arXiv subjects

M. Lattanzi

Publications and source records attributed to M. Lattanzi.

At least 37 records · Page 2Linked to original sources

arXiv2024

Multi-dimensional optimisation of the scanning strategy for the LiteBIRD space mission

Large angular scale surveys in the absence of atmosphere are essential for measuring the primordial $B$-mode power spectrum of the Cosmic Microwave Background (CMB). Since this proposed measurement is about three to four orders of magnitude fainter than the temperature anisotropies of the CMB, in-flight calibration of the instruments and active suppression of systematic effects are crucial. We investigate the effect of changing the parameters of the scanning strategy on the in-flight calibration effectiveness, the suppression of the systematic effects themselves, and the ability to distinguish systematic effects by null-tests. Next-generation missions such as LiteBIRD, modulated by a Half-Wave Plate (HWP), will be able to observe polarisation using a single detector, eliminating the need to combine several detectors to measure polarisation, as done in many previous experiments and hence avoiding the consequent systematic effects. While the HWP is expected to suppress many systematic effects, some of them will remain. We use an analytical approach to comprehensively address the mitigation of these systematic effects and identify the characteristics of scanning strategies that are the most effective for implementing a variety of calibration strategies in the multi-dimensional space of common spacecraft scan parameters. We also present Falcons, a fast spacecraft scanning simulator that we developed to investigate this scanning parameter space.

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arXiv2024

Conversations in the dark: cross-correlating birefringence and LSS to constrain axions

Unveiling the dark sector of the Universe is one of the leading efforts in theoretical physics. Among the many models proposed, axions and axion-like particles stand out due to their solid theoretical foundation, capacity to contribute significantly to both dark matter and dark energy, and potential to address the small-scale crisis of $Λ$CDM. Moreover, these pseudo-scalar fields couple to the electromagnetic sector through a Chern-Simons parity-violating term, leading to a rotation of the plane of linearly polarized waves, namely cosmic birefringence. We explore the impact of the axion-parameters on anisotropic birefringence and study, for the first time, its cross-correlation with the spatial distribution of galaxies, focusing on ultralight axions with masses $10^{-33}\,{\rm eV}\le m_ϕ\le10^{-28}\,{\rm eV}$. Through this novel approach, we investigate the axion-parameter space in the mass $m_ϕ$ and initial misalignment angle $θ_i$, within the framework of early dark energy models, and constrain the axion-photon coupling $g_{ϕγ}$ required to achieve unity in the signal-to-noise ratio of the underlying cross-correlation, computed with the instrument specifications of Euclid and forthcoming CMB-polarization data. Our findings reveal that for masses below $10^{-32}\,{\rm eV}$ and initial misalignment angles greater in absolute value than $π/4$, the signal-to-noise ratio not only exceeds unity but also surpasses that achievable from the auto-correlation of birefringence alone (up to a factor 7), highlighting the informative potential of this new probe. Additionally, given the late-time evolution of these low-mass axions, the signal stems from the epoch of reionization, providing an excellent tool to single out the birefringence generated during this period.

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arXiv2024

LiteBIRD Science Goals and Forecasts. Mapping the Hot Gas in the Universe

We assess the capabilities of the LiteBIRD mission to map the hot gas distribution in the Universe through the thermal Sunyaev-Zeldovich (SZ) effect. Our analysis relies on comprehensive simulations incorporating various sources of Galactic and extragalactic foreground emission, while accounting for specific instrumental characteristics of LiteBIRD, such as detector sensitivities, frequency-dependent beam convolution, inhomogeneous sky scanning, and $1/f$ noise. We implement a tailored component-separation pipeline to map the thermal SZ Compton $y$-parameter over 98% of the sky. Despite lower angular resolution for galaxy cluster science, LiteBIRD provides full-sky coverage and, compared to the Planck satellite, enhanced sensitivity, as well as more frequency bands to enable the construction of an all-sky $y$-map, with reduced foreground contamination at large and intermediate angular scales. By combining LiteBIRD and Planck channels in the component-separation pipeline, we obtain an optimal $y$-map that leverages the advantages of both experiments, with the higher angular resolution of the Planck channels enabling the recovery of compact clusters beyond the LiteBIRD beam limitations, and the numerous sensitive LiteBIRD channels further mitigating foregrounds. The added value of LiteBIRD is highlighted through the examination of maps, power spectra, and one-point statistics of the various sky components. After component separation, the $1/f$ noise from LiteBIRD is effectively mitigated below the thermal SZ signal at all multipoles. Cosmological constraints on $S_8=σ_8\left(Ω_{\rm m}/0.3\right)^{0.5}$ obtained from the LiteBIRD-Planck combined $y$-map power spectrum exhibits a 15% reduction in uncertainty compared to constraints from Planck alone. This improvement can be attributed to the increased portion of uncontaminated sky available in the LiteBIRD-Planck combined $y$-map.

