arXiv subjects

V. Lindholm

Publications and source records attributed to V. Lindholm.

At least 145 records · Page 8Linked to original sources

arXiv2024

Euclid preparation. Optical emission-line predictions of intermediate-z galaxy populations in GAEA for the Euclid Deep and Wide Surveys

In anticipation of the Euclid Wide and Deep Surveys, we present optical emission-line predictions at intermediate redshifts from 0.4 to 2.5. Our approach combines a mock light cone from the GAEA semi-analytic model to self-consistently model nebular emission from HII regions, narrow-line regions of active galactic nuclei (AGN), and evolved stellar populations. Our analysis focuses on seven optical emission lines: H$α$, H$β$, [SII]$λλ6717, 6731$, [NII]$λ6584$, [OI]$λ6300$, [OIII]$λ5007$, and [OII]$λλ3727, 3729$. We find that Euclid will predominantly observe massive, star-forming, and metal-rich line-emitters. Interstellar dust, modelled using a Calzetti law with mass-dependent scaling, may decrease observable percentages by a further 20-30% with respect to our underlying emission-line populations from GAEA. We predict Euclid to observe around 30-70% of H$α$-, [NII]-, [SII]-, and [OIII]-emitting galaxies at redshift below 1 and under 10% at higher redshift. Observability of H$β$-, [OII]-, and [OI]- emission is limited to below 5%. For the Euclid-observable sample, we find that BPT diagrams can effectively distinguish between different galaxy types up to around redshift 1.8, attributed to the bias toward metal-rich systems. Moreover, we show that the relationships of H$α$ and [OIII]+H$β$ to the star-formation rate, and the [OIII]-AGN luminosity relation, exhibit minimal changes with increasing redshift. Based on line ratios [NII]/H$α$, [NII]/[OII], and [NII]/[SII], we further propose novel z-invariant tracers for the black hole accretion rate-to-star formation rate ratio. Lastly, we find that commonly used metallicity estimators display gradual shifts in normalisations with increasing redshift, while maintaining the overall shape of local calibrations. This is in tentative agreement with recent JWST data.

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arXiv2024

Euclid Preparation XXXIII. Characterization of convolutional neural networks for the identification of galaxy-galaxy strong lensing events

Forthcoming imaging surveys will potentially increase the number of known galaxy-scale strong lenses by several orders of magnitude. For this to happen, images of tens of millions of galaxies will have to be inspected to identify potential candidates. In this context, deep learning techniques are particularly suitable for the finding patterns in large data sets, and convolutional neural networks (CNNs) in particular can efficiently process large volumes of images. We assess and compare the performance of three network architectures in the classification of strong lensing systems on the basis of their morphological characteristics. We train and test our models on different subsamples of a data set of forty thousand mock images, having characteristics similar to those expected in the wide survey planned with the ESA mission \Euclid, gradually including larger fractions of faint lenses. We also evaluate the importance of adding information about the colour difference between the lens and source galaxies by repeating the same training on single-band and multi-band images. Our models find samples of clear lenses with $\gtrsim 90\%$ precision and completeness, without significant differences in the performance of the three architectures. Nevertheless, when including lenses with fainter arcs in the training set, the three models' performance deteriorates with accuracy values of $\sim 0.87$ to $\sim 0.75$ depending on the model. Our analysis confirms the potential of the application of CNNs to the identification of galaxy-scale strong lenses. We suggest that specific training with separate classes of lenses might be needed for detecting the faint lenses since the addition of the colour information does not yield a significant improvement in the current analysis, with the accuracy ranging from $\sim 0.89$ to $\sim 0.78$ for the different models.

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arXiv2024

Euclid Preparation. XXXVII. Galaxy colour selections with Euclid and ground photometry for cluster weak-lensing analyses

