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This brochure summarises the Planck mission and gives a glimpse of its main achievements.

Planck set out to map the very faint anisotropies in the Cosmic Microwave Background to an angular resolution and sensitivity that would exhaust all the cosmological information that can be extracted from them. In addition Planck has mapped the much fainter polarised fraction of these same anisotropies. The resulting maps of the sky contain traces from the very earliest times, revealing the recipe that embodies our most precise understanding of the structure, composition, and evolution of the Universe that we inhabit.

Contents:

  • Foreword
  • Making sense of the Universe
  • The early Universe
  • The Planck mission
  • An almost perfect Universe
  • Planck's view of the Cosmic Microwave Background
  • The big and the small
  • Structure formation and gravitational lensing
  • The first stars
  • Mapping foreground emission from the Milky Way
  • A lasting legacy

 

Published: 11 November 2020
The European Space Agency’s Planck satellite, which was dedicated to studying the early Universe and its subsequent evolution, was launched on 14 May 2009. It scanned the microwave and submillimetre sky continuously between 12 August 2009 and 23 October 2013, producing deep, high-resolution, all-sky maps in nine frequency bands from 30 to 857 GHz. This paper presents the cosmological legacy of Planck, which currently provides our strongest constraints on the parameters of the standard cosmological model and some of the tightest limits available on deviations from that model. The 6-parameter ΛCDM model continues to provide an excellent fit to the cosmic microwave background data at high and low redshift, describing the cosmological information in over a billion map pixels with just six parameters. With 18 peaks in the temperature and polarization angular power spectra constrained well, Planck measures five of the six parameters to better than 1 % (simultaneously), with the best-determined parameter (θ) now known to 0.03 %. We describe the multi-component sky as seen by Planck, the success of the ΛCDM model, and the connection to lower-redshift probes of structure formation. We also give a comprehensive summary of the major changes introduced in this 2018 release. The Planck data, alone and in combination with other probes, provide stringent constraints on our models of the early Universe and the large-scale structure within which all astrophysical objects form and evolve. We discuss some lessons learned from the Planck mission, and highlight areas ripe for further experimental advances.
Published: 18 July 2018
A&A, Forthcoming article

This paper describes the identification, modelling, and removal of previously unexplained systematic effects in the polarization data of the Planck High Frequency Instrument (HFI) on large angular scales, including new mapmaking and calibration procedures, new and more complete end-to-end simulations, and a set of robust internal consistency checks on the resulting maps. These maps, at 100, 143, 217, and 353 GHz, are early versions of those that will be released in final form later in 2016. The improvements allow us to determine the cosmic reionization optical depth τ using, for the first time, the low-multipole EE data from HFI, reducing significantly the central value and uncertainty, and hence the upper limit. Two different likelihood procedures are used to constrain τ from two estimators of the CMB E- and B-mode angular power spectra at 100 and 143 GHz, after debiasing the spectra from a small remaining systematic contamination. These all give fully consistent results. A further consistency test is performed using cross-correlations derived from the Low Frequency Instrument maps of the Planck 2015 data release and the new HFI data. For this purpose, end-to-end analyses of systematic effects from the two instruments are used to demonstrate the near independence of their dominant systematic error residuals. The tightest result comes from the HFI-based τ posterior distribution using the maximum likelihood power spectrum estimator from EE data only, giving a value 0.055 ± 0.009. In a companion paper these results are discussed in the context of the best-fit Planck ΛCDM cosmological model and recent models of reionization.

Published: 01 September 2016
A&A, Forthcoming article.

We investigate constraints on cosmic reionization extracted from the Planck cosmic microwave background (CMB) data. We combine the Planck CMB anisotropy data in temperature with the low-multipole polarization data to fit ΛCDM models with various parameterizations of the reionization history. We obtain a Thomson optical depth τ = 0.058 ± 0.012 for the commonly adopted instantaneous reionization model. This confirms, with data solely from CMB anisotropies, the low value suggested by combining Planck 2015 results with other data sets, and also reduces the uncertainties. We reconstruct the history of the ionization fraction using either a symmetric or an asymmetric model for the transition between the neutral and ionized phases. To determine better constraints on the duration of the reionization process, we also make use of measurements of the amplitude of the kinetic Sunyaev-Zeldovich (kSZ) effect using additional information from the high-resolution Atacama Cosmology Telescope and South Pole Telescope experiments. The average redshift at which reionization occurs is found to lie between z = 7.8 and 8.8, depending on the model of reionization adopted. Using kSZ constraints and a redshift-symmetric reionization model, we find an upper limit to the width of the reionization period of ∆z < 2.8. In all cases, we find that the Universe is ionized at less than the 10 % level at redshifts above z ~ 10. This suggests that an early onset of reionization is strongly disfavoured by the Planck data. We show that this result also reduces the tension between CMB-based analyses and constraints from other astrophysical sources.

