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Boudewijn F. Roukema

Publications and source records attributed to Boudewijn F. Roukema.

At least 55 records · Page 3Linked to original sources
arXiv2010

On the suspected timing-offset-induced calibration error in the Wilkinson microwave anisotropy probe time-ordered data

In the time-ordered data (TOD) files of the WMAP CMB observations, there is an undocumented timing offset of -25.6 ms between the spacecraft attitude and radio flux density timestamps. If the offset induced an error during calibration of the raw TOD, then estimates of the WMAP CMB quadrupole might be substantially in error. A timing error during calibration would not only induce an artificial quadrupole-like signal in the mean sky map, it would also add variance per pixel. This variance would be present in the calibrated TOD. Low-resolution map-making as a function of timing offset should show a minimum variance for the correct timing offset. Three years of the calibrated, filtered WMAP 3-year TOD are compiled into sky maps at HEALPix resolution N_side=8, individually for each of the K, Ka, Q, V and W band differencing assemblies (DA's), as a function of timing offset. The median per map of the temperature fluctuation variance per pixel is calculated and minimised against timing offset. Minima are clearly present. The timing offsets that minimise the median variance are -38 \pm 8 ms (K, Ka), -27 \pm 3 ms (Q), -43 \pm 8 ms (V), and -47 \pm 194 ms (W), i.e. an average of -30 \pm 3 ms, where the WMAP collaboration's preferred offset is 0 \pm 1.7 ms. A non-parametric bootstrap analysis rejects the latter at a significance of 99.999%. The hypothesis of a -25.6 ms offset, suggested by Liu, Xiong & Li from the TOD file timing offset, is consistent with these minima. It is difficult to avoid the conclusion that the WMAP calibrated TOD and inferred maps are wrongly calibrated. CMB quadrupole estimates (3/pi)C_2 based on the incorrectly calibrated TOD are overestimated by roughly 64 \pm 6% (KQ85 mask) to 94 \pm 10% (KQ75 mask). Ideally, the WMAP map-making pipelines should be redone starting from the uncalibrated TOD and using the -25.6 ms timing offset correction.

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arXiv2010

A measure on the set of compact Friedmann-Lemaitre-Robertson-Walker models

Compact, flat Friedmann-Lemaitre-Robertson-Walker (FLRW) models have recently regained interest as a good fit to the observed cosmic microwave background temperature fluctuations. However, it is generally thought that a globally, exactly-flat FLRW model is theoretically improbable. Here, in order to obtain a probability space on the set F of compact, comoving, 3-spatial sections of FLRW models, a physically motivated hypothesis is proposed, using the density parameter Omega as a derived rather than fundamental parameter. We assume that the processes that select the 3-manifold also select a global mass-energy and a Hubble parameter. The inferred range in Omega consists of a single real value for any 3-manifold. Thus, the obvious measure over F is the discrete measure. Hence, if the global mass-energy and Hubble parameter are a function of 3-manifold choice among compact FLRW models, then probability spaces parametrised by Omega do not, in general, give a zero probability of a flat model. Alternatively, parametrisation by the injectivity radius r_inj ("size") suggests the Lebesgue measure. In this case, the probability space over the injectivity radius implies that flat models occur almost surely (a.s.), in the sense of probability theory, and non-flat models a.s. do not occur.

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arXiv2010

Galactic Plane image sharpness as a check on cosmic microwave background mapmaking

The largest uncollapsed inhomogeneity in the observable Universe is statistically represented in the quadrupole signal of the cosmic microwave background (CMB) sky maps as observed by the Wilkinson Microwave Anisotropy Probe (WMAP). The constant temporal offset of -25.6 ms between the timestamps of the spacecraft attitude and observational data records in the time-ordered data (TOD) of the WMAP observations was suspected to imply that previously derived all-sky CMB maps are erroneous, and that the quadrupole is in large part an artefact. The optimal focussing of bright objects in the Galactic Plane plays a key role in showing that no error occurred at the step of mapmaking from the calibrated TOD. Instead, the error had an effect when the uncalibrated TOD were calibrated. Estimates of the high-latitude quadrupole based on the wrongly calibrated WMAP maps are overestimated by about 15-60%.