We derived galaxy colour selections from Euclid and ground-based photometry, aiming to accurately define background galaxy samples in cluster weak-lensing analyses. Given any set of photometric bands, we developed a method for the calibration of optimal galaxy colour selections that maximises the selection completeness, given a threshold on purity. We calibrated galaxy selections using simulated ground-based $griz$ and Euclid $Y_{\rm E}J_{\rm E}H_{\rm E}$ photometry. Both selections produce a purity higher than 97%. The $griz$ selection completeness ranges from 30% to 84% in the lens redshift range $z_{\rm l}\in[0.2,0.8]$. With the full $grizY_{\rm E}J_{\rm E}H_{\rm E}$ selection, the completeness improves by up to $25$ percentage points, and the $z_{\rm l}$ range extends up to $z_{\rm l}=1.5$. The calibrated colour selections are stable to changes in the sample limiting magnitudes and redshift, and the selection based on $griz$ bands provides excellent results on real external datasets. The $griz$ selection is also purer at high redshift and more complete at low redshift compared to colour selections found in the literature. We find excellent agreement in terms of purity and completeness between the analysis of an independent, simulated Euclid galaxy catalogue and our calibration sample, except for galaxies at high redshifts, for which we obtain up to 50 percent points higher completeness. The combination of colour and photo-$z$ selections applied to simulated Euclid data yields up to 95% completeness, while the purity decreases down to 92% at high $z_{\rm l}$. We show that the calibrated colour selections provide robust results even when observations from a single band are missing from the ground-based data. Finally, we show that colour selections do not disrupt the shear calibration for stage III surveys.

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arXiv2024

Euclid: Improving the efficiency of weak lensing shear bias calibration. Pixel noise cancellation and the response method on trial

To obtain an accurate cosmological inference from upcoming weak lensing surveys such as the one conducted by Euclid, the shear measurement requires calibration using galaxy image simulations. We study the efficiency of different noise cancellation methods that aim at reducing the simulation volume required to reach a given precision in the shear measurement. Explicitly, we compared fit methods with different noise cancellations and a method based on responses. We used GalSim to simulate galaxies both on a grid and at random positions in larger scenes. Placing the galaxies at random positions requires their detection, which we performed with SExtractor. On the grid, we neglected the detection step and, therefore, the potential detection bias arising from it. The shear of the simulated images was measured with the fast moment-based method KSB, for which we note deviations from purely linear shear measurement biases. For the estimation of uncertainties, we used bootstrapping as an empirical method. We find that each method we studied on top of shape noise cancellation can further increase the efficiency of calibration simulations. The improvement depends on the considered shear amplitude range and the type of simulations (grid-based or random positions). The response method on a grid for small shears provides the biggest improvement. In the more realistic case of randomly positioned galaxies, we still find an improvement factor of 70 for small shears using the response method. Alternatively, the runtime can be lowered by a factor of 7 already using pixel noise cancellation on top of shape noise cancellation. Furthermore, we demonstrate that the efficiency of shape noise cancellation can be enhanced in the presence of blending if entire scenes are rotated instead of individual galaxies.

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arXiv2024

Euclid preparation. Spectroscopy of active galactic nuclei with NISP

The statistical distribution and evolution of key properties (e.g. accretion rate, mass, or spin) of active galactic nuclei (AGN), remain an open debate in astrophysics. The ESA Euclid space mission, launched on July 1st 2023, promises a breakthrough in this field. We create detailed mock catalogues of AGN spectra, from the rest-frame near-infrared down to the ultraviolet, including emission lines, to simulate what Euclid will observe for both obscured (type 2) and unobscured (type 1) AGN. We concentrate on the red grisms of the NISP instrument, which will be used for the wide-field survey, opening a new window for spectroscopic AGN studies in the near-infrared. We quantify the efficiency in the redshift determination as well as in retrieving the emission line flux of the H$α$+[NII] complex as Euclid is mainly focused on this emission line as it is expected to be the brightest one in the probed redshift range. Spectroscopic redshifts are measured for 83% of the simulated AGN in the interval where the H$α$+[NII] is visible (0.89 2x10^{-16}$ erg s$^{-1}$ cm$^{-2}$, encompassing the peak of AGN activity at $z\simeq 1-1.5$) within the spectral coverage of the red grism. Outside this redshift range, the measurement efficiency decreases significantly. Overall, a spectroscopic redshift is correctly determined for ~90% of type 2 AGN down to an emission line flux of $3x10^{-16}$ erg s$^{-1}$ cm$^{-2}$, and for type 1 AGN down to $8.5x10^{-16}$ erg s$^{-1}$ cm$^{-2}$. Recovered black hole mass values show a small offset with respect to the input values ~10%, but the agreement is good overall. With such a high spectroscopic coverage at z<2, we will be able to measure AGN demography, scaling relations, and clustering from the epoch of the peak of AGN activity down to the present-day Universe for hundreds of thousand AGN with homogeneous spectroscopic information.