Published: 01 September 2016
The nearby Chamaeleon clouds have been observed in γ rays by the Fermi Large Area Telescope (LAT) and in thermal dust emission by Planck and IRAS. Cosmic rays and large dust grains, if smoothly mixed with gas, can jointly serve with the HI and 12CO radio data to (i) map the hydrogen column densities, NH, in the different gas phases, in particular at the dark neutral medium (DNM) transition between the HI-bright and CO-bright media; (ii) constrain the CO-to-H2conversion factor, XCO; and (iii) probe the dust properties per gas nucleon in each phase and map their spatial variations across the clouds. We have separated clouds at local, intermediate, and Galactic velocities in HI and 12CO line emission to model in parallel the γ-ray intensity recorded between 0.4 and 100 GeV; the dust optical depth at 353 GHz, τ353; the thermal radiance of the large grains; and an estimate of the dust extinction, AVQ, empirically corrected for the starlight intensity. The dust and γ-ray models have been coupled to account for the DNM gas. The consistent γ-ray emissivity spectra recorded in the different phases confirm that the GeV–TeV cosmic rays probed by the LAT uniformly permeate all gas phases up to the 12CO cores. The dust and cosmic rays both reveal large amounts of DNM gas, with comparable spatial distributions and twice as much mass as in the CO-bright clouds. We give constraints on the HI-DNM-CO transitions for five separate clouds. CO-dark H2dominates the molecular columns up to AV ≃ 0.9 and its mass often exceeds the one-third of the molecular mass expected by theory. The corrected AVQ extinction largely provides the best fit to the total gas traced by the γ rays.
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Published: 01 October 2015
We present the results of approximately three years of observations of Planck Sunyaev-Zeldovich (SZ) sources with the Russian-Turkish 1.5 m telescope (RTT150), as a part of the optical follow-up programme undertaken by the Planck collaboration. During this time period approximately 20% of all dark and grey clear time available at the telescope was devoted to observations of Planck objects. Some observations of distant clusters were also done at the 6 m Bolshoi Telescope Alt-azimutalnyi (BTA) of the Special Astrophysical Observatory of the Russian Academy of Sciences. In total, deep, direct images of more than one hundred fields were obtained in multiple filters. We identified 47 previously unknown galaxy clusters, 41 of which are included in the Planck catalogue of SZ sources. The redshifts of 65 Planck clusters were measured spectroscopically and 14 more were measured photometrically. We discuss the details of cluster optical identifications and redshift measurements. We also present new spectroscopic redshifts for 39 Planck clusters that were not included in the Planck SZ source catalogue and are published here for the first time.
Published: 01 October 2015
The Andromeda galaxy (M 31) is one of a few galaxies that has sufficient angular size on the sky to be resolved by the Planck satellite. Planck has detected M 31 in all of its frequency bands, and has mapped out the dust emission with the High Frequency Instrument, clearly resolving multiple spiralarms and sub-features. We examine the morphology of this long-wavelength dust emission as seen by Planck, including a study of its outermost spiral arms, and investigate the dust heating mechanism across M 31. We find that dust dominating the longer wavelength emission (≳0.3 mm) is heated by the diffuse stellar population (as traced by 3.6 μm emission), with the dust dominating the shorter wavelength emission heated by a mix of the old stellar population and star-forming regions (as traced by 24 μm emission). We also fit spectral energy distributions for individual 5′ pixels and quantify the dust properties across the galaxy, taking into account these different heating mechanisms, finding that there is a linear decrease in temperature with galactocentric distance for dust heated by the old stellar population, as would be expected, with temperatures ranging from around 22 K in the nucleus to 14 K outside of the 10 kpc ring. Finally, we measure the integrated spectrum of the whole galaxy, which we find to be well-fitted with a global dust temperature of (18.2 ± 1.0) K with a spectral index of 1.62 ± 0.11 (assuming a single modified blackbody), and a significant amount of free-free emission at intermediate frequencies of 20–60 GHz, which corresponds to a star formation rate of around 0.12 M yr-1. We find a 2.3σ detection of the presence of spinning dust emission, with a 30 GHz amplitude of 0.7 ± 0.3 Jy, which is in line with expectations from our Galaxy.