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arXiv2024

Unveiling V Modes: Enhancing CMB Sensitivity to BSM Physics with a Non-Ideal Half-Wave Plate

V-mode polarization of the cosmic microwave background is expected to be vanishingly small in the $Λ$CDM model and, hence, usually ignored. Nonetheless, several astrophysical effects, as well as beyond standard model physics could produce it at a detectable level. A realistic half-wave plate - an optical element commonly used in CMB experiments to modulate the polarized signal - can provide sensitivity to V modes without significantly spoiling that to linear polarization. We assess this sensitivity for some new-generation CMB experiments, such as the LiteBIRD satellite, the ground-based Simons Observatory and a CMB-S4-like experiment. We forecast the efficiency of these experiments to constrain the phenomenology of certain classes of BSM models inducing mixing of linear polarization states and generation of V modes in the CMB. We find that new-generation experiments can improve current limits by 1-to-3 orders of magnitude, depending on the data combination. The inclusion of V-mode information dramatically boosts the sensitivity to these BSM models.

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arXiv2024

The Simons Observatory: impact of bandpass, polarization angle and calibration uncertainties on small-scale power spectrum analysis

We study the effects due to mismatches in passbands, polarization angles, and temperature and polarization calibrations in the context of the upcoming cosmic microwave background experiment Simons Observatory (SO). Using the SO multi-frequency likelihood, we estimate the bias and the degradation of constraining power in cosmological and astrophysical foreground parameters assuming different levels of knowledge of the instrumental effects. We find that incorrect but reasonable assumptions about the values of all the systematics examined here can have significant effects on cosmological analyses, hence requiring marginalization approaches at the likelihood level. When doing so, we find that the most relevant effect is due to bandpass shifts. When marginalizing over them, the posteriors of parameters describing astrophysical microwave foregrounds (such as radio point sources or dust) get degraded, while cosmological parameters constraints are not significantly affected. Marginalization over polarization angles with up to 0.25$^\circ$ uncertainty causes an irrelevant bias $\lesssim 0.05 σ$ in all parameters. Marginalization over calibration factors in polarization broadens the constraints on the effective number of relativistic degrees of freedom $N_\mathrm{eff}$ by a factor 1.2, interpreted here as a proxy parameter for non standard model physics targeted by high-resolution CMB measurements.

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arXiv2024

The LiteBIRD mission to explore cosmic inflation

LiteBIRD, the next-generation cosmic microwave background (CMB) experiment, aims for a launch in Japan's fiscal year 2032, marking a major advancement in the exploration of primordial cosmology and fundamental physics. Orbiting the Sun-Earth Lagrangian point L2, this JAXA-led strategic L-class mission will conduct a comprehensive mapping of the CMB polarization across the entire sky. During its 3-year mission, LiteBIRD will employ three telescopes within 15 unique frequency bands (ranging from 34 through 448 GHz), targeting a sensitivity of 2.2\,$μ$K-arcmin and a resolution of 0.5$^\circ$ at 100\,GHz. Its primary goal is to measure the tensor-to-scalar ratio $r$ with an uncertainty $δr = 0.001$, including systematic errors and margin. If $r \geq 0.01$, LiteBIRD expects to achieve a $>5σ$ detection in the $\ell=$2-10 and $\ell=$11-200 ranges separately, providing crucial insight into the early Universe. We describe LiteBIRD's scientific objectives, the application of systems engineering to mission requirements, the anticipated scientific impact, and the operations and scanning strategies vital to minimizing systematic effects. We will also highlight LiteBIRD's synergies with concurrent CMB projects.

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arXiv2024

Echoes from a long time ago: Chewbacca inflation

The cosmic microwave background (CMB) radiation offers a unique avenue for exploring the early Universe's dynamics and evolution. In this paper, we delve into the fascinating realm of slow-roll inflation, contextualizing the primordial acoustic perturbations as the resonant echoes akin to the iconic sound of Chewbacca from the Star Wars universe. By extrapolating polynomial potentials for these primordial sounds, we illuminate their role in shaping the inflationary landscape. Leveraging this framework, we calculate the scalar spectral index ($n_s$) and tensor-to-scalar ratio ($r$), providing insights into the underlying physics governing the inflationary epoch. Employing a rigorous chi-square ($χ^2$) analysis, we meticulously scrutinize the Planck data combined with that offered by the BICEP/Keck collaboration to identify the Chewbacca sound profile that best aligns with observational constraints. Our findings not only shed light on the intricate interplay between sound and cosmology but also unveil intriguing parallels between the cosmic symphony of the early universe and beloved cultural icons.

