Aims. We test the isotropy of the expansion of the Universe by estimating the hemispherical anisotropy of supernova type Ia (SN Ia) Hubble diagrams at low redshifts (z < 0.2). Methods. We compare the best fit Hubble diagrams in pairs of hemispheres and search for the maximal asymmetric orientation. For an isotropic Universe, we expect only a small asymmetry due to noise and the presence of nearby structures. This test does not depend on the assumed content of the Universe, the assumed model of gravity, or the spatial curvature of the Universe. The expectation for possible fluctuations due to large scale structure is evaluated for the Λ cold dark matter (ΛCDM) model and is compared to the supernova data from the Constitution set for four different light curve fitters, thus allowing a study of the systematic effects. Results. The expected order of magnitude of the hemispherical asymmetry of the Hubble expansion agrees with the observed one. The direction of the Hubble asymmetry is established at 95% confidence level (C.L.) using both, the MLCS2k2 and the SALT II light curve fitter. The highest expansion rate is found towards ( , b) ≈ (−35 • , −19 • ), which agrees with directions reported by other studies. Its amplitude is not in contradiction to expectations from the ΛCDM model. The measured Hubble anisotropy is ΔH/H ∼ 0.026. With 95% C.L. the expansion asymmetry is ΔH/H < 0.038.
We develop a practical methodology to remove modes from a galaxy survey power spectrum that are associated with systematic errors. We apply this to the BOSS CMASS sample, to see if it removes the excess power previously observed beyond the best-fit ΛCDM model on very large scales. We consider several possible sources of data contamination, and check whether they affect the number of targets that can be observed and the power spectrum measurements. We describe a general framework for how such knowledge can be transformed into template fields. Mode subtraction can then be used to remove these systematic contaminants at least as well as applying corrective weighting to the observed galaxies, but benefits from giving an unbiased power. Even after applying templates for all known systematics, we find a large-scale power excess, but this is reduced compared with that observed using the weights provided by the BOSS team. This excess is at much larger scales than the BAO scale and does not affect the main results of BOSS. However, it will be important for the measurement of a scale-dependent bias due to primordial non-Gaussianity. The excess is beyond that allowed by any simple model of non-Gaussianity matching Planck data, and is not matched in other surveys. We show that this power excess can further be reduced but is still present using "phenomenological" templates, designed to consider further potentially unknown sources of systematic contamination. As all discrepant angular modes can be removed using "phenomenological" templates, the potentially remaining contaminant acts radially.
We consider the shape of the posterior distribution to be used when fitting cosmological models to power spectra measured from galaxy surveys. At very large scales, Gaussian posterior distributions in the power do not approximate the posterior distribution P R we expect for a Gaussian density field δ k , even if we vary the covariance matrix according to the model to be tested. We compare alternative posterior distributions with P R , both mode-by-mode and in terms of expected measurements of primordial non-Gaussianity parameterised by f NL . Marginalising over a Gaussian posterior distribution P f with fixed covariance matrix yields a posterior mean value of f NL which, for a data set with the characteristics of Euclid, will be underestimated by △f NL = 0.4, while for the data release 9 (DR9) of the Sloan Digital Sky Survey (SDSS)-III Baryon Oscillation Spectroscopic Survey (BOSS) it will be underestimated by △f NL = 19.1. Adopting a different form of the posterior function means that we do not necessarily require a different covariance matrix for each model to be tested: this dependence is absorbed into the functional form of the posterior. Thus, the computational burden of analysis is significantly reduced.
We assess and develop techniques to remove contaminants when calculating the 3D galaxy power spectrum. We separate the process into three separate stages: (i) removing the contaminant signal, (ii) estimating the uncontaminated cosmological power spectrum, (iii) debiasing the resulting estimates. For (i), we show that removing the best-fit contaminant ( mode subtraction), and setting the contaminated components of the covariance to be infinite (mode deprojection) are mathematically equivalent. For (ii), performing a Quadratic Maximum Likelihood (QML) estimate after mode deprojection gives an optimal unbiased solution, although it requires the manipulation of large N 2 mode matrices (N mode being the total number of modes), which is unfeasible for recent 3D galaxy surveys. Measuring a binned average of the modes for (ii) as proposed by Feldman, Kaiser & Peacock (1994, FKP) is faster and simpler, but is sub-optimal and gives rise to a biased solution. We present a method to debias the resulting FKP measurements that does not require any large matrix calculations. We argue that the suboptimality of the FKP estimator compared with the QML estimator, caused by contaminants is less severe than that commonly ignored due to the survey window.
We present a short (and necessarily incomplete) review of the evidence for the accelerated expansion of the Universe. The most direct probe of acceleration relies on the detailed study of supernovae (SN) of type Ia. Assuming that these are standardizable candles and that they fairly sample a homogeneous and isotropic Universe, the evidence for acceleration can be tested in a model-and calibration-independent way. Various light-curve fitting procedures have been proposed and tested. While several fitters give consistent results for the so-called Constitution set, they lead to inconsistent results for the recently released SDSS SN. Adopting the SALT fitter and relying on the Union set, cosmic acceleration is detected by a purely kinematic test at 7σ when spatial flatness is assumed and at 4σ without assumption on the spatial geometry. A weak point of the described method is the local set of SN (at z < 0.2), as these SN are essential to anchor the Hubble diagram. These SN are drawn from a volume much smaller than the Hubble volume and could be affected by local structure. Without the assumption of homogeneity, there is no evidence for acceleration, as the effects of acceleration are degenerate with the effects of inhomogeneities. Unless we sit in the centre of the Universe, such inhomogeneities can be constrained by SN observations by means of tests of the isotropy of the Hubble flow.
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