Published: 01 October 2015
We update the all-sky Planck catalogue of 1227 clusters and cluster candidates (PSZ1) published in March 2013, derived from detections of the Sunyaev–Zeldovich (SZ) effect using the first 15.5 months of Planck satellite observations. As an addendum, we deliver an updated version of the PSZ1 catalogue, reporting the further confirmation of 86 Planck-discovered clusters. In total, the PSZ1 now contains 947 confirmed clusters, of which 214 were confirmed as newly discovered clusters through follow-up observations undertaken by the Planck Collaboration. The updated PSZ1 contains redshifts for 913 systems, of which 736 (~ 80.6%) are spectroscopic, and associated mass estimates derived from the Yz mass proxy. We also provide a new SZ quality flag for the remaining 280 candidates. This flag was derived from a novel artificial neural-network classification of the SZ signal. Based on this assessment, the purity of the updated PSZ1 catalogue is estimated to be 94%. In this release, we provide the full updated catalogue and an additional readme file with further information on the Planck SZ detections.
Published: 26 August 2015
Planck data when combined with ancillary data provide a unique opportunity to separate the diffuse emission components of the inner Galaxy. The purpose of the paper is to elucidate the morphology of the various emission components in the strong star-formation region lying inside the solar radius and to clarify the relationship between the various components. The region of the Galactic plane covered is l = 300° → 0° → 60° where star-formation is highest and the emission is strong enough to make meaningful component separation. The latitude widths in this longitude range lie between 1° and 2°, which correspond to FWHM z-widths of 100−200 pc at a typical distance of 6 kpc. The four emission components studied here are synchrotron, free-free, anomalous microwave emission (AME), and thermal (vibrational) dust emission. These components are identified by constructing spectral energy distributions (SEDs) at positions along the Galactic plane using the wide frequency coverage of Planck (28.4−857 GHz) in combination with low-frequency radio data at 0.408−2.3 GHz plus WMAP data at 23−94 GHz, along with far-infrared (FIR) data from COBE-DIRBE and IRAS. The free-free component is determined from radio recombination line (RRL) data. AME is found to be comparable in brightness to the free-free emission on the Galactic plane in the frequency range 20−40 GHz with a width in latitude similar to that of the thermal dust; it comprises 45 ± 1% of the total 28.4 GHz emission in the longitude range l = 300° → 0° → 60°. The free-free component is the narrowest, reflecting the fact that it is produced by current star-formation as traced by the narrow distribution of OB stars. It is the dominant emission on the plane between 60 and 100 GHz. RRLs from this ionized gas are used to assess its distance, leading to a free-free z-width of FWHM ≈ 100 pc.
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Published: 21 July 2015
Planck has mapped the intensity and polarization of the sky at microwave frequencies with unprecedented sensitivity. We use these data to characterize the frequency dependence of dust emission. We make use of the Planck 353 GHz I, Q, and U Stokes maps as dust templates, and cross-correlate them with the Planck and WMAP data at 12 frequencies from 23 to 353 GHz, over circular patches with 10° radius. The cross-correlation analysis is performed for both intensity and polarization data in a consistent manner. The results are corrected for the chance correlation between the templates and the anisotropies of the cosmic microwave background. We use a mask that focuses our analysis on the diffuse interstellar medium at intermediate Galactic latitudes. We determine the spectral indices of dust emission in intensity and polarization between 100 and 353 GHz, for each sky patch. Both indices are found to be remarkably constant over the sky. The mean values, 1.59 ± 0.02 for polarization and 1.51 ± 0.01 for intensity, for a mean dust temperature of 19.6 K, are close, but significantly different (3.6σ). We determine the mean spectral energy distribution (SED) of the microwave emission, correlated with the 353 GHz dust templates, by averaging the results of the correlation over all sky patches. We find that the mean SED increases for decreasing frequencies at ν< 60 GHz for both intensity and polarization. The rise of the polarization SED towards low frequencies may be accounted for by a synchrotron component correlated with dust, with no need for any polarization of the anomalous microwave emission. We use a spectral model to separate the synchrotron and dust polarization and to characterize the spectral dependence of the dust polarization fraction. The polarization fraction (p) of the dust emission decreases by (21 ± 6)% from 353 to 70 GHz. We discuss this result within the context of existing dust models.
