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This paper presents the Planck 2015 likelihoods, statistical descriptions of
the 2-point correlation functions of CMB temperature and polarization. They use
the hybrid approach employed previously: pixel-based at low multipoles, $\ell$,
and a Gaussian approximation to the distribution of cross-power spectra at
higher $\ell$. The main improvements are the use of more and better processed
data and of Planck polarization data, and more detailed foreground and
instrumental models. More than doubling the data allows further checks and
enhanced immunity to systematics. Progress in foreground modelling enables a
larger sky fraction, contributing to enhanced precision. Improvements in
processing and instrumental models further reduce uncertainties. Extensive
tests establish robustness and accuracy, from temperature, from polarization,
and from their combination, and show that the {\Lambda}CDM model continues to
offer a very good fit. We further validate the likelihood against specific
extensions to this baseline, such as the effective number of neutrino species.
For this first detailed analysis of Planck polarization, we concentrate at high
$\ell$ on E modes. At low $\ell$ we use temperature at all Planck frequencies
along with a subset of polarization. These data take advantage of Planck's wide
frequency range to improve the separation of CMB and foregrounds. Within the
baseline cosmology this requires a reionization optical depth
$\tau=0.078\pm0.019$, significantly lower than without high-frequency data for
explicit dust monitoring. At high $\ell$ we detect residual errors in E,
typically at the {\mu}K$^2$ level; we thus recommend temperature alone as the
high-$\ell$ baseline. Nevertheless, Planck high-$\ell$ polarization spectra are
already good enough to allow a separate high-accuracy determination of the
{\Lambda}CDM parameters, consistent with those established from temperature
alone.

Content uploaded by Gianfranco De Zotti

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All content in this area was uploaded by Gianfranco De Zotti on Jul 21, 2015

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... A quatidade de expansão é usualmente descrita pela grandeza chamada número de e-folds, definida como sendo N ⌘ a(t f )/a(t i ). A partir de um ajuste do espectro de potências com os dados de temperatura do Planck [51], foi mostrado em [49] que no contexto de LQC, o número total de e-folds de expansão desde o bounce até hoje deve ser, ...

... Ao considerar a contribuição das GWs primordiais para o número efetivo de espécies relativísticas N GW ef f e assumindo a física de partículas padrão, discutimos os efeitos da contribuição N GW ef f para os vínculos no parâmetro H 0 . Nesta análise usamos dados recentes da RCF [51] advindos da colaboração Planck e BICEP, dados de oscilações acústicas de bárions (BAO), além do resultado de Riess et al. para a taxa de expansão local [30], baseada em medidas diretas obtidas com o Hubble Space Telescope e o Gaia. Para os modelos explorados, mostramos que a contribuição adicional das ondas gravitacionais para N ef f alivia o problema da tensão em H 0 . ...

... It is evident that the inferred values of A L agree with the canonical value of the lensing amplitude, suggesting that the removal of low-ℓ data might indeed resolve the lensing anomaly. These results are consistent with the claimed inconsistency in the Planck likelihood for ℓ > 800 and ℓ < 800 [96]. ...

We scrutinize the reported lensing anomaly of the CMB by considering several phenomenological modifications of the lensing consistency parameter, $A_{\rm L}$. Considering Planck spectra alone, we find statisically significant evidence for scale dependence (`running') of $A_{\rm L}$. We then demonstrate that the anomaly is entirely driven by Planck's low multipoles, $\ell \leq 30$. When these data points are excluded a joint analysis with several other datasets clearly favors $\Lambda$CDM over the extended $\Lambda \rm CDM+A_L$ model. Not only that the lensing anomaly and low $\ell$ anomaly of the CMB go away in this case, but also the $S_8$ tension is ameliorated, and only the Hubble tension persists.

... In order to satisfy the thermal relic abundance of Ω DM h 2 ≃ 0.12, as required by cosmological considerations [59,60], the Higgsino-like neutralino LSP must be around 1 TeV and can be lowered further in the presence of coannihilation [33]. Below this mass scale, it is generally under abundant. ...

