Cosmic Microwave Background Power Spectrum Research Articles

Candl: cosmic microwave background analysis with a differentiable likelihood

We present candl, an automatically differentiable python likelihood for analysing cosmic microwave background power spectrum measurements. candl is powered by JAX, which makes it fast and easy to calculate derivatives of the likelihood. This facilitates, for example, robust Fisher matrices without finite-difference methods. We show the benefits of candl through a series of example calculations, covering forecasting, robustness tests, and gradient-based Markov chain Monte Carlo sampling. These also include optimising the band power bin width to minimise parameter errors of a realistic mock data set. Moreover, we calculate the correlation of parameter constraints from correlated and partially overlapping subsets of the SPT-3G 2018 TT/TE/EE data release. In a traditional analysis framework, these tasks are slow and require careful fine-tuning to obtain stable results. As such, a fully differentiable pipeline allows for a higher level of scrutiny; we argue that this is the paradigm shift required to leverage incoming data from ground-based experiments, which will significantly improve the cosmological parameter constraints from the Planck mission. candl comes with the latest primary and lensing power spectrum data from the South Pole Telescope and Atacama Cosmology Telescope collaborations and will be used as part of the upcoming SPT-3G TT/TE/EE and ϕϕ data releases. Along with the core code, we release a series of auxiliary tools, which simplify common analysis tasks and interface the likelihood with other cosmological software. candl is pip-installable and publicly available on Github.

Challenges to Inflation in the Post-Planck Era

Space-based missions studying the cosmic microwave background (CMB) have progressively refined the parameter space in conventional models of inflation shortly (∼10−37 s) after the Big Bang. While most inflationary scenarios proposed thus far in the context of general relativity have since been ruled out, the basic idea of inflation may still be tenable, albeit with several unresolved conundrums, such as conflicting initial conditions and inconsistencies with the measured CMB power spectrum. In the new slow-roll inflationary picture, inflation arising in plateau-like potentials requires an initiation beyond the Planck time. This delay may be consistent with the cutoff, kmin , measured recently in the primordial power spectrum. However, the actual value of kmin would imply an initiation time too far beyond the Big Bang for inflation to solve the horizon problem. In this paper, we also describe several other undesirable consequences of this delay, including an absence of well-motivated initial conditions and a significant difficulty in providing a viable mechanism for properly quantizing the primordial fluctuations. Nevertheless, many of these inconsistencies may still be avoided if one introduces nonconventional modifications to inflation, such as a brief departure from slow-roll dynamics, possibly due to a dramatic change in the inflationary potential, inflation driven by multiple fields, or a nonminimal coupling to gravity. In addition, some of these difficulties could be mitigated via the use of alternative cosmologies based, e.g., on loop quantum gravity, which replaces the initial Big Bang singularity with finite conditions at a bounce-like beginning.

Enhancing CMB map reconstruction and power spectrum estimation with convolutional neural networks

The accurate reconstruction of Cosmic Microwave Background (CMB) maps and the measurement of its power spectrum are crucial for studying the early universe. In this paper, we implement a convolutional neural network to apply the Wiener Filter to CMB temperature maps, and use it intensively to compute an optimal quadratic estimation of the power spectrum. Our neural network has a UNet architecture as that implemented in WienerNet, but with novel aspects such as being written in python 3 and TensorFlow 2. It also includes an extra channel for the noise variance map, to account for inhomogeneous noise, and a channel for the mask. The network is very efficient, overcoming the bottleneck that is typically found in standard methods to compute the Wiener Filter, such as those that apply the conjugate gradient. It scales efficiently with the size of the map, making it a useful tool to include in CMB data analysis. The accuracy of the Wiener Filter reconstruction is satisfactory, as compared with the standard method. We heavily use this approach to efficiently estimate the power spectrum, by performing a simulation-based analysis of the optimal quadratic estimator. We further evaluate the quality of the reconstructed maps in terms of the power spectrum and find that we can properly recover the statistical properties of the signal. We find that the proposed architecture can account for inhomogeneous noise efficiently. Furthermore, increasing the complexity of the variance map presents a more significant challenge for the convergence of the network than the noise level does.