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arXiv2024

LiteBIRD Science Goals and Forecasts: Primordial Magnetic Fields

We present detailed forecasts for the constraints on primordial magnetic fields (PMFs) that will be obtained with the LiteBIRD satellite. The constraints are driven by the effects of PMFs on the CMB anisotropies: the gravitational effects of magnetically-induced perturbations; the effects on the thermal and ionization history of the Universe; the Faraday rotation imprint on the CMB polarization; and the non-Gaussianities induced in polarization anisotropies. LiteBIRD represents a sensitive probe for PMFs and by exploiting all the physical effects, it will be able to improve the current limit coming from Planck. In particular, thanks to its accurate $B$-mode polarization measurement, LiteBIRD will improve the constraints on infrared configurations for the gravitational effect, giving $B_{\rm 1\,Mpc}^{n_{\rm B} =-2.9} < 0.8$ nG at 95% C.L., potentially opening the possibility to detect nanogauss fields with high significance. We also observe a significant improvement in the limits when marginalized over the spectral index, $B_{1\,{\rm Mpc}}^{\rm marg}< 2.2$ nG at 95% C.L. From the thermal history effect, which relies mainly on $E$-mode polarization data, we obtain a significant improvement for all PMF configurations, with the marginalized case, $\sqrt{\langle B^2\rangle}^{\rm marg}<0.50$ nG at 95% C.L. Faraday rotation constraints will take advantage of the wide frequency coverage of LiteBIRD and the high sensitivity in $B$ modes, improving the limits by orders of magnitude with respect to current results, $B_{1\,{\rm Mpc}}^{n_{\rm B} =-2.9} < 3.2$ nG at 95% C.L. Finally, non-Gaussianities of the $B$-mode polarization can probe PMFs at the level of 1 nG, again significantly improving the current bounds from Planck. Altogether our forecasts represent a broad collection of complementary probes, providing conservative limits on PMF characteristics that will be achieved with LiteBIRD.

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arXiv2023

LiteBIRD Science Goals and Forecasts: A full-sky measurement of gravitational lensing of the CMB

We explore the capability of measuring lensing signals in $LiteBIRD$ full-sky polarization maps. With a $30$ arcmin beam width and an impressively low polarization noise of $2.16\,μ$K-arcmin, $LiteBIRD$ will be able to measure the full-sky polarization of the cosmic microwave background (CMB) very precisely. This unique sensitivity also enables the reconstruction of a nearly full-sky lensing map using only polarization data, even considering its limited capability to capture small-scale CMB anisotropies. In this paper, we investigate the ability to construct a full-sky lensing measurement in the presence of Galactic foregrounds, finding that several possible biases from Galactic foregrounds should be negligible after component separation by harmonic-space internal linear combination. We find that the signal-to-noise ratio of the lensing is approximately $40$ using only polarization data measured over $90\%$ of the sky. This achievement is comparable to $Planck$'s recent lensing measurement with both temperature and polarization and represents a four-fold improvement over $Planck$'s polarization-only lensing measurement. The $LiteBIRD$ lensing map will complement the $Planck$ lensing map and provide several opportunities for cross-correlation science, especially in the northern hemisphere.

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arXiv2023

LiteBIRD Science Goals and Forecasts: Improving Sensitivity to Inflationary Gravitational Waves with Multitracer Delensing

We estimate the efficiency of mitigating the lensing $B$-mode polarization, the so-called delensing, for the $LiteBIRD$ experiment with multiple external data sets of lensing-mass tracers. The current best bound on the tensor-to-scalar ratio, $r$, is limited by lensing rather than Galactic foregrounds. Delensing will be a critical step to improve sensitivity to $r$ as measurements of $r$ become more and more limited by lensing. In this paper, we extend the analysis of the recent $LiteBIRD$ forecast paper to include multiple mass tracers, i.e., the CMB lensing maps from $LiteBIRD$ and CMB-S4-like experiment, cosmic infrared background, and galaxy number density from $Euclid$- and LSST-like survey. We find that multi-tracer delensing will further improve the constraint on $r$ by about $20\%$. In $LiteBIRD$, the residual Galactic foregrounds also significantly contribute to uncertainties of the $B$-modes, and delensing becomes more important if the residual foregrounds are further reduced by an improved component separation method.