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arXiv2023

Euclid Preparation. TBD. Impact of magnification on spectroscopic galaxy clustering

In this paper we investigate the impact of lensing magnification on the analysis of Euclid's spectroscopic survey, using the multipoles of the 2-point correlation function for galaxy clustering. We determine the impact of lensing magnification on cosmological constraints, and the expected shift in the best-fit parameters if magnification is ignored. We consider two cosmological analyses: i) a full-shape analysis based on the $Λ$CDM model and its extension $w_0w_a$CDM and ii) a model-independent analysis that measures the growth rate of structure in each redshift bin. We adopt two complementary approaches in our forecast: the Fisher matrix formalism and the Markov chain Monte Carlo method. The fiducial values of the local count slope (or magnification bias), which regulates the amplitude of the lensing magnification, have been estimated from the Euclid Flagship simulations. We use linear perturbation theory and model the 2-point correlation function with the public code coffe. For a $Λ$CDM model, we find that the estimation of cosmological parameters is biased at the level of 0.4-0.7 standard deviations, while for a $w_0w_a$CDM dynamical dark energy model, lensing magnification has a somewhat smaller impact, with shifts below 0.5 standard deviations. In a model-independent analysis aiming to measure the growth rate of structure, we find that the estimation of the growth rate is biased by up to $1.2$ standard deviations in the highest redshift bin. As a result, lensing magnification cannot be neglected in the spectroscopic survey, especially if we want to determine the growth factor, one of the most promising ways to test general relativity with Euclid. We also find that, by including lensing magnification with a simple template, this shift can be almost entirely eliminated with minimal computational overhead.

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arXiv2022

Euclid: Fast two-point correlation function covariance through linear construction

We present a method for fast evaluation of the covariance matrix for a two-point galaxy correlation function (2PCF) measured with the Landy-Szalay estimator. The standard way of evaluating the covariance matrix consists in running the estimator on a large number of mock catalogs, and evaluating their sample covariance. With large random catalog sizes (data-to-random objects ratio M>>1) the computational cost of the standard method is dominated by that of counting the data-random and random-random pairs, while the uncertainty of the estimate is dominated by that of data-data pairs. We present a method called Linear Construction (LC), where the covariance is estimated for small random catalogs of size M = 1 and M = 2, and the covariance for arbitrary M is constructed as a linear combination of these. We validate the method with PINOCCHIO simulations in range r = 20-200 Mpc/h, and show that the covariance estimate is unbiased. With M = 50 and with 2 Mpc/h bins, the theoretical speed-up of the method is a factor of 14. We discuss the impact on the precision matrix and parameter estimation, and derive a formula for the covariance of covariance.

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arXiv2021

Euclid preparation: XVI. Exploring the ultra low-surface brightness Universe with Euclid/VIS

While Euclid is an ESA mission specifically designed to investigate the nature of Dark Energy and Dark Matter, the planned unprecedented combination of survey area ($\sim15\,000$ deg$^2$), spatial resolution, low sky-background, and depth also make Euclid an excellent space observatory for the study of the low surface brightness Universe. Scientific exploitation of the extended low surface brightness structures requires dedicated calibration procedures yet to be tested. We investigate the capabilities of Euclid to detect extended low surface brightness structure by identifying and quantifying sky background sources and stray-light contamination. We test the feasibility of generating sky flat-fields to reduce large-scale residual gradients in order to reveal the extended emission of galaxies observed in the Euclid Survey. We simulate a realistic set of Euclid/VIS observations, taking into account both instrumental and astronomical sources of contamination, including cosmic rays, stray-light, zodiacal light, ISM, and the CIB, while simulating the effects of the presence of background sources in the FOV. We demonstrate that a combination of calibration lamps, sky flats and self-calibration would enable recovery of emission at a limiting surface brightness magnitude of $μ=29.5^{+0.08}_{-0.27} $ mag arcsec$^{-2}$ ($3σ$, $10\times10$ arcsec$^2$) in the Wide Survey, reaching regions 2 magnitudes deeper in the Deep Surveys. Euclid/VIS has the potential to be an excellent low surface brightness observatory. Covering the gap between pixel-to-pixel calibration lamp flats and self-calibration observations for large scales, the application of sky flat-fielding will enhance the sensitivity of the VIS detector at scales of larger than 1 degree, up to the size of the FOV, enabling Euclid to detect extended surface brightness structures below $μ=31$ mag arcsec$^{-2}$ and beyond.

