07. This illustrates the potential power of BEAMS for future large photometric supernova surveys such as LSST.
Even in a universe that is homogeneous on large scales, local density fluctuations can imprint a systematic signature on the cosmological inferences we make from distant sources. One example is the effect of a local under-density on supernova cosmology. Also known as a Hubble-bubble, it has been suggested that a large enough under-density could account for the supernova magnitude- redshift relation without the need for dark energy or acceleration. Although the size and depth of under-density required for such an extreme result is extremely unlikely to be a random fluctuation in an on-average homogeneous universe, even a small under-density can leave residual effects on our cosmological inferences. In this paper we show that there remain systematic shifts in our cosmological parameter measure- ments, even after excluding local supernovae that are likely to be within any small Hubble-bubble. We study theoretically the low-redshift cutoff typically imposed by supernova cosmology analyses, and show that a low-redshift cut of z0 sim 0.02 may be too low based on the observed inhomogeneity in our local universe. Neglecting to impose any low-redshift cutoff can have a significant effect on the cosmological pa- rameters derived from supernova data. A slight local under-density, just 30% under-dense with scale 70h^{-1} Mpc, causes an error in the inferred cosmological constant density {Omega}{Lambda} of sim 4%. Imposing a low-redshift cutoff reduces this systematic error but does not remove it entirely. A residual systematic shift of 0.99% remains in the inferred value {Omega}{Lambda} even when neglecting all data within the currently pre- ferred low-redshift cutoff of 0.02. Given current measurement uncertainties this shift is not negligible, and will need to be accounted for when future measurements yield higher precision.
We present an analysis of peculiar velocities and their effect on supernova cosmology. In particular, we study (a) the corrections due to our own motion, (b) the effects of correlations in peculiar velocities induced by large-scale structure, and (c) uncertainties arising from a possible local under- or over-density. For all of these effects we present a case study of their impact on the cosmology derived by the Sloan Digital Sky Survey-II Supernova Survey (SDSS-II SN Survey). Correcting supernova redshifts for the CMB dipole slightly over-corrects nearby supernovae that share some of our local motion. We show that while neglecting the CMB dipole would cause a shift in the derived equation of state of Delta w ~ 0.04 (at fixed matter density) the additional local-motion correction is currently negligible (Delta w<0.01). We use a covariance-matrix approach to statistically account for correlated peculiar velocities. This down-weights nearby supernovae and effectively acts as a graduated version of the usual sharp low-redshift cut. Neglecting coherent velocities in the current sample causes a systematic shift of ~2% in the preferred value of w and will therefore have to be considered carefully when future surveys aim for percent-level accuracy. Finally, we perform n-body simulations to estimate the likely magnitude of any local density fluctuation (monopole) and estimate the impact as a function of the low-redshift cutoff. We see that for this aspect the low-z cutoff of z=0.02 is well-justified theoretically, but that living in a putative local density fluctuation leaves an indelible imprint on the magnitude-redshift relation.
We study correlated fluctuations of Type~Ia supernova observables due to peculiar velocities of both the observer and the supernova host galaxies, and their impact on cosmological parameter estimation. We demonstrate using the CosmicFlows-3 dataset that at low redshifts the corrections for peculiar velocities in the JLA catalogue have been systematically underestimated. By querying a horizon-size N-body simulation we find that compared to a randomly placed observer, an observer in an environment like our local Universe will see 2-8 times stronger correlations between supernovae in the JLA catalogue. Hence the covariances usually employed assuming a typical observer are unphysical and underestimate the effects of coherent motion of the supernova host galaxies. Contrary to previous studies which asserted that this should have negligible effect on cosmological parameter estimation, we find that when peculiar velocities are treated consistently the JLA data favours significantly smaller values of the dark energy density than in the standard $Lambda$CDM model. A joint fit to simultaneously determine the cosmological parameters and the bulk flow indicates that the latter is around 250 km/s even beyond 200$h^{-1}$ Mpc. The local bulk flow is thus an essential nuisance parameter which must be included in cosmological model fitting when analysing supernova data.
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