Cosmological constraints on neutrino mass within consistent cosmological models* *We acknowledge the use of HPC Cluster of ITP-CAS. XZ is supported by the National Natural Science Foundation of China (12005183). QGH is supported by the National Natural Science Foundation of China (12250010, 11975019, 11991052, 12047503), and the Key Research Program of Frontier Sciences, CAS, (ZDBS-LY-7009)

Recently, the emergence of cosmological tension has raised doubts about the consistency of the ΛCDM model. To constrain the neutrino mass within a consistent cosmological framework, we investigate three massive neutrinos with normal hierarchy (NH) and inverted hierarchy (IH) in both the axion-like early dark energy (Axi-EDE) and AdS-EDE models. We use joint datasets including the cosmic microwave background power spectrum from Planck 2018, Pantheon of type Ia supernova, baryon acoustic oscillation, and data from SH0ES. For the νAxi-EDE model, we obtain < 0.152 eV and < 0.178 eV, whereas for the νAdS-EDE model, we find < 0.135 eV and < 0.167 eV. Our results exhibit a preference for NH in both the νAxi-EDE and νAdS-EDE models.

Testing CCC+TL Cosmology with Observed Baryon Acoustic Oscillation Features

The primary purpose of this paper is to see how well a recently proposed new model fits (a) the position of the baryon acoustic oscillation (BAO) features observed in the large-scale distribution of galaxies and (b) the angular size measured for the sound horizon due to BAO imprinted in the cosmic microwave background (CMB) anisotropy. The new model is a hybrid model that combines the tired light (TL) theory with a variant of the ΛCDM model in which the cosmological constant is replaced with a covarying coupling constants’ (CCC) parameter α. This model, dubbed the CCC+TL model, can fit the Type Ia supernovae Pantheon+ data as accurately as the ΛCDM model, and also fit the angular size of cosmic dawn galaxies observed by the James Webb Space Telescope, which is in tension with the ΛCDM model. The results we obtained are 151.0 (±5.1) Mpc for the absolute BAO scale at the current epoch, and the angular size of the sound horizon θ sh = 0.°60, matching Planck’s observations at the surface of the last scattering when the baryon density is set to 100% of the matter density and ∣α∣ is increased by 5.6%. It remains to be seen if the new model is consistent with the CMB power spectrum, the Big Bang nucleosynthesis of light elements, and other critical observations.

The Atacama Cosmology Telescope: A Measurement of the DR6 CMB Lensing Power Spectrum and Its Implications for Structure Growth

We present new measurements of cosmic microwave background (CMB) lensing over 9400 deg2 of the sky. These lensing measurements are derived from the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) CMB data set, which consists of five seasons of ACT CMB temperature and polarization observations. We determine the amplitude of the CMB lensing power spectrum at 2.3% precision (43σ significance) using a novel pipeline that minimizes sensitivity to foregrounds and to noise properties. To ensure that our results are robust, we analyze an extensive set of null tests, consistency tests, and systematic error estimates and employ a blinded analysis framework. Our CMB lensing power spectrum measurement provides constraints on the amplitude of cosmic structure that do not depend on Planck or galaxy survey data, thus giving independent information about large-scale structure growth and potential tensions in structure measurements. The baseline spectrum is well fit by a lensing amplitude of A lens = 1.013 ± 0.023 relative to the Planck 2018 CMB power spectra best-fit ΛCDM model and A lens = 1.005 ± 0.023 relative to the ACT DR4 + WMAP best-fit model. From our lensing power spectrum measurement, we derive constraints on the parameter combination S8CMBL≡σ8Ωm/0.30.25 of S8CMBL=0.818±0.022 from ACT DR6 CMB lensing alone and S8CMBL=0.813±0.018 when combining ACT DR6 and Planck NPIPE CMB lensing power spectra. These results are in excellent agreement with ΛCDM model constraints from Planck or ACT DR4 + WMAP CMB power spectrum measurements. Our lensing measurements from redshifts z ∼ 0.5–5 are thus fully consistent with ΛCDM structure growth predictions based on CMB anisotropies probing primarily z ∼ 1100. We find no evidence for a suppression of the amplitude of cosmic structure at low redshifts.