The lightest neutralino ( χ ˜ 1 0 ) is a good dark matter (DM) candidate in the R -parity conserving minimal supersymmetric Standard Model. In this work, we consider the light Higgsino-like neutralino as the lightest stable particle, thanks to a rather small Higgsino mass parameter μ . We then estimate the prominent radiative corrections to the neutralino-neutralino-Higgs boson vertices. We show that for Higgsino-like χ ˜ 1 0 , these corrections can significantly influence the spin-independent direct detection cross section, even contributing close to 100% in certain regions of the parameter space. These corrections, therefore, play an important role in deducing constraints on the mass of the Higgsino-like lightest neutralino DM, and thus the μ parameter.
Published by the American Physical Society 2024

... Based on the unique signatures of cosmic string [14][15][16][17][18][19], various investigations have been conducted to detect the string [20][21][22][23][24]. The simplest cosmic string spacetime is characterized by a flat metric with a deficit angle, which is described by an infinite, straight and static cylindrically symmetric cosmic string, and many quantum effects exhibit significant characteristics in such spacetime [25][26][27][28][29][30]. ...

Quantum metrology studies the ultimate precision limit of physical quantities by using quantum strategy. In this paper we apply the quantum metrology technologies to the relativistic framework for estimating the deficit angle parameter of cosmic string spacetime. We use a two-level atom coupled to electromagnetic fields as the probe and derive its dynamical evolution by treating it as an open quantum system. We estimate the deficit angle parameter by calculating its quantum Fisher information(QFI). It is found that the quantum Fisher information depends on the deficit angle, evolution time, detector initial state, polarization direction, and its position. We then identify the optimal estimation strategies, i.e., maximize the quantum Fisher information via all the associated parameters, and therefore optimize the precision of estimation. Our results show that for different polarization cases the QFIs have different behaviors and different orders of magnitude, which may shed light on the exploration of cosmic string spacetime.

... Based on the unique signatures of cosmic string [14][15][16][17][18][19], various investigations have been conducted to detect the string [20][21][22][23][24]. The simplest cosmic string spacetime is characterized by a flat metric with a deficit angle, which is described by an infinite, straight and static cylindrically symmetric cosmic string, and many quantum effects exhibit significant characteristics in such spacetime [25][26][27][28][29][30]. ...

Quantum metrology studies the ultimate precision limit of physical quantities by using quantum strategy. In this paper we apply the quantum metrology technologies to the relativistic framework for estimating the deficit angle parameter of cosmic string spacetime. We use a two-level atom coupled to electromagnetic fields as the probe and derive its dynamical evolution by treating it as an open quantum system. We estimate the deficit angle parameter by calculating its quantum Fisher information(QFI). It is found that the quantum Fisher information depends on the deficit angle, evolution time, detector initial state, polarization direction, and its position. We then identify the optimal estimation strategies, i.e., maximize the quantum Fisher information via all the associated parameters, and therefore optimize the precision of estimation. Our results show that for different polarization cases the QFIs have different behaviors and different orders of magnitude, which may shed light on the exploration of cosmic string spacetime.

... Various fractional versions of SPDEs have also been constructed in diverse applications [9,10,6,12,21,23,29,30,31,35,37]. A distinct merit of these fractional models is that they can be used to maintain long-range dependence in the evolution of complex systems, such as models of climate change and density fluctuations in the primordial universe as inferred from the cosmic microwave background (CMB) [4,16,17,18,1,2,3]. ...

This paper develops a fractional stochastic partial differential equation (SPDE) to model the evolution of a random tangent vector field on the unit sphere. The SPDE is governed by a fractional diffusion operator to model the L\'{e}vy-type behaviour of the spatial solution, a fractional derivative in time to depict the intermittency of its temporal solution, and is driven by vector-valued fractional Brownian motion on the unit sphere to characterize its temporal long-range dependence. The solution to the SPDE is presented in the form of the Karhunen-Lo\`{e}ve expansion in terms of vector spherical harmonics. Its covariance matrix function is established as a tensor field on the unit sphere that is an expansion of Legendre tensor kernels. The variance of the increments and approximations to the solutions are studied and convergence rates of the approximation errors are given. It is demonstrated how these convergence rates depend on the decay of the power spectrum and variances of the fractional Brownian motion.

