arXiv subjects

J. Errard

Publications and source records attributed to J. Errard.

At least 19 recordsLinked to original sources

arXiv2026

LiteBIRD Mission Overview after Mission Reformation

LiteBIRD is a JAXA-led space mission designed to produce all-sky microwave polarization maps. Its primary science goal is to test representative inflationary models by measuring the cosmic microwave background $B$-mode polarization generated by primordial gravitational waves, while also providing new insights into cosmology, particle physics, and astrophysics. The mission concept has been updated following the reformation activities initiated after the Mission Definition Review in 2024. The current concept preserves the central scientific objectives, while simplifying the payload configuration: a single telescope covers 12 frequency bands with band centers spanning 40 to 402~GHz, corresponding to an optical coverage of 34--448~GHz. The telescope is a cross-Dragone reflector with a 500~mm aperture diameter, cooled to approximately 5~K and coupled to transition-edge-sensor bolometer arrays operated at 0.1~K. LiteBIRD will observe from a Lissajous orbit around the Sun--Earth L2 point during a nominal 3-year survey. More specifically, the primary scientific objective is to achieve total uncertainty in the tensor-to-scalar ratio of $\delta r < 0.002$ (68\% C.L.), including contributions from foreground residuals, statistical uncertainties, instrumental systematics, and margin contingency. The corresponding map-noise requirements are specified separately for the low-, mid-, and high-frequency ranges over the reionization and recombination multipole ranges. This sensitivity makes LiteBIRD unique not only for inflationary science but also for a broad range of scientific investigations probing the history of both the early and late Universe, as well as for astrophysical processes, including Galactic science. This paper summarizes the scientific objectives, updated payload and instrument concepts, observation strategy, and ground segment plans.

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arXiv2026

Galactic Science with the LiteBIRD satellite: Spectral characterization of diffuse Galactic polarized emission at the angular power spectrum level

Detection of primordial $B$-mode polarization in the cosmic microwave background (CMB) from tensor perturbations generated during inflation is a major scientific goal of future CMB missions. Its success will strongly depend on the characterization of polarized foregrounds, a challenge that the LiteBIRD satellite aims to tackle with its 15 frequency bands ranging from 40 to 402 GHz. In this work, we forecast the ability of LiteBIRD to characterize polarized dust and synchrotron emission in the diffuse interstellar medium (ISM), at the angular power spectrum level. From simulated LiteBIRD intensity and polarization maps with different foreground complexities, we compute cross-frequency angular power spectra and fit them to dust and synchrotron spectral energy distributions, which are modeled by a modified black body and a power law, respectively. We find that LiteBIRD will be able to measure the dust temperature, dust and synchrotron spectral indices and spatial correlation with dispersions as low as $\sigma(T_{\rm d})\sim0.2$ K, $\sigma(\beta_{\rm d})\sim0.006$, $\sigma(\beta_{\rm s})\sim0.04$ and $\sigma(\rho)\sim10^{-2}$, as well as to detect and quantify deviations from the proposed parametric model due to variations of the emission properties in the three dimensions of our Galaxy. Additionally, LiteBIRD is likely to rule out the power-law model of polarized foreground angular power spectra suggested by Planck data. It will also be able to detect differences in the values of $\beta_{\rm d}$, $T_{\rm d}$, and $\beta_{\rm s}$ between $E$ modes, $B$ modes, and intensity in the diffuse ISM for the first time, highlighting the joint variations of the physical conditions and the magnetic field structure across the Galaxy. We conclude that in addition to detailed studies of CMB polarization, LiteBIRD will open a new window onto the physical conditions governing the ISM of the Milky Way.