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Published: 14 April 2015
The Planck survey provides unprecedented full-sky coverage of the submillimetre polarized emission from Galactic dust. In addition to the information on the direction of the Galactic magnetic field, this also brings new constraints on the properties of dust. The dust grains that emit the radiation seen by Planck in the submillimetre also extinguish and polarize starlight in the visible. Comparison of the polarization of the emission and of the interstellar polarization on selected lines of sight probed by stars provides unique new diagnostics of the emission and light scattering properties of dust, and therefore of the important dust model parameters, composition, size, and shape. Using ancillary catalogues of interstellar polarization and extinction of starlight, we obtain the degree of polarization, pV, and the optical depth in the V band to the star, τV. Toward these stars we measure the submillimetre polarized intensity, PS, and total intensity, IS, in the Planck 353 GHz channel. We compare the column density measure in the visible, E(B − V), with that inferred from the Planck product map of the submillimetre dust optical depth and compare the polarization direction (position angle) in the visible with that in the submillimetre. For those lines of sight through the diffuse interstellar medium with comparable values of the estimated column density and polarization directions close to orthogonal, we correlate properties in the submillimetre and visible to find two ratios, RS/V = (PS/IS) / (pVV) and RP/p = PS/pV, the latter focusing directly on the polarization properties of the aligned grain population alone.
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Published: 14 April 2015
Polarized emission observed by Planck HFI at 353 GHz towards a sample of nearby fields is presented, focusing on the statistics of polarization fractions p and angles ψ. The polarization fractions and column densities in these nearby fields are representative of the range of values obtained over the whole sky. We find that: (i) the largest polarization fractions are reached in the most diffuse fields; (ii) the maximum polarization fraction pmax decreases with column density NH in the more opaque fields with NH>1021 cm-2; and (iii) the polarization fraction along a given line of sight is correlated with the local spatial coherence of the polarization angle. These observations are compared to polarized emission maps computed in simulations of anisotropic magnetohydrodynamical turbulence in which we assume a uniform intrinsic polarization fraction of the dust grains. We find that an estimate of this parameter may be recovered from the maximum polarization fraction pmax in diffuse regions where the magnetic field is ordered on large scales and perpendicular to the line of sight. This emphasizes the impact of anisotropies of the magnetic field on the emerging polarization signal. The decrease of the maximum polarization fraction with column density in nearby molecular clouds is well reproduced in the simulations, indicating that it is essentially due to the turbulent structure of the magnetic field: an accumulation of variously polarized structures along the line of sight leads to such an anti-correlation. In the simulations, polarization fractions are also found to anti-correlate with the angle dispersion function .
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Published: 14 April 2015
We have used the Planck all-sky submillimetre and millimetre maps to search for rare sources distinguished by extreme brightness, a few hundred millijanskies, and their potential for being situated at high redshift. These "cold" Planck sources, selected using the High Frequency Instrument (HFI) directly from the maps and from the Planck Catalogue of Compact Sources (PCCS), all satisfy the criterion of having their rest-frame far-infrared peak redshifted to the frequency range 353–857 GHz. This colour-selection favours galaxies in the redshift range z = 2–4, which we consider as cold peaks in the cosmic infrared background. With a 4.5' beam at the four highest frequencies, our sample is expected to include overdensities of galaxies in groups or clusters, lensed galaxies, and chance line-of-sight projections. We perform a dedicated Herschel-SPIRE follow-up of 234 such Planck targets, finding a significant excess of red 350 and 500 μm sources, in comparison to reference SPIRE fields. About 94% of the SPIRE sources in the Planck fields are consistent with being overdensities of galaxies peaking at 350 μm, with 3% peaking at 500 μm, and none peaking at 250 μm. About 3% are candidate lensed systems, all 12 of which have secure spectroscopic confirmations, placing them at redshifts z > 2.2. Only four targets are Galactic cirrus, yielding a success rate in our search strategy for identifying extragalactic sources within the Planck beam of better than 98%. The galaxy verdensities are detected with high significance, half of the sample showing statistical significance above 10σ. The SPIRE photometric redshifts of galaxies in overdensities suggest a peak at z ≃ 2, assuming a single common dust temperature for the sources of Td = 35 K.