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arXiv2010

On the suspected timing error in WMAP map-making

A large fraction of the previously estimated WMAP CMB quadrupole signal would be an artefact of incorrect Doppler dipole subtraction if the hypothesis of a small timing interpolation error were correct. Observations of bright foreground objects constitute part of the time-ordered-data (TOD). Scans of an object in different directions should be shifted by the would-be timing error, causing a blurring effect. Three half-years of the calibrated, filtered WMAP TOD are compiled individually for the four W band differencing assemblies (DA's), with no masking of bright objects, giving 12 maps for each timing offset. Percentiles of the temperature-fluctuation distribution in each map at HEALPix resolution N_side=2048 are used to determine the dependence of all-sky image sharpness on the timing offset. In the W band, the 99.999% percentile, i.e. the temperature fluctuation in the approx 503-rd brightest pixel, is the least noisy percentile. Using this statistic, the hypothesis that a -25.6 ms offset relative to the timing adopted by the WMAP collaboration gives a focus at least as sharp as the uncorrected timing is rejected at 4.6σsignificance. The Q and V band maps also reject the -25.6 ms offset hypothesis at high statistical significance. The requirement that the correct choice of timing offset must maximise image sharpness implies that the hypothesis of a timing error in the WMAP collaboration's compilation of the WMAP calibrated, filtered TOD is rejected at high statistical significance in each of the Q, V and W wavebands. However, the hypothesis that a timing error was applied during calibration of the raw TOD, leading to a dipole-induced difference signal, is not excluded by this method.

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arXiv2010

Which FLRW comoving 3-manifold is preferred observationally and theoretically?

The lack of structure greater than 10 Gpc/h in Wilkinson Microwave Anisotropy Probe (WMAP) observations of the cosmic microwave background (CMB) favours compact Friedmann-Lemaitre-Robertson-Walker (FLRW) models of the Universe. The present best candidates based on observations are the Poincare dodecahedral space S^3/I^* and the 3-torus T^3. The residual gravity effect favours the Poincare space, while a measure space argument where the density parameter is a derived parameter favours flat spaces almost surely.

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arXiv2009

There was movement that was stationary, for the four-velocity had passed around

Is the Doppler interpretation of galaxy redshifts in a Friedmann-Lemaitre-Robertson-Walker (FLRW) model valid in the context of the approach to comoving spatial sections pioneered by de Sitter, Friedmann, Lemaitre and Robertson, i.e. according to which the 3-manifold of comoving space is characterised by both its curvature and topology? Holonomy transformations for flat, spherical and hyperbolic FLRW spatial sections are proposed. By quotienting a simply-connected FLRW spatial section by an appropriate group of holonomy transformations, the Doppler interpretation in a non-expanding Minkowski space-time, obtained via four-velocity parallel transport along a photon path, is found to imply that an inertial observer is receding from herself at a speed greater than zero, implying contradictory world-lines. The contradiction in the multiply-connected case occurs for arbitrary redshifts in the flat and spherical cases, and for certain large redshifts in the hyperbolic case. The link between the Doppler interpretation of redshifts and cosmic topology can be understood physically as the link between parallel transport along a photon path and the fact that the comoving spatial geodesic corresponding to a photon's path can be a closed loop in an FLRW model of any curvature. Closed comoving spatial loops are fundamental to cosmic topology.