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arXiv2026

Setting requirements on out-of-band rejection for next-generation CMB experiments. Application to the LiteBIRD instrument

Next-generation cosmic microwave background experiments have very stringent constraints to achieve the required sensitivity to target polarization $B$ modes. In this work, we intend to set requirements on the out-of-band rejection level, with out-of-band referring to frequencies outside the telescope band-pass. The method developed is applied to the LiteBIRD Medium and High Frequency Telescopes. In order to determine the impact of out-of-band power, we model the instrument's optical response and the spectral emissions of the sky and of the instrument itself. This allows us to propagate optical power inside the telescope. Using this tool, we address both the impact of out-of-band power on the detection chain and on the thermal heat load, together with the impact on the process of separation between astrophysical components. The role of additional static power as well as dynamic power variations is studied. The requirement derived consist in attenuation factors (in dB) in frequency subdomains. They will be used to design the telescope filters.

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arXiv2025

LiteBIRD Science Goals and Forecasts: constraining isotropic cosmic birefringence

Cosmic birefringence (CB) is the rotation of the photons' linear polarisation plane during propagation. Such an effect is a tracer of parity-violating extensions of standard electromagnetism and would probe the existence of a new cosmological field acting as dark matter or dark energy. It has become customary to employ cosmic microwave background (CMB) polarised data to probe such a phenomenon. Recent analyses on Planck and WMAP data provide a hint of detection of the isotropic CB angle with an amplitude of around $0.3^\circ$ at the level of $2.4$ to $3.6σ$. In this work, we explore the LiteBIRD capabilities in constraining such an effect, accounting for the impact of the more relevant systematic effects, namely foreground emission and instrumental polarisation angles. We build five semi-independent pipelines and test these against four different simulation sets with increasing complexity in terms of non-idealities. All the pipelines are shown to be robust and capable of returning the expected values of the CB angle within statistical fluctuations for all the cases considered. We find that the uncertainties in the CB estimates increase with more complex simulations. However, the trend is less pronounced for pipelines that account for the instrumental polarisation angles. For the most complex case analysed, we find that LiteBIRD will be able to detect a CB angle of $0.3^\circ$ with a statistical significance ranging from $5$ to $13 \, σ$, depending on the pipeline employed, where the latter uncertainty corresponds to a total error budget of the order of $0.02^\circ$.

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arXiv2025

LiteBIRD Science Goals and Forecasts. A Case Study of the Origin of Primordial Gravitational Waves using Large-Scale CMB Polarization

We study the possibility of using the $LiteBIRD$ satellite $B$-mode survey to constrain models of inflation producing specific features in CMB angular power spectra. We explore a particular model example, i.e. spectator axion-SU(2) gauge field inflation. This model can source parity-violating gravitational waves from the amplification of gauge field fluctuations driven by a pseudoscalar "axionlike" field, rolling for a few e-folds during inflation. The sourced gravitational waves can exceed the vacuum contribution at reionization bump scales by about an order of magnitude and can be comparable to the vacuum contribution at recombination bump scales. We argue that a satellite mission with full sky coverage and access to the reionization bump scales is necessary to understand the origin of the primordial gravitational wave signal and distinguish among two production mechanisms: quantum vacuum fluctuations of spacetime and matter sources during inflation. We present the expected constraints on model parameters from $LiteBIRD$ satellite simulations, which complement and expand previous studies in the literature. We find that $LiteBIRD$ will be able to exclude with high significance standard single-field slow-roll models, such as the Starobinsky model, if the true model is the axion-SU(2) model with a feature at CMB scales. We further investigate the possibility of using the parity-violating signature of the model, such as the $TB$ and $EB$ angular power spectra, to disentangle it from the standard single-field slow-roll scenario. We find that most of the discriminating power of $LiteBIRD$ will reside in $BB$ angular power spectra rather than in $TB$ and $EB$ correlations.