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Published: 01 April 2015
Late stages of stellar evolution are characterized by copious mass-loss events whose signature is the formation of circumstellar envelopes (CSE). Planck multi-frequency measurements have provided relevant information on a sample of Galactic planetary nebulae (PNe) in the important and relatively unexplored observational band between 30 and 857 GHz. Planck enables the assembly of comprehensive PNe spectral energy distributions (SEDs) from radio to far-IR frequencies. Modelling the derived SEDs provides us with information on physical properties of CSEs and the mass content of both main components: ionized gas, traced by the free-free emission at cm–mm waves; and thermal dust, traced by the millimetre and far-IR emission. In particular, the amount of ionized gas and dust has been derived here. Such quantities have also been estimated for the very young PN CRL 618, where the strong variability observed in its radio and millimetre emission has previously prevented constructing its SED. A morphological study of the Helix Nebula was also performed. Planck maps reveal, for the first time, the spatial distribution of the dust inside the envelope, allowing us to identify different components, the most interesting of which is a very extended component (up to 1 pc) that may be related to a region where the slow expanding envelope is interacting with the surrounding interstellar medium.
Published: 08 December 2014
The Planck design and scanning strategy provide many levels of redundancy that can be exploited to provide tests of internal consistency. One of the most important is the comparison of the 70 GHz (amplifier) and 100 GHz (bolometer) channels. Based on different instrument technologies, with feeds located differently in the focal plane, analysed independently by different teams using different software, and near the minimum of diffuse foreground emission, these channels are in effect two different experiments. The 143 GHz channel has the lowest noise level on Planck, and is near the minimum of unresolved foreground emission. In this paper, we analyse the level of consistency achieved in the 2013 Planck data. We concentrate on comparisons between the 70, 100, and 143 GHz channel maps and power spectra, particularly over the angular scales of the first and second acoustic peaks, on maps masked for diffuse Galactic emission and for strong unresolved sources. Difference maps covering angular scales from 8° to 15′ are consistent with noise, and show no evidence of cosmic microwave background structure. Including small but important corrections for unresolved-source residuals, we demonstrate agreement (measured by deviation of the ratio from unity) between 70 and 100 GHz power spectra averaged over 70 ≤ ℓ ≤ 390 at the 0.8% level, and agreement between 143 and 100 GHz power spectra of 0.4% over the same ℓ range. These values are within and consistent with the overall uncertainties in calibration given in the Planck 2013 results. We also present results based on the 2013 likelihood analysis showing consistency at the 0.35% between the 100, 143, and 217 GHz power spectra.
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Published: 29 October 2014
We present new measurements of cosmic infrared background (CIB) anisotropies using Planck. Combining HFI data with IRAS, the angular auto- and cross-frequency power spectrum is measured from 143 to 3000  GHz, and the auto-bispectrum from 217 to 545  GHz. The total areas used to compute the CIB power spectrum and bispectrum are about 2240 and 4400 deg2, respectively. After careful removal of the contaminants (cosmic microwave background anisotropies, Galactic dust, and Sunyaev-Zeldovich emission), and a complete study of systematics, the CIB power spectrum is measured with unprecedented signal to noise ratio from angular multipoles ℓ ~ 150 to 2500. The bispectrum due to the clustering of dusty, star-forming galaxies is measured from ℓ ~ 130 to 1100, with a total signal to noise ratio of around 6, 19, and 29 at 217, 353, and 545  GHz, respectively. Two approaches are developed for modelling CIB power spectrum anisotropies. The first approach takes advantage of the unique measurements by Planck at large angular scales, and models only the linear part of the power spectrum, with a mean bias of dark matter haloes hosting dusty galaxies at a given redshift weighted by their contribution to the emissivities. The second approach is based on a model that associates star-forming galaxies with dark matter haloes and their subhaloes, using a parametrized relation between the dust-processed infrared luminosity and (sub-)halo mass. The two approaches simultaneously fit all auto- and cross-power spectra very well. We find that the star formation history is well constrained up to redshifts around 2, and agrees with recent estimates of the obscured star-formation density using Spitzer and Herschel. However, at higher redshift, the accuracy of the star formation history measurement is strongly degraded by the uncertainty in the spectral energy distribution of CIB galaxies.