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arXiv2023

Tensor-to-scalar ratio forecasts for extended LiteBIRD frequency configurations

LiteBIRD is a planned JAXA-led CMB B-mode satellite experiment aiming for launch in the late 2020s, with a primary goal of detecting the imprint of primordial inflationary gravitational waves. Its current baseline focal-plane configuration includes 15 frequency bands between 40 and 402 GHz, fulfilling the mission requirements to detect the amplitude of gravitational waves with the total uncertainty on the tensor-to-scalar ratio, $δr$, down to $δr<0.001$. A key aspect of this performance is accurate astrophysical component separation, and the ability to remove polarized thermal dust emission is particularly important. In this paper we note that the CMB frequency spectrum falls off nearly exponentially above 300 GHz relative to the thermal dust SED, and a relatively minor high frequency extension can therefore result in even lower uncertainties and better model reconstructions. Specifically, we compare the baseline design with five extended configurations, while varying the underlying dust modeling, in each of which the HFT (High-Frequency Telescope) frequency range is shifted logarithmically towards higher frequencies, with an upper cutoff ranging between 400 and 600 GHz. In each case, we measure the tensor-to-scalar ratio $r$ uncertainty and bias using both parametric and minimum-variance component-separation algorithms. When the thermal dust sky model includes a spatially varying spectral index and temperature, we find that the statistical uncertainty on $r$ after foreground cleaning may be reduced by as much as 30--50 % by extending the upper limit of the frequency range from 400 to 600 GHz, with most of the improvement already gained at 500 GHz. We also note that a broader frequency range leads to better ability to discriminate between models through higher $χ^2$ sensitivity. (abridged)

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arXiv2023

Probing Cosmic Inflation with the LiteBIRD Cosmic Microwave Background Polarization Survey

LiteBIRD, the Lite (Light) satellite for the study of B-mode polarization and Inflation from cosmic background Radiation Detection, is a space mission for primordial cosmology and fundamental physics. The Japan Aerospace Exploration Agency (JAXA) selected LiteBIRD in May 2019 as a strategic large-class (L-class) mission, with an expected launch in the late 2020s using JAXA's H3 rocket. LiteBIRD is planned to orbit the Sun-Earth Lagrangian point L2, where it will map the cosmic microwave background (CMB) polarization over the entire sky for three years, with three telescopes in 15 frequency bands between 34 and 448 GHz, to achieve an unprecedented total sensitivity of 2.2$μ$K-arcmin, with a typical angular resolution of 0.5$^\circ$ at 100 GHz. The primary scientific objective of LiteBIRD is to search for the signal from cosmic inflation, either making a discovery or ruling out well-motivated inflationary models. The measurements of LiteBIRD will also provide us with insight into the quantum nature of gravity and other new physics beyond the standard models of particle physics and cosmology. We provide an overview of the LiteBIRD project, including scientific objectives, mission and system requirements, operation concept, spacecraft and payload module design, expected scientific outcomes, potential design extensions and synergies with other projects.

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arXiv2022

Do you smell something decaying? Updated linear constraints on decaying dark matter scenarios

The stability of particles in the cosmic soup is an important property that can affect the cosmic evolution. In this work, we update the constraints on the decaying cold dark matter scenario, when the decay products are effectively massless. We assume, as a base case, that all of dark matter is unstable and it can decay on cosmological time scales. We then extend the analysis to include the scenario where only a fraction of dark matter is unstable, while the remaining part is composed of the standard, stable, dark matter. We consider observations of cosmological probes at linear scales, i.e., Planck 2018 cosmic microwave background temperature, polarization, and lensing measurements, along with geometrical information from baryon acoustic oscillation (BAO) measurements from SDSS DR7, BOSS DR12, eBOSS DR16 and 6dFGS, to derive conservative constraints on the dark matter decay rate. We consider these dataset separately, to asses the relative constraining power of each dataset, as well as together to asses the joint constraints. We find the most stringent upper limit on the decay rate of decaying cold dark matter particles to be $\Gammadm < 0.129 \times 10^{-18}\,\mathrm{s}^{-1}$ (or, equivalently, the dark matter lifetime $\taudm > 246$ Gyr) at 95\% C.L. for the combination of Planck primary anisotropies, lensing and BAO. We further explore one-parameter extensions of our baseline DCDM model. Namely, we vary the sum of neutrino masses, the curvature density parameter, and the tensor-to-scalar ratio along with the DCDM parameters. When varying the tensor-to-scalar ratio we also add data from the BICEP/Keck experiment.