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arXiv2009

Dark energy as a spatial continuity condition

Observational evidence of dark energy that makes the Universe nearly flat at the present epoch is very strong. We study the link between spatial continuity and dark energy. We assume that comoving space is a compact 3-manifold of constant curvature, described by a homogeneous Friedman-Lemaitre-Robertson-Walker metric. We assume that spatial continuity cannot be violated, i.e. that the global topology of the comoving section of the Universe cannot change during post-quantum epochs. We find that if the Universe was flat and compact during early epochs, then the presently low values of the radiation and matter densities imply that dark energy was created as a spatial continuity effect. Moreover, if the Universe is compact, then Omega_tot=1 is dynamically stable, where Omega_tot is the total density parameter in units of the critical density. Dark energy was observationally detected as a geometrical phenomenon. It is difficult to imagine a simpler explanation for dark energy than spatial continuity, finiteness and homogeneity.

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arXiv2009

A residual acceleration effect due to an inhomogeneity

The perturbed Friedmann-Lemaitre-Robertson-Walker models allow many different possibilities for the 3-manifold of the comoving spatial section of the Universe. It used to be thought that global properties of the spatial section, including the topology of the space, have no feedback effect on dynamics. However, an elementary, weak-limit calculation shows that in the presence of a density perturbation, a gravitational feedback effect that is algebraically similar to dark energy does exist. Moreover, the effect differs between different 3-spaces. Among the well-proportioned spaces, the effect disappears down to third order in several cases, and down to fifth order for the Poincare dodecahedral space S^3/I^*. The Poincare space, that which also is preferred in many observational analyses, is better-balanced than the other spaces.

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arXiv2009

Some spaces are more equal than others

It has generally been thought that in perturbed Friedmann-Lemaitre-Robertson-Walker models of the Universe, global topology should not have any feedback effects on dynamics. However, a weak-field limit heuristical argument, assuming a finite particle horizon for the transmission of gravitational signals, shows that a residual acceleration effect can occur. The nature of this effect differs algebraically between different constant curvature 3-manifolds. This potentially provides a selection mechanism for the 3-manifold of comoving space.

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arXiv2009

The residual gravity acceleration effect in the Poincare dodecahedral space

In a flat space, the global topology of comoving space can induce a weak acceleration effect similar to dark energy. Does a similar effect occur in the case of the Poincare dodecahedral space S^3/I^*? Does the effect distinguish the Poincare space from other well-proportioned spaces? The residual acceleration effect in the Poincare space is studied here using a massive particle and a nearby test particle of negligible mass, in S^3 embedded in R^4. The weak limit gravitational attraction on a test particle at distance r is set \propto [r_C \sin(r/r_C)]^{-2}, where r_C = curvature radius, in order to satisfy Stokes' theorem. A finite particle horizon large enough to include the adjacent topological images of the massive particle is assumed. The regular, flat, 3-torus T^3 is re-examined, and two other well-proportioned spaces, S^3/T^* and S^3/O^*, are also studied. The residual gravity effect occurs in all four cases. In a perfectly regular 3-torus of side length L_a, and in S^3/T^* and S^3/O^*, the highest order term in the residual acceleration is the third order term in the Taylor expansion of r/L_a (3-torus), or r/r_C, respectively. However, the Poincare dodecahedral space is unique among the four spaces. The third order cancels, leaving the fifth order term \sim \pm 300 (r/r_C)^5 as the most significant. Not only are three of the four perfectly regular well-proportioned spaces better balanced than most other multiply connected spaces in terms of the residual acceleration effect by a factor of about a million (setting r/L_a = r/r_C \sim 10^{-3}), but the fourth of these spaces is about 10^4 times better balanced than the other three. This is the Poincare dodecahedral space. Is this unique dynamical property of the Poincare space a clue towards a theory of cosmic topology?

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arXiv2009

Does gravity prefer the Poincare dodecahedral space?

The missing fluctuations problem in cosmic microwave background observations is naturally explained by well-proportioned small universe models. Among the well-proportioned models, the Poincare dodecahedral space is empirically favoured. Does gravity favour this space? The residual gravity effect is the residual acceleration induced by weak limit gravity from multiple topological images of a massive object on a nearby negligible mass test object. At the present epoch, the residual gravity effect is about a million times weaker in three of the well-proportioned spaces than in ill-proportioned spaces. However, in the Poincare space, the effect is 10,000 times weaker still, i.e. the Poincare space is about 10^{10} times "better balanced" than ill-proportioned spaces. Both observations and weak limit dynamics select the Poincare space to be special.