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Published: 29 October 2014
We describe the all-sky Planck catalogue of clusters and cluster candidates derived from Sunyaev-Zeldovich (SZ) effect detections using the first 15.5 months of Planck satellite observations. The catalogue contains 1227 entries, making it over six times the size of the Planck Early SZ (ESZ) sample and the largest SZ-selected catalogue to date. It contains 861 confirmed clusters, of which 178 have been confirmed as clusters, mostly through follow-up observations, and a further 683 are previously-known clusters. The remaining 366 have the status of cluster candidates, and we divide them into three classes according to the quality of evidence that they are likely to be true clusters. The Planck SZ catalogue is the deepest all-sky cluster catalogue, with redshifts up to about one, and spans the broadest cluster mass range from (0.1 to 1.6) × 1015 M. Confirmation of cluster candidates through comparison with existing surveys or cluster catalogues is extensively described, as is the statistical characterization of the catalogue in terms of completeness and statistical reliability. The outputs of the validation process are provided as additional information. This gives, in particular, an ensemble of 813 cluster redshifts, and for all these Planck clusters we also include a mass estimated from a newly-proposed SZ-mass proxy. A refined measure of the SZ Compton parameter for the clusters with X-ray counter-parts is provided, as is an X-ray flux for all the Planck clusters not previously detected in X-ray surveys.
Published: 29 October 2014
The Planck Catalogue of Compact Sources (PCCS) is the catalogue of sources detected in the first 15 months of Planck operations, the "nominal" mission. It consists of nine single-frequency catalogues of compact sources, both Galactic and extragalactic, detected over the entire sky. The PCCS covers the frequency range 30–857 GHz with higher sensitivity (it is 90% complete at 180 mJy in the best channel) and better angular resolution (from 32.88′ to 4.33′) than previous all-sky surveys in this frequency band. By construction its reliability is >80% and more than 65% of the sources have been detected in at least two contiguous Planck channels. In this paper we present the construction and validation of the PCCS, its contents and its statistical characterization.
Published: 29 October 2014
Our velocity relative to the rest frame of the cosmic microwave background (CMB) generates a dipole temperature anisotropy on the sky which has been well measured for more than 30 years, and has an accepted amplitude of v/c = 1.23 × 10-3, or v = 369. In addition to this signal generated by Doppler boosting of the CMB monopole, our motion also modulates and aberrates the CMB temperature fluctuations (as well as every other source of radiation at cosmological distances). This is an order 10-3 effect applied to fluctuations which are already one part in roughly 105, so it is quite small. Nevertheless, it becomes detectable with the all-sky coverage, high angular resolution, and low noise levels of the Planck satellite. Here we report a first measurement of this velocity signature using the aberration and modulation effects on the CMB temperature anisotropies, finding a component in the known dipole direction, (l,b) = (264°,48°), of 384 km s-1 ± 78 km s-1 (stat.) ± 115 km s-1 (syst.). This is a significant confirmation of the expected velocity.
Published: 29 October 2014
The new cosmic microwave background (CMB) temperature maps from Planck provide the highest-quality full-sky view of the surface of last scattering available to date. This allows us to detect possible departures from the standard model of a globally homogeneous and isotropic cosmology on the largest scales. We search for correlations induced by a possible non-trivial topology with a fundamental domain intersecting, or nearly intersecting, the last scattering surface (at comoving distance χrec), both via a direct search for matched circular patterns at the intersections and by an optimal likelihood search for specific topologies. For the latter we consider flat spaces with cubic toroidal (T3), equal-sided chimney (T2) and slab (T1) topologies, three multi-connected spaces of constant positive curvature (dodecahedral, truncated cube and octahedral) and two compact negative-curvature spaces. These searches yield no detection of the compact topology with the scale below the diameter of the last scattering surface. For most compact topologies studied the likelihood maximized over the orientation of the space relative to the observed map shows some preference for multi-connected models just larger than the diameter of the last scattering surface. Since this effect is also present in simulated realizations of isotropic maps, we interpret it as the inevitable alignment of mild anisotropic correlations with chance features in a single sky realization; such a feature can also be present, in milder form, when the likelihood is marginalized over orientations.
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Published: 29 October 2014
7-Oct-2024 11:10 UT

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