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arXiv2021

$Euclid$ preparation: XV. Forecasting cosmological constraints for the $Euclid$ and CMB joint analysis

The combination and cross-correlation of the upcoming $Euclid$ data with cosmic microwave background (CMB) measurements is a source of great expectation since it will provide the largest lever arm of epochs, ranging from recombination to structure formation across the entire past light cone. In this work, we present forecasts for the joint analysis of $Euclid$ and CMB data on the cosmological parameters of the standard cosmological model and some of its extensions. This work expands and complements the recently published forecasts based on $Euclid$-specific probes, namely galaxy clustering, weak lensing, and their cross-correlation. With some assumptions on the specifications of current and future CMB experiments, the predicted constraints are obtained from both a standard Fisher formalism and a posterior-fitting approach based on actual CMB data. Compared to a $Euclid$-only analysis, the addition of CMB data leads to a substantial impact on constraints for all cosmological parameters of the standard $Λ$-cold-dark-matter model, with improvements reaching up to a factor of ten. For the parameters of extended models, which include a redshift-dependent dark energy equation of state, non-zero curvature, and a phenomenological modification of gravity, improvements can be of the order of two to three, reaching higher than ten in some cases. The results highlight the crucial importance for cosmological constraints of the combination and cross-correlation of $Euclid$ probes with CMB data.

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arXiv2021

Planck 2018 results. VI. Cosmological parameters

We present cosmological parameter results from the final full-mission Planck measurements of the CMB anisotropies. We find good consistency with the standard spatially-flat 6-parameter $Λ$CDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted "base $Λ$CDM" in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density $Ω_c h^2 = 0.120\pm 0.001$, baryon density $Ω_b h^2 = 0.0224\pm 0.0001$, scalar spectral index $n_s = 0.965\pm 0.004$, and optical depth $τ= 0.054\pm 0.007$ (in this abstract we quote $68\,\%$ confidence regions on measured parameters and $95\,\%$ on upper limits). The angular acoustic scale is measured to $0.03\,\%$ precision, with $100θ_*=1.0411\pm 0.0003$. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-$Λ$CDM cosmology, the inferred late-Universe parameters are: Hubble constant $H_0 = (67.4\pm 0.5)$km/s/Mpc; matter density parameter $Ω_m = 0.315\pm 0.007$; and matter fluctuation amplitude $σ_8 = 0.811\pm 0.006$. We find no compelling evidence for extensions to the base-$Λ$CDM model. Combining with BAO we constrain the effective extra relativistic degrees of freedom to be $N_{\rm eff} = 2.99\pm 0.17$, and the neutrino mass is tightly constrained to $\sum m_ν< 0.12$eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base -$Λ$CDM at over $2\,σ$, which pulls some parameters that affect the lensing amplitude away from the base-$Λ$CDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. (Abridged)

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arXiv2021

The large scale polarization explorer (LSPE) for CMB measurements: performance forecast

[Abridged] The measurement of the polarization of the Cosmic Microwave Background radiation is one of the current frontiers in cosmology. In particular, the detection of the primordial B-modes, could reveal the presence of gravitational waves in the early Universe. The detection of such component is at the moment the most promising technique to probe the inflationary theory describing the very early evolution of the Universe. We present the updated performance forecast of the Large Scale Polarization Explorer (LSPE), a program dedicated to the measurement of the CMB polarization. LSPE is composed of two instruments: Strip, a radiometer-based telescope on the ground in Tenerife, and SWIPE (Short-Wavelength Instrument for the Polarization Explorer) a bolometer-based instrument designed to fly on a winter arctic stratospheric long-duration balloon. The program is among the few dedicated to observation of the Northern Hemisphere, while most of the international effort is focused into ground-based observation in the Southern Hemisphere. Measurements are currently scheduled in Winter 2021/22 for SWIPE, with a flight duration up to 15 days, and in Summer 2021 with two years observations for Strip. We describe the main features of the two instruments, identifying the most critical aspects of the design, in terms of impact into performance forecast. We estimate the expected sensitivity of each instrument and propagate their combined observing power to the sensitivity to cosmological parameters, including the effect of scanning strategy, component separation, residual foregrounds and partial sky coverage. We also set requirements on the control of the most critical systematic effects and describe techniques to mitigate their impact. LSPE can reach a sensitivity in tensor-to-scalar ratio of $σ_r<0.01$, and improve constrains on other cosmological parameters.

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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.

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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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