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arXiv2008

Poincare dodecahedral space parameter estimates

We aim to improve the surface of last scattering (SLS) optimal cross-correlation method in order to refine estimates of the Poincaré dodecahedral space (PDS) cosmological parameters. We analytically derive the formulae required to exclude points on the sky that cannot be members of close SLS-SLS cross-pairs. These enable more efficient pair selection without sacrificing uniformity of the underlying selection process. In certain cases this decreases the calculation time and increases the number of pairs per separation bin. (i) We recalculate Monte Carlo Markov Chains (MCMC) on the five-year WMAP data; and (ii) we seek PDS solutions in a small number of Gaussian random fluctuation (GRF) simulations. For 5 < alpha/deg < 60, a calculation speed-up of 3-10 is obtained. (i) The best estimates of the PDS parameters for the five-year WMAP data are similar to those for the three-year data. (ii) Comparison of the optimal solutions found by the MCMC chains in the observational map to those found in the simulated maps yields a slightly stronger rejection of the simply connected model using $α$ than using the twist angle $ϕ$. The best estimate of $α$ implies that_given a large scale auto-correlation as weak as that observed,_ the PDS-like cross-correlation signal in the WMAP data is expected with a probability of less than about 10%. The expected distribution of $ϕ$ from the GRF simulations is approximately Gaussian around zero, it is not uniform on $[-π,π]$. We infer that for an infinite, flat, cosmic concordance model with Gaussian random fluctuations, the chance of finding_both_ (a) a large scale auto-correlation as weak as that observed,_and_ (b) a PDS-like signal similar to that observed is less than about 0.015% to 1.25%.

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arXiv2008

Homotopy symmetry in the multiply connected twin paradox of special relativity

In a multiply connected space, the two twins of the special relativity twin paradox move with constant relative speed and meet a second time without acceleration. The twins' situations appear to be symmetrical despite the need for one to be younger due to time dilation. Here, the suggestion that the apparent symmetry is broken by homotopy classes of the twins' worldlines is reexamined using space-time diagrams. It is found that each twin finds her own spatial path to have zero winding index and that of the other twin to have unity winding index, i.e. the twins' worldlines' relative homotopy classes are symmetrical. Although the twins' apparent symmetry is in fact broken by the need for the non-favoured twin to non-simultaneously identify spatial domain boundaries, the non-favoured twin {\em cannot} detect her disfavoured state if she only measures the homotopy classes of the two twins' projected worldlines, contrary to what was previously suggested. We also note that for the non-favoured twin, the fundamental domain can be chosen by identifying time boundaries (with a spatial offset) instead of space boundaries (with a temporal offset).

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arXiv2008

The optimal phase of the generalised Poincare dodecahedral space hypothesis implied by the spatial cross-correlation function of the WMAP sky maps

Several studies have proposed that the shape of the Universe may be a Poincare dodecahedral space (PDS) rather than an infinite, simply connected, flat space. Both models assume a close to flat FLRW metric of about 30% matter density. We study two predictions of the PDS model. (i) For the correct model, the spatial two-point cross-correlation function, $\ximc$, of temperature fluctuations in the covering space, where the two points in any pair are on different copies of the surface of last scattering (SLS), should be of a similar order of magnitude to the auto-correlation function, $\xisc$, on a single copy of the SLS. (ii) The optimal orientation and identified circle radius for a "generalised" PDS model of arbitrary twist $ϕ$, found by maximising $\ximc$ relative to $\xisc$ in the WMAP maps, should yield $ϕ\in \{\pm 36°\}$. We optimise the cross-correlation at scales < 4.0 h^-1 Gpc using a Markov chain Monte Carlo (MCMC) method over orientation, circle size and $ϕ$. Both predictions were satisfied: (i) an optimal "generalised" PDS solution was found, with a strong cross-correlation between points which would be distant and only weakly correlated according to the simply connected hypothesis, for two different foreground-reduced versions of the WMAP 3-year all-sky map, both with and without the kp2 Galaxy mask: the face centres are $(l,b)_{i=1,6}\approx (184d, 62d), (305d, 44d), (46d, 49d), (117d, 20d), (176d, -4d), (240d, 13d) to within ~2d, and their antipodes; (ii) this solution has twist ϕ= (+39 \pm 2.5)d, in agreement with the PDS model. The chance of this occurring in the simply connected model, assuming a uniform distribution $ϕ\in [0,2π]$, is about 6-9%.