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arXiv2024

Absolute reference for microwave polarization experiments -- The COSMOCal project and its proof of concept

The cosmic microwave background (CMB), a remnant of the Big Bang, provides unparalleled insights into the primordial universe, its energy content, and the origin of cosmic structures. The success of forthcoming terrestrial and space experiments hinges on meticulously calibrated data. Specifically, the ability to achieve an absolute calibration of the polarization angles with a precision of < 0.1 deg is crucial to identify the signatures of primordial gravitational waves and cosmic birefringence within the CMB polarization. We introduce the COSMOCal project, designed to deploy a polarized source in space for calibrating microwave frequency observations. The project aims to integrate microwave polarization observations from small and large telescopes, ground-based and in space, into a unified scale, enhancing the effectiveness of each observatory and allowing robust combination of data. To demonstrate the feasibility and confirm the observational approach of our project, we developed a prototype instrument that operates in the atmospheric window centered at 260 GHz, specifically tailored for use with the NIKA2 camera at the IRAM 30 m telescope. We present the instrument components and their laboratory characterization. The results of tests performed with the fully assembled prototype using a KIDs-based instrument, similar concept of NIKA2, are also reported. This study paves the way for an observing campaign using the IRAM 30m telescope and contributes to the development of a space-based instrument.

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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

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 Simons Observatory: pipeline comparison and validation for large-scale B-modes

The upcoming Simons Observatory Small Aperture Telescopes aim at achieving a constraint on the primordial tensor-to-scalar ratio $r$ at the level of $σ(r=0)\lesssim0.003$, observing the polarized CMB in the presence of partial sky coverage, cosmic variance, inhomogeneous non-white noise, and Galactic foregrounds. We present three different analysis pipelines able to constrain $r$ given the latest available instrument performance, and compare their predictions on a set of sky simulations that allow us to explore a number of Galactic foreground models and elements of instrumental noise, relevant for the Simons Observatory. The three pipelines employ different combinations of parametric and non-parametric component separation at the map and power spectrum levels, and use B-mode purification to estimate the CMB B-mode power spectrum. We applied them to a common set of simulated realistic frequency maps, and compared and validated them with focus on their ability to extract robust constraints on the tensor-to-scalar ratio $r$. We evaluated their performance in terms of bias and statistical uncertainty on this parameter. In most of the scenarios the three methodologies achieve similar performance. Nevertheless, several simulations with complex foreground signals lead to a $>2σ$ bias on $r$ if analyzed with the default versions of these pipelines, highlighting the need for more sophisticated pipeline components that marginalize over foreground residuals. We show two such extensions, using power-spectrum-based and map-based methods, that are able to fully reduce the bias on $r$ below the statistical uncertainties in all foreground models explored, at a moderate cost in terms of $σ(r)$.

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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

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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arXiv2024

Identifying frequency decorrelated dust residuals in B-mode maps by exploiting the spectral capability of bolometric interferometry

Astrophysical polarized foregrounds represent the most critical challenge in Cosmic Microwave Background (CMB) B-mode experiments. Multi-frequency observations can be used to constrain astrophysical foregrounds to isolate the CMB contribution. However, recent observations indicate that foreground emission may be more complex than anticipated. We investigate how the increased spectral resolution provided by band splitting in Bolometric Interferometry (BI) through a technique called spectral imaging can help control the foreground contamination in the case of unaccounted Galactic dust frequency decorrelation along the line-of-sight. We focus on the next generation ground-based CMB experiment CMB-S4, and compare its anticipated sensitivities, frequency and sky coverage with a hypothetical version of the same experiment based on BI. We perform a Monte-Carlo analysis based on parametric component separation methods (FGBuster and Commander) and compute the likelihood on the recovered tensor-to-scalar ratio. The main result of this analysis is that spectral imaging allows us to detect systematic uncertainties on r from frequency decorrelation when this effect is not accounted for in component separation. Conversely, an imager would detect a biased value of r and would be unable to spot the presence of a systematic effect. We find a similar result in the reconstruction of the dust spectral index, where we show that with BI we can measure more precisely the dust spectral index also when frequency decorrelation is present. The in-band frequency resolution provided by BI allows us to identify dust LOS frequency decorrelation residuals where an imager of similar performance would fail. This opens the prospect to exploit this potential in the context of future CMB polarization experiments that will be challenged by complex foregrounds in their quest for B-modes detection.