astro-ph.IM↗

arXiv2020

Planck 2018 results. IV. Diffuse component separation

We present full-sky maps of the cosmic microwave background (CMB) and polarized synchrotron and thermal dust emission, derived from the third set of Planck frequency maps. These products have significantly lower contamination from instrumental systematic effects than previous versions. The methodologies used to derive these maps follow those described in earlier papers, adopting four methods (Commander, NILC, SEVEM, and SMICA) to extract the CMB component, as well as three methods (Commander, GNILC, and SMICA) to extract astrophysical components. Our revised CMB temperature maps agree with corresponding products in the Planck 2015 delivery, whereas the polarization maps exhibit significantly lower large-scale power, reflecting the improved data processing described in companion papers; however, the noise properties of the resulting data products are complicated, and the best available end-to-end simulations exhibit relative biases with respect to the data at the few percent level. Using these maps, we are for the first time able to fit the spectral index of thermal dust independently over 3 degree regions. We derive a conservative estimate of the mean spectral index of polarized thermal dust emission of beta_d = 1.55 +/- 0.05, where the uncertainty marginalizes both over all known systematic uncertainties and different estimation techniques. For polarized synchrotron emission, we find a mean spectral index of beta_s = -3.1 +/- 0.1, consistent with previously reported measurements. We note that the current data processing does not allow for construction of unbiased single-bolometer maps, and this limits our ability to extract CO emission and correlated components. The foreground results for intensity derived in this paper therefore do not supersede corresponding Planck 2015 products. For polarization the new results supersede the corresponding 2015 products in all respects.

astro-ph.CO↗

arXiv2020

Planck 2018 results. V. CMB power spectra and likelihoods

This paper describes the 2018 Planck CMB likelihoods, following a hybrid approach similar to the 2015 one, with different approximations at low and high multipoles, and implementing several methodological and analysis refinements. With more realistic simulations, and better correction and modelling of systematics, we can now make full use of the High Frequency Instrument polarization data. The low-multipole 100x143 GHz EE cross-spectrum constrains the reionization optical-depth parameter $τ$ to better than 15% (in combination with with the other low- and high-$\ell$ likelihoods). We also update the 2015 baseline low-$\ell$ joint TEB likelihood based on the Low Frequency Instrument data, which provides a weaker $τ$ constraint. At high multipoles, a better model of the temperature-to-polarization leakage and corrections for the effective calibrations of the polarization channels (polarization efficiency or PE) allow us to fully use the polarization spectra, improving the constraints on the $Λ$CDM parameters by 20 to 30% compared to TT-only constraints. Tests on the modelling of the polarization demonstrate good consistency, with some residual modelling uncertainties, the accuracy of the PE modelling being the main limitation. Using our various tests, simulations, and comparison between different high-$\ell$ implementations, we estimate the consistency of the results to be better than the 0.5$σ$ level. Minor curiosities already present before (differences between $\ell$<800 and $\ell$>800 parameters or the preference for more smoothing of the $C_\ell$ peaks) are shown to be driven by the TT power spectrum and are not significantly modified by the inclusion of polarization. Overall, the legacy Planck CMB likelihoods provide a robust tool for constraining the cosmological model and represent a reference for future CMB observations. (Abridged)

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arXiv2020

Planck 2018 results. VII. Isotropy and Statistics of the CMB

Analysis of the Planck 2018 data set indicates that the statistical properties of the cosmic microwave background (CMB) temperature anisotropies are in excellent agreement with previous studies using the 2013 and 2015 data releases. In particular, they are consistent with the Gaussian predictions of the $Λ$CDM cosmological model, yet also confirm the presence of several so-called "anomalies" on large angular scales. The novelty of the current study, however, lies in being a first attempt at a comprehensive analysis of the statistics of the polarization signal over all angular scales, using either maps of the Stokes parameters, $Q$ and $U$, or the $E$-mode signal derived from these using a new methodology (which we describe in an appendix). Although remarkable progress has been made in reducing the systematic effects that contaminated the 2015 polarization maps on large angular scales, it is still the case that residual systematics (and our ability to simulate them) can limit some tests of non-Gaussianity and isotropy. However, a detailed set of null tests applied to the maps indicates that these issues do not dominate the analysis on intermediate and large angular scales (i.e., $\ell \lesssim 400$). In this regime, no unambiguous detections of cosmological non-Gaussianity, or of anomalies corresponding to those seen in temperature, are claimed. Notably, the stacking of CMB polarization signals centred on the positions of temperature hot and cold spots exhibits excellent agreement with the $Λ$CDM cosmological model, and also gives a clear indication of how Planck provides state-of-the-art measurements of CMB temperature and polarization on degree scales.