... Various fractional versions of SPDEs have also been constructed in diverse applications [9,10,6,12,21,23,29,30,31,35,37]. A distinct merit of these fractional models is that they can be used to maintain long-range dependence in the evolution of complex systems, such as models of climate change and density fluctuations in the primordial universe as inferred from the cosmic microwave background (CMB) [4,16,17,18,1,2,3]. ...

This paper develops a fractional stochastic partial differential equation (SPDE) to model the evolution of a random tangent vector field on the unit sphere. The SPDE is governed by a fractional diffusion operator to model the Lévy-type behaviour of the spatial solution, a fractional derivative in time to depict the intermittency of its temporal solution, and is driven by vector-valued fractional Brownian motion on the unit sphere to characterize its temporal long-range dependence. The solution to the SPDE is presented in the form of the Karhunen-Loève expansion in terms of vector spherical harmonics. Its covariance matrix function is established as a tensor field on the unit sphere that is an expansion of Legendre tensor kernels. The variance of the increments and approximations to the solutions are studied and convergence rates of the approximation errors are given. It is demonstrated how these convergence rates depend on the decay of the power spectrum and variances of the fractional Brownian motion.

Accurate covariance matrices are required for a reliable estimation of cosmological parameters from pseudo-power spectrum estimators. In this work, we focus on the analytical calculation of covariance matrices. We consider the case of observations of the Cosmic Microwave Background in temperature and polarization on a small footprint such as in the SPT-3G experiment, which observes 4% of the sky. Power spectra evaluated on small footprints are expected to have large correlations between modes, and these need to be accurately modelled. We present, for the first time, an algorithm that allows an efficient (but computationally expensive) exact calculation of analytic covariance matrices. Using it as our reference, we test the accuracy of existing fast approximations of the covariance matrix. We find that, when the power spectrum is binned in wide bandpowers, current approaches are correct up to the 5% level on the SPT-3G small sky footprint. Furthermore, we propose a new approximation which improves over the previous ones reaching a precision of 1% in the wide bandpowers case and generally more than 4 times more accurate than current approaches. Finally, we derive the covariance matrices for mask-corrected power spectra estimated by the PolSpice code. In particular, we include, in the case of a small sky fraction, the effect of the apodization of the large scale modes. While we considered the specific case of the CMB, our results are applicable to any other cosmological probe which requires the calculation of pseudo-power spectrum covariance matrices.

The standard Λ Cold Dark Matter (ΛCDM) cosmological model provides a good description of a wide range of astrophysical and cosmological data. However, there are a few big open questions that make the standard model look like an approximation to a more realistic scenario yet to be found. In this paper, we list a few important goals that need to be addressed in the next decade, taking into account the current discordances between the different cosmological probes, such as the disagreement in the value of the Hubble constant H0, the σ8–S8 tension, and other less statistically significant anomalies. While these discordances can still be in part the result of systematic errors, their persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the necessity for new physics or generalisations beyond the standard model. In this paper, we focus on the 5.0σ tension between the Planck CMB estimate of the Hubble constant H0 and the SH0ES collaboration measurements. After showing the H0 evaluations made from different teams using different methods and geometric calibrations, we list a few interesting new physics models that could alleviate this tension and discuss how the next decade's experiments will be crucial. Moreover, we focus on the tension of the Planck CMB data with weak lensing measurements and redshift surveys, about the value of the matter energy density Ωm, and the amplitude or rate of the growth of structure (σ8,fσ8). We list a few interesting models proposed for alleviating this tension, and we discuss the importance of trying to fit a full array of data with a single model and not just one parameter at a time. Additionally, we present a wide range of other less discussed anomalies at a statistical significance level lower than the H0–S8 tensions which may also constitute hints towards new physics, and we discuss possible generic theoretical approaches that can collectively explain the non-standard nature of these signals. Finally, we give an overview of upgraded experiments and next-generation space missions and facilities on Earth that will be of crucial importance to address all these open questions.

The latest 2018 legacy release from the Planck satellite [1] of the Cosmic Microwave Background (CMB) temperature and polarization anisotropies power spectra, has provided a fantastic confirmation of the standard $\Lambda$ Cold Dark Matter ($\Lambda$CDM) cosmological model.