Cluster profiles from beyond-the-QE CMB lensing mass maps

Clusters of galaxies, being the largest collapsed structures in the universe, offer valuable insights into the nature of cosmic evolution. Precise calibration of the mass of clusters can be obtained by extracting their gravitational lensing signal on the Cosmic Microwave Background (CMB) fluctuations. We extend and test here the performance achieved on cluster scales by the parameter-free, maximum a posteriori (MAP) CMB lensing reconstruction method, which has been shown to be optimal in the broader context of CMB lensing mass map and power spectrum estimation. In the context of cluster lensing, the lensing signal of other large-scale structures acts as an additional source of noise. We show here that by delensing the CMB fluctuations around each and every cluster, this noise variance is reduced according to expectations. We also demonstrate that the well-known bias in the temperature quadratic estimator in this regime, sourced by the strong non-Gaussianity of the signal, is almost entirely mitigated without any scale cuts. Being statistically speaking an optimal and blind lensing mass map reconstruction, the MAP estimator is a promising tool for the calibration of the masses of clusters.

Inference of the optical depth to reionization τ from Planck CMB maps with convolutional neural networks

The optical depth to reionization, τ, is the least constrained parameter of the cosmological Λ cold dark matter (ΛCDM) model. To date, its most precise value is inferred from large-scale polarized cosmic microwave background (CMB) power spectra from the High Frequency Instrument (HFI) aboard the Planck satellite. These maps are known to contain significant contamination by residual non-Gaussian systematic effects, which are hard to model analytically. Therefore, robust constraints on τ are currently obtained through an empirical cross-spectrum likelihood built from simulations. In this paper, we present a likelihood-free inference of τ from polarized Planck HFI maps which, for the first time, is fully based on neural networks (NNs). NNs have the advantage of not requiring an analytical description of the data and can be trained on state-of-the-art simulations, combining the information from multiple channels. By using Gaussian sky simulations and Planck SRoll2 simulations, including CMB, noise, and residual instrumental systematic effects, we trained, tested, and validated NN models considering different setups. We inferred the value of τ directly from Stokes Q and U maps at ∼4° pixel resolution, without computing angular power spectra. On Planck data, we obtained τNN = 0.0579 ± 0.0082, which is compatible with current EE cross-spectrum results but with a ∼30% larger uncertainty, which can be assigned to the inherent nonoptimality of our estimator and to the retraining procedure applied to avoid biases. While this paper does not improve on current cosmological constraints on τ, our analysis represents a first robust application of NN-based inference on real data, and highlights its potential as a promising tool for complementary analysis of near-future CMB experiments, also in view of the ongoing challenge to achieve the first detection of primordial gravitational waves.

Constraining the spatial curvature with cosmic expansion history in a cosmological model with a non-standard sound horizon

Spatial curvature is one of the most fundamental parameters in our current concordance flat ΛCDM model of the Universe. The goal of this work is to investigate how the constraint on the spatial curvature is affected by an assumption on the sound horizon scale. The sound horizon is an essential quantity to use the standard ruler from the Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillations (BAOs). As an example, we study the curvature constraint in an axion-like Early Dark Energy (EDE) model in light of recent cosmological datasets from Planck, the South Pole Telescope (SPT), and the Atacama Cosmology Telescope (ACT), as well as BAO data compiled in Sloan Digital Sky Survey Data Release 16. We find that, independent of the CMB datasets, the EDE model parameters are constrained only by the CMB power spectra as precisely and consistently as the flat case in previous work, even with the spatial curvature. We also demonstrate that combining CMB with BAO is extremely powerful to constrain the curvature parameter even with a reduction of the sound-horizon scale in an EDE model, resulting in Ω K = -0.0058± 0.0031 in the case of ACT+BAO after marginalizing over the parameters of the EDE model. This constraint is as competitive as the Planck+BAO result in a ΛCDM model, Ω K = -0.0001± 0.0018.