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arXiv2020

Planck intermediate results. LV. Reliability and thermal properties of high-frequency sources in the Second Planck Catalogue of Compact Sources

We describe an extension of the most recent version of the Planck Catalogue of Compact Sources (PCCS2), produced using a new multi-band Bayesian Extraction and Estimation Package (BeeP). BeeP assumes that the compact sources present in PCCS2 at 857 GHz have a dust-like spectral energy distribution, which leads to emission at both lower and higher frequencies, and adjusts the parameters of the source and its SED to fit the emission observed in Planck's three highest frequency channels at 353, 545, and 857 GHz, as well as the IRIS map at 3000 GHz. In order to reduce confusion regarding diffuse cirrus emission, BeeP's data model includes a description of the background emission surrounding each source, and it adjusts the confidence in the source parameter extraction based on the statistical properties of the spatial distribution of the background emission. BeeP produces the following three new sets of parameters for each source: (a) fits to a modified blackbody (MBB) thermal emission model of the source; (b) SED-independent source flux densities at each frequency considered; and (c) fits to an MBB model of the background in which the source is embedded. BeeP also calculates, for each source, a reliability parameter, which takes into account confusion due to the surrounding cirrus. We define a high-reliability subset (BeeP/base), containing 26 083 sources (54.1 per cent of the total PCCS2 catalogue), the majority of which have no information on reliability in the PCCS2. The results of the BeeP extension of PCCS2, which are made publicly available via the PLA, will enable the study of the thermal properties of well-defined samples of compact Galactic and extra-galactic dusty sources.

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arXiv2020

Planck intermediate results. LVI. Detection of the CMB dipole through modulation of the thermal Sunyaev-Zeldovich effect: Eppur si muove II

The largest temperature anisotropy in the cosmic microwave background (CMB) is the dipole, which has been measured with increasing accuracy for more than three decades, particularly with the Planck satellite. The simplest interpretation of the dipole is that it is due to our motion with respect to the rest frame of the CMB. Since current CMB experiments infer temperature anisotropies from angular intensity variations, the dipole modulates the temperature anisotropies with the same frequency dependence as the thermal Sunyaev-Zeldovich (tSZ) effect. We present the first, and significant, detection of this signal in the tSZ maps and find that it is consistent with direct measurements of the CMB dipole, as expected. The signal contributes power in the tSZ maps, which is modulated in a quadrupolar pattern, and we estimate its contribution to the tSZ bispectrum, noting that it contributes negligible noise to the bispectrum at relevant scales.

astro-ph.CO↗

arXiv2020

Planck intermediate results. LVII. Joint Planck LFI and HFI data processing

We present the NPIPE processing pipeline, which produces calibrated frequency maps in temperature and polarization from data from the Planck Low Frequency Instrument (LFI) and High Frequency Instrument (HFI) using high-performance computers. NPIPE represents a natural evolution of previous Planck analysis efforts, and combines some of the most powerful features of the separate LFI and HFI analysis pipelines. The net effect of the improvements is lower levels of noise and systematics in both frequency and component maps at essentially all angular scales, as well as notably improved internal consistency between the various frequency channels. Based on the NPIPE maps, we present the first estimate of the Solar dipole determined through component separation across all nine Planck frequencies. The amplitude is ($3366.6 \pm 2.7$)$μ$K, consistent with, albeit slightly higher than, earlier estimates. From the large-scale polarization data, we derive an updated estimate of the optical depth of reionization of $τ= 0.051 \pm 0.006$, which appears robust with respect to data and sky cuts. There are 600 complete signal, noise and systematics simulations of the full-frequency and detector-set maps. As a Planck first, these simulations include full time-domain processing of the beam-convolved CMB anisotropies. The release of NPIPE maps and simulations is accompanied with a complete suite of raw and processed time-ordered data and the software, scripts, auxiliary data, and parameter files needed to improve further on the analysis and to run matching simulations.

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arXiv2020

CODEX clusters. The Survey, the Catalog, and Cosmology of the X-ray Luminosity Function