We present a cross-spectra-based approach for the analysis of cosmic microwave background data at large angular scales to
constrain the reionization optical depth τ, the tensor to scalar ratio r and the amplitude of the primordial scalar perturbations As. With respect to the pixel-based approach developed so far, using cross-spectra has the unique advantage to eliminate spurious
noise bias and to give a better handle over residual systematics, allowing to efficiently combine the cosmological information
encoded in cross-frequency or cross-data set spectra. We present two solutions to deal with the non-Gaussianity of the $\hat{C}_\ell$ estimator distributions at large angular scales: the first one relies on an analytical parametrization of the estimator distribution,
while the second one is based on modification of the Hamimache and Lewis (HL) likelihood approximation at large angular scales.
The modified HL method (oHL) is powerful and complete. It allows us to deal with multipole and mode correlations for a combined
temperature and polarization analysis. We validate our likelihoods on numerous simulations that include the realistic noise
levels of the Wilkinson Microwave Anisotropy Probe, Planck-Low Frequency Instrument and Planck-High Frequency Instrument experiments, demonstrating their validity over a broad range of cross-spectra configurations.

We present measurements of secondary cosmic microwave background (CMB)
anisotropies and cosmic infrared background (CIB) fluctuations using data from
the South Pole Telescope (SPT) covering the complete 2540 sq.deg. SPT-SZ survey
area. Data in the three SPT-SZ frequency bands centered at 95, 150, and 220
GHz, are used to produce six angular power spectra (three single-frequency
auto-spectra and three cross-spectra) covering the multipole range 2000 < ell <
11000 (angular scales 5' > \theta > 1'). These are the most precise
measurements of the angular power spectra at ell > 2500 at these frequencies.
The main contributors to the power spectra at these angular scales and
frequencies are the primary CMB, CIB, thermal and kinematic Sunyaev-Zel'dovich
effects (tSZ and kSZ), and radio galaxies. We include a constraint on the tSZ
power from a measurement of the tSZ bispectrum from 800 sq.deg. of the SPT-SZ
survey. We measure the tSZ power at 143 GHz to be DtSZ = 4.08 +0.58 -0.67 \mu
K^2 and the kSZ power to be DkSZ = 2.9 +- 1.3 \mu K^2. The data prefer positive
kSZ power at 98.1% CL. We measure a correlation coefficient of \xi = 0.113
+0.057 -0.054 between sources of tSZ and CIB power, with \xi < 0 disfavored at
a confidence level of 99.0%. The constraint on kSZ power can be interpreted as
an upper limit on the duration of reionization. When the post-reionization
homogeneous kSZ signal is accounted for, we find an upper limit on the duration
\Delta z < 5.4 at 95% CL.

We present the temperature and polarization angular power spectra of the CMB measured by the Atacama Cosmology Telescope (ACT) from 5400 deg² of the 2013–2016 survey, which covers >15000 deg² at 98 and 150 GHz. For this analysis we adopt a blinding strategy to help avoid confirmation bias and, related to this, show numerous checks for systematic error done before unblinding. Using the likelihood for the cosmological analysis we constrain secondary sources of anisotropy and foreground emission, and derive a "CMB-only" spectrum that extends to ℓ=4000. At large angular scales, foreground emission at 150 GHz is ~1% of TT and EE within our selected regions and consistent with that found by Planck. Using the same likelihood, we obtain the cosmological parameters for ΛCDM for the ACT data alone with a prior on the optical depth of τ=0.065±0.015. ΛCDM is a good fit. The best-fit model has a reduced χ² of 1.07 (PTE=0.07) with H₀=67.9±1.5 km/s/Mpc. We show that the lensing BB signal is consistent with ΛCDM and limit the celestial EB polarization angle to ψP =−0.07o±0.09o. We directly cross correlate ACT with Planck and observe generally good agreement but with some discrepancies in TE. All data on which this analysis is based will be publicly released.