Cosmic birefringence from neutrino and dark matter asymmetries

In light of the recent measurement of the nonzero Cosmic Microwave Background (CMB) polarization rotation angle from the Planck 2018 data, we explore the possibility that such a cosmic birefringence effect is induced by coupling a fermionic current with photons via a Chern-Simons-like term. We begin our discussion by rederiving the general formulae of the cosmic birefringence angle with correcting a mistake in the previous study.We then identify the fermions in the current as the left-handed electron neutrinos and asymmetric dark matter (ADM) particles, since the rotation angle is sourced by the number density difference between particles and antiparticles. For the electron neutrino case, with the value of the degeneracy parameter ξν e recently measured by the EMPRESS survey, we find a large parameter space which can explain the CMB photon polarization rotations. On the other hand, for the ADM solution, we consider two benchmark cases with Mχ = 5 GeV and 5 keV. The former is the natural value of the ADM mass if the observed ADM and baryon asymmetry in the Universe are produced by the same mechanism, while the latter provides a warm DM candidate. In addition, we explore the experimental constraints from the CMB power spectra and the DM direct detections.

Confronting interacting dark radiation scenarios with cosmological data

Dark radiation (DR) is generally predicted in new physics scenarios that address fundamental puzzles of the Standard Model or tensions in the cosmological data. Cosmological data have the sensitivity to constrain not only the energy density of DR but also whether it is interacting. In this paper, we present a systematic study of five types of interacting DR (free-streaming, fluid, decoupling, instantaneous decoupling, and recoupling DR) and their impact on cosmological observables. We modify the Boltzmann hierarchy to describe all these types of interacting DR under the relaxation time approximation. We, for the first time, robustly calculate the collision terms for recoupling scalar DR and provide a better estimation of the recoupling transition redshift. We demonstrate the distinct features of each type of DR on the cosmic microwave background and matter power spectra. We perform Markov-chain Monte Carlo scans using the Planck 2018 data and baryon acoustic oscillation data. Assuming no new physics in the standard model neutrino sector, we find no statistically significant constraints on the couplings of DR, although there is a slight preference for the fluidlike limit of all the cases. In the case of instantaneous decoupling DR, this limit corresponds to a late transition redshift around recombination. The $\mathrm{\ensuremath{\Delta}}{N}_{\mathrm{eff}}$ constraint varies marginally depending on the type of DR.

Ultra-light axions and the S 8 tension: joint constraints from the cosmic microwave background and galaxy clustering

We search for ultra-light axions as dark matter (DM) and dark energy particle candidates, for axion masses 10-32 eV ≤ m a ≤ 10-24 eV, by a joint analysis of cosmic microwave background (CMB) and galaxy clustering data — and consider if axions can resolve the tension in inferred values of the matter clustering parameter S 8. We give legacy constraints from Planck 2018 CMB data, improving 2015 limits on the axion density Ωa h 2 by up to a factor of three; CMB data from the Atacama Cosmology Telescope and the South Pole Telescope marginally weaken Planck bounds at m a = 10-25 eV, owing to lower (and theoretically-consistent) gravitational lensing signals. We jointly infer, from Planck CMB and full-shape galaxy power spectrum and bispectrum data from the Baryon Oscillation Spectroscopic Survey (BOSS), that axions are, today, < 10% of the DM for m a ≤ 10-26 eV and < 1% for 10-30 eV ≤ m a ≤ 10-28 eV. BOSS data strengthen limits, in particular at higher m a by probing high-wavenumber modes (k < 0.4h Mpc-1). BOSS alone finds a preference for axions at 2.7σ, for m a = 10-26 eV, but Planck disfavours this result. Nonetheless, axions in a window 10-28 eV ≤ m a ≤ 10-25 eV can improve consistency between CMB and galaxy clustering data, e.g., reducing the S 8 discrepancy from 2.7σ to 1.6σ, since these axions suppress structure growth at