arXiv subjects

Martin J. France

Publications and source records attributed to Martin J. France.

4 recordsLinked to original sources

arXiv2021

The variance of the CMB temperature gradient: a new signature of a multiply connected Universe

In this work we investigate the standard deviation of the Cosmic Microwave Background (CMB) temperature gradient field as a signature for a multiply connected nature of the Universe. CMB simulations of a spatially infinite universe model within the paradigm of the standard cosmological model present non-zero two-point correlations at any angular scale. This is in contradiction with the extreme suppression of correlations at scales above $60^{\circ}$ in the observed CMB maps. Universe models with spatially multiply connected topology contain typically a discrete spectrum of the Laplacian with a specific wave-length cut-off and thus lead to a suppression of the correlations at large angular scales, as observed in the CMB (in general there can be also an additional continuous spectrum). Among the simplest examples are 3-dimensional tori which possess only a discrete spectrum. To date, the universe models with non-trivial topology such as the toroidal space are the only models that possess a two-point correlation function showing a similar behaviour as the one derived from the observed Planck CMB maps. In this work it is shown that the normalized standard deviation of the CMB temperature gradient field does hierarchically detect the change in size of the cubic 3-torus, if the volume of the Universe is smaller than $\simeq 2.5 \cdot 10^3$ Gpc$^3$. It is also shown that the variance of the temperature gradient of the Planck maps is consistent with the median value of simulations within the standard cosmological model. All flat tori are globally homogeneous, but are globally anisotropic. However, this study also presents a test showing a level of homogeneity and isotropy of all the CMB map ensembles for the different torus sizes considered that are nearly at the same weak level of anisotropy revealed by the CMB in the standard cosmological model.

astro-ph.CO↗

arXiv2017

Model-independent analyses of non-Gaussianity in Planck CMB maps using Minkowski Functionals

Despite the wealth of $Planck$ results, there are difficulties in disentangling the primordial non-Gaussianity of the Cosmic Microwave Background (CMB) from the secondary and the foreground non-Gaussianity (NG). For each of these forms of NG the lack of complete data introduces model-dependencies. Aiming at detecting the NGs of the CMB temperature anisotropy $δT$, while paying particular attention to a model-independent quantification of NGs, our analysis is based upon statistical and morphological univariate descriptors, respectively: the probability density function $P(δT)$, related to ${\mathrm v}_{0}$, the first Minkowski Functional (MF), and the two other MFs, ${\mathrm v}_{1}$ and ${\mathrm v}_{2}$. From their analytical Gaussian predictions we build the discrepancy functions $Δ_{k}$ ($k=P,0,1,2$) which are applied to an ensemble of $10^{5}$ CMB realization maps of the $Λ$CDM model and to the $Planck$ CMB maps. In our analysis we use general Hermite expansions of the $Δ_{k}$ up to the $12^{th}$ order, where the coefficients are explicitly given in terms of cumulants. Assuming hierarchical ordering of the cumulants, we obtain the perturbative expansions generalizing the $2^{nd}$ order expansions of Matsubara to arbitrary order in the standard deviation $σ_0$ for $P(δT)$ and ${\mathrm v}_0$, where the perturbative expansion coefficients are explicitly given in terms of complete Bell polynomials. The comparison of the Hermite expansions and the perturbative expansions is performed for the $Λ$CDM map sample and the $Planck$ data. We confirm the weak level of non-Gaussianity ($1$-$2$)$σ$ of the foreground corrected masked $Planck$ $2015$ maps.

astro-ph.CO↗

arXiv2015

Evidence for an environment-dependent shift in the baryon acoustic oscillation peak

The Friedmann-Lemaitre-Robertson-Walker (FLRW) metric assumes comoving spatial rigidity of metrical properties. The curvature term in comoving coordinates is environment-independent and cannot evolve. In the standard model, structure formation is interpreted accordingly: structures average out on the chosen metrical background, which remains rigid in comoving coordinates despite nonlinear structure growth. The latter claim needs to be tested, since it is a hypothesis that is not derived using general relativity. We introduce a test of the comoving rigidity assumption by measuring the two-point auto-correlation function on comoving scales---assuming FLRW comoving spatial rigidity---in order to detect shifts in the baryon acoustic oscillation (BAO) peak location for Large Red Galaxy (LRG) pairs of the Sloan Digital Sky Survey Data Release 7. In tangential directions, subsets of pairs overlapping with superclusters or voids show the BAO peak. The tangential BAO peak location for overlap with Nadathur & Hotchkiss superclusters is $4.3\pm1.6$ Mpc/h less than that for LRG pairs unselected for supercluster overlap, and $6.6\pm2.8$ Mpc/h less than that of the complementary pairs. Liivamagi et al. superclusters give corresponding differences of $3.7\pm2.9$ Mpc/h and $6.3\pm2.6$ Mpc/h, respectively. We have found moderately significant evidence (Kolmogorov--Smirnov tests suggest very significant evidence) that the BAO peak location for supercluster-overlapping pairs is compressed by about 6% compared to that of the complementary sample, providing a potential challenge to FLRW models and a benchmark for predictions from models based on an averaging approach that leaves the spatial metric a priori unspecified.

astro-ph.CO↗

arXiv2013

Deep redshift topological lensing: strategies for the T^3 candidate

The 3-torus (T^3) FLRW model better fits the nearly zero large-scale auto-correlation of the WMAP CMB sky maps than the infinite flat model. The T^3 model's WMAP parameters imply approximately equal-redshift topological lensing at z \sim 6. We investigate observational strategies for rejecting the T^3 solution or providing candidate topologically lensed galaxy pairs. T^3 holonomies are applied to (i) existing z \sim 6 observations and (ii) simulated observations, creating multiply connected catalogues. Corresponding simply connected catalogues are generated. Each catalogue is analysed using a successive filter method and collecting matched quadruples. Quadruple statistics between the multiply and simply connected catalogues are compared. The expected rejection of the hypothesis, or detection of candidate topologically lensed galaxies, is possible at a significance of 5% for a pair of T^3 axis-centred northern and southern surveys if photometric redshift accuracy is σ(\zphot) < 0.01 for a pair of nearly complete 100 deg^2 surveys with a total of > 500 galaxies over 4.3 < z < 6.6, or for a pair of 196 deg^2 surveys with > 400 galaxies and σ(\zphot) < 0.02 over 4<z<7. Dropping the maximum time interval in a pair from Δt =1 Gyr/h to Δt =0.1 Gyr/h yields a requirement of σ(\zphot) < 0.005 or σ(\zphot) < 0.01, respectively. Millions of z \sim 6 galaxies will be observed over fields of these sizes during the coming decades, implying much stronger constraints. The question is not if the hypothesis will be rejected or confirmed, it is when.

astro-ph.CO↗