An improved measurement of the mass of the Higgs boson is derived from a combined fit to the reconstructed invariant mass spectra of the decay channels H→γγ and H→ZZ∗→4ℓ. The analysis uses the pp collision data sample recorded by the ATLAS experiment at the CERN Large Hadron Collider at center-of-mass energies of 7 TeV and 8 TeV, corresponding to an integrated luminosity of 25 fb−1. The measured value of the Higgs boson mass is mH=125.36±0.37(stat)±0.18(syst) GeV. This result is based on improved energy-scale calibrations for photons, electrons, and muons as well as other analysis improvements, and supersedes the previous result from ATLAS. Upper limits on the total width of the Higgs boson are derived from fits to the invariant mass spectra of the H→γγ and H→ZZ∗→4ℓ decay channels.

We present a point-source catalog from 771 deg^2 of the South Pole Telescope Sunyaev-Zel'dovich survey at 95, 150, and 220 GHz. We detect 1545 sources above 4.5σ significance in at least one band. Based on their relative brightness between survey bands, we classify the sources into two populations, one dominated by synchrotron emission from active galactic nuclei, and one dominated by thermal emission from dust-enshrouded star-forming galaxies. We find 1238 synchrotron and 307 dusty sources. We cross-match all sources against external catalogs and find 189 unidentified synchrotron sources and 189 unidentified dusty sources. The dusty sources without counterparts are good candidates for high-redshift, strongly lensed submillimeter galaxies. We derive number counts for each population from 1 Jy down to roughly 11, 4, and 11 mJy at 95, 150, and 220 GHz. We compare these counts with galaxy population models and find that none of the models we consider for either population provide a good fit to the measured counts in all three bands. The disparities imply that these measurements will be an important input to the next generation of millimeter-wave extragalactic source population models.

We report an improved measurement of the cosmic microwave background (CMB) $B$-mode polarization power spectrum with the POLARBEAR experiment. By adding new data collected during the second season of observations (2013-2014) to re-analyzed data from the first season (2012-2013), we have reduced twofold the band-power uncertainties. The band powers are reported over angular multipoles $500 \leq \ell \leq 2100$, where the dominant $B$-mode signal is expected to be due to the gravitational lensing of $E$-modes. We reject the null hypothesis of no $B$-mode polarization at a confidence of 3.1$\sigma$ including both statistical and systematic uncertainties. We test the consistency of the measured $B$-modes with the $\Lambda$ Cold Dark Matter ($\Lambda$CDM) framework by fitting for a single lensing amplitude parameter $A_L$ relative to the Planck best-fit model prediction. We obtain $A_L = 0.60 ^{+0.26} _{-0.24} ({\rm stat}) ^{+0.00} _{-0.04}({\rm inst}) \pm 0.14 ({\rm foreground}) \pm 0.04 ({\rm multi})$, where $A_{L}=1$ is the fiducial $\Lambda$CDM value, and the details of the reported uncertainties are explained later in the manuscript.

We present measurements of $E$-mode polarization and temperature-$E$-mode
correlation in the cosmic microwave background (CMB) using data from the first
season of observations with SPTpol, the polarization-sensitive receiver
currently installed on the South Pole Telescope (SPT). The observations used in
this work cover 100~\sqdeg\ of sky with arcminute resolution at $150\,$GHz. We
report the $E$-mode angular auto-power spectrum ($EE$) and the
temperature-$E$-mode angular cross-power spectrum ($TE$) over the multipole
range $500 < \ell \leq5000$. These power spectra improve on previous
measurements in the high-$\ell$ (small-scale) regime. We fit the combination of
the SPTpol power spectra, data from \planck\, and previous SPT measurements
with a six-parameter \LCDM cosmological model. We find that the best-fit
parameters are consistent with previous results. The improvement in high-$\ell$
sensitivity over previous measurements leads to a significant improvement in
the limit on polarized point-source power: after masking sources brighter than
50\,mJy in unpolarized flux at 150\,GHz, we find a 95\% confidence upper limit
on unclustered point-source power in the $EE$ spectrum of D_\ell = \ell
(\ell+1) C_\ell / 2 \pi < 0.40 \ \mu{\mbox{K}}^2 at $\ell=3000$, indicating
that future $EE$ measurements will not be limited by power from unclustered
point sources in the multipole range $\ell < 3600$, and possibly much higher in
$\ell.$