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arXiv2023

Impact of beam far side-lobe knowledge in the presence of foregrounds for LiteBIRD

We present a study of the impact of an uncertainty in the beam far side-lobe knowledge on the measurement of the Cosmic Microwave Background $B$-mode signal at large scale. It is expected to be one of the main source of systematic effects in future CMB observations. Because it is crucial for all-sky survey missions to take into account the interplays between beam systematic effects and all the data analysis steps, the primary goal of this paper is to provide the methodology to carry out the end-to-end study of their effect for a space-borne CMB polarization experiment, up to the cosmological results in the form of a bias $δr$ on the tensor-to-scalar ratio $r$. LiteBIRD is dedicated to target the measurement of CMB primordial $B$ modes by reaching a sensitivity of $σ\left( r \right) \leq 10^{-3}$ assuming $r=0$. As a demonstration of our framework, we derive the relationship between the knowledge of the beam far side-lobes and the tentatively allocated error budget under given assumptions on design, simulation and component separation method. We assume no mitigation of the far side-lobes effect at any stage of the analysis pipeline. We show that $δr$ is mostly due to the integrated fractional power difference between the estimated beams and the true beams in the far side-lobes region, with little dependence on the actual shape of the beams, for low enough $δr$. Under our set of assumptions, in particular considering the specific foreground cleaning method we used, we find that the integrated fractional power in the far side-lobes should be known at a level as tight as $\sim 10^{-4}$, to achieve the required limit on the bias $δr < 1.9 \times 10^{-5}$. The framework and tools developed for this study can be easily adapted to provide requirements under different design, data analysis frameworks and for other future space-borne experiments beyond 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

Polarization angle accuracy for future CMB experiments. The COSMOCal project and its prototype in the 1mm band

The Cosmic Microwave Background (CMB) radiation offers a unique window into the early Universe, facilitating precise examinations of fundamental cosmological theories. However, the quest for detecting B-modes in the CMB, predicted by theoretical models of inflation, faces substantial challenges in terms of calibration and foreground modeling. The COSMOCal (COsmic Survey of Millimeter wavelengths Objects for CMB experiments Calibration) project aims at enhancing the accuracy of the absolute calibration of the polarization angle $ψ$ of current and future CMB experiments. The concept includes the build of a very well known artificial source emitting in the frequency range [20-350] GHz that would act as an absolute calibrator for several polarization facilities on Earth. A feasibility study to place the artificial source in geostationary orbit, in the far field for all the telescopes on Earth, is ongoing. In the meanwhile ongoing hardware work is dedicated to build a prototype to test the technology, the precision and the stability of the polarization recovering in the 1 mm band (220-300 GHz). High-resolution experiments as the NIKA2 camera at the IRAM 30m telescope will be deployed for such use. Once carefully calibrated ($Δψ$ < 0.1 degrees) it will be used to observe astrophysical sources such as the Crab nebula, which is the best candidate in the sky for the absolute calibration of CMB experiments.

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arXiv2023

The advantage of Bolometric Interferometry for controlling Galactic foreground contamination in CMB primordial B-modes measurements

In the quest for the faint primordial B-mode polarization of the Cosmic Microwave Background, three are the key requirements for any present or future experiment: an utmost sensitivity, excellent control over instrumental systematic effects and over Galactic foreground contamination. Bolometric Interferometry (BI) is a novel technique that matches them all by combining the sensitivity of bolometric detectors, the control of instrumental systematics from interferometry and a software-based, tunable, in-band spectral resolution due to its ability to perform band-splitting during data analysis (spectral imaging). In this paper, we investigate how the spectral imaging capability of BI can help in detecting residual contamination in case an over-simplified model of foreground emission is assumed in the analysis. To mimic this situation, we focus on the next generation of ground-based CMB experiment, CMB-S4, and compare its anticipated sensitivities, frequency and sky coverage with a hypothetical version of the same experiment based on BI, CMB-S4/BI, assuming that line-of-sight (LOS) frequency decorrelation is present in dust emission but is not accounted for during component separation. We show results from a Monte-Carlo analysis based on a parametric component separation method (FGBuster), highlighting how BI has the potential to diagnose the presence of foreground residuals in estimates of the tensor-to-scalar ratio $r$ in the case of unaccounted Galactic dust LOS frequency decorrelation.

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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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