Large area catalogs of galaxy clusters constructed from ROSAT All Sky Survey provide the base for our knowledge on the population of clusters thanks to the long-term multiwavelength efforts on their follow-up. Advent of large area photometric surveys superseding in depth previous all-sky data allows us to revisit the construction of X-ray cluster catalogs, extending the study to lower cluster masses and to higher redshifts and to provide the modelling of the selection function. We perform a wavelet detection of X-ray sources and make extensive simulations of the detection of clusters in the RASS data. We assign an optical richness to each of the 24,788 detected X-ray sources in the 10,382 square degrees of SDSS BOSS area, using redMaPPer version 5.2. We name this survey COnstrain Dark Energy with X-ray (CODEX) clusters. We show that there is no obvious separation of sources on galaxy clusters and AGN, based on distribution of systems on their richness. This is a combination of increasing number of galaxy groups and their selection as identification of an X-ray sources either by chance or due to groups hosting an AGN. To clean the sample, we use a cut on the optical richness at the level corresponding to the 10\% completeness of the survey and include it into the modelling of cluster selection function. We present the X-ray catalog extending to a redshift of 0.6 down to X-ray fluxes of $10^{-13}$ ergs s$^{-1}$ cm$^{-2}$. We provide the modelling of the sample selection and discuss the redshift evolution of the high end of the X-ray luminosity function (XLF). Our results on $z<0.3$ XLF are in agreement with previous studies, while we provide new constraints on the $0.3<z<0.6$ XLF. We find a lack of strong redshift evolution of the XLF, provide exact modeling of the effect of low number statistics and AGN contamination and present the resulting constraints on the flat $Λ$CDM.

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arXiv2020

Beam-deconvolved Planck LFI maps

The Planck Collaboration made its final data release in 2018. In this paper we describe beam-deconvolution map products made from Planck LFI data using the artDeco deconvolution code to symmetrize the effective beam. The deconvolution results are auxiliary data products, available through the Planck Legacy Archive. Analysis of these deconvolved survey difference maps reveals signs of residual signal in the 30-GHz and 44-GHz frequency channels. We produce low-resolution maps and corresponding noise covariance matrices (NCVMs). The NCVMs agree reasonably well with the half-ring noise estimates except for 44 GHz, where we observe an asymmetry between $EE$ and $BB$ noise spectra, possibly a sign of further unresolved systematics.

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arXiv2019

Estimating the galaxy two-point correlation function using a split random catalog

The two-point correlation function of the galaxy distribution is a key cosmological observable that allows us to constrain the dynamical and geometrical state of our Universe. To measure the correlation function we need to know both the galaxy positions and the expected galaxy density field. The expected field is commonly specified using a Monte-Carlo sampling of the volume covered by the survey and, to minimize additional sampling errors, this random catalog has to be much larger than the data catalog. Correlation function estimators compare data-data pair counts to data-random and random-random pair counts, where random-random pairs usually dominate the computational cost. Future redshift surveys will deliver spectroscopic catalogs of tens of millions of galaxies. Given the large number of random objects required to guarantee sub-percent accuracy, it is of paramount importance to improve the efficiency of the algorithm without degrading its precision. We show both analytically and numerically that splitting the random catalog into a number of subcatalogs of the same size as the data catalog when calculating random-random pairs, and excluding pairs across different subcatalogs provides the optimal error at fixed computational cost. For a random catalog fifty times larger than the data catalog, this reduces the computation time by a factor of more than ten without affecting estimator variance or bias.

astro-ph.CO↗

arXiv2019

Planck 2018 results. X. Constraints on inflation

We report on the implications for cosmic inflation of the 2018 Release of the Planck CMB anisotropy measurements. The results are fully consistent with the two previous Planck cosmological releases, but have smaller uncertainties thanks to improvements in the characterization of polarization at low and high multipoles. Planck temperature, polarization, and lensing data determine the spectral index of scalar perturbations to be $n_\mathrm{s}=0.9649\pm 0.0042$ at 68% CL and show no evidence for a scale dependence of $n_\mathrm{s}.$ Spatial flatness is confirmed at a precision of 0.4% at 95% CL with the combination with BAO data. The Planck 95% CL upper limit on the tensor-to-scalar ratio, $r_{0.002}<0.10$, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtain $r_{0.002}<0.056$. In the framework of single-field inflationary models with Einstein gravity, these results imply that: (a) slow-roll models with a concave potential, $V" (ϕ) < 0,$ are increasingly favoured by the data; and (b) two different methods for reconstructing the inflaton potential find no evidence for dynamics beyond slow roll. Non-parametric reconstructions of the primordial power spectrum consistently confirm a pure power law. A complementary analysis also finds no evidence for theoretically motivated parameterized features in the Planck power spectrum, a result further strengthened for certain oscillatory models by a new combined analysis that includes Planck bispectrum data. The new Planck polarization data provide a stringent test of the adiabaticity of the initial conditions. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadrupolar modulation of the primordial fluctuations. However, the polarization data do not confirm physical models for a scale-dependent dipolar modulation.

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