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arXiv2006

A weak acceleration effect due to residual gravity in a multiply connected universe

Could cosmic topology imply dark energy? We use a weak field (Newtonian) approximation of gravity and consider the gravitational effect from distant, multiple copies of a large, collapsed (virialised) object today (i.e. a massive galaxy cluster), taking into account the finite propagation speed of gravity, in a flat, multiply connected universe, and assume that due to a prior epoch of fast expansion (e.g. inflation), the gravitational effect of the distant copies is felt locally, from beyond the naively calculated horizon. We find that for a universe with a $T^1xR^2$ spatial section, the residual Newtonian gravitational force (to first order) provides an anisotropic effect that repels test particles from the cluster in the compact direction, in a way algebraically similar to that of dark energy. For a typical test object at comoving distance $χ$ from the nearest dense nodes of the cosmic web of density perturbations, the pressure-to-density ratio $w$ of the equation of state in an FLRW universe, is w \sim - (χ/L)^3, where $L$ is the size of the fundamental domain, i.e. of the universe. Clearly, |w|<<1. For a T^3 spatial section of exactly equal fundamental lengths, the effect cancels to zero. For a T^3 spatial section of unequal fundamental lengths, the acceleration effect is anisotropic in the sense that it will *tend to equalise the three fundamental lengths*. Provided that at least a modest amount of inflation occurred in the early Universe, and given some other conditions, multiple connectedness does generate an effect similar to that of dark energy, but the amplitude of the effect at the present epoch is too small to explain the observed dark energy density and its anisotropy makes it an unrealistic candidate for the observed dark energy.

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arXiv2006

WMAP First Year Sky Map: Hints of Poincare Dodecahedral Topology

Several analyses of the cosmic microwave background map made by the satellite WMAP suggest that the global shape of a spatial section of the Universe is that of a Poincare dodecahedral space. A summary of some of these analyses and a description of independent tests which should be able to either increase confidence in the hypothesis or else refute it to extremely high significance will be presented.

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arXiv2005

A constraint on any topological lensing hypothesis in the spherical case: it must be a root of the identity

Three-dimensional catalogues of objects at cosmological distances can potentially yield candidate topologically lensed pairs of sets of objects, which would be a sign of the global topology of the Universe. In the spherical case, a necessary condition, which does not exist for either null or negative curvature, can be used to falsify such hypotheses, without needing to loop through a list of individual spherical 3-manifolds. This condition is that the isometry between the two sets of objects must be a root of the identity isometry in the covering space S^3. This enables numerical falsification of topological lensing hypotheses without needing to assume any particular spherical 3-manifold. By embedding S^3 in R^4, this condition can be expressed as the requirement that M^n = I for an integer n, where M is the matrix representation of the hypothesised lensing isometry and I is the identity. Moreover, this test becomes even simpler with the requirement that the two rotation angles, theta, phi, corresponding to the given isometry, satisfy 2π/ θ, 2π/ ϕ\in Z. The calculation of this test involves finding the two eigenplanes of the matrix M. A GNU General Public Licence numerical package, called eigenplane, is made available at http://cosmo.torun.pl/GPLdownload/eigen/ for finding the rotation angles and eigenplanes of an arbitrary isometry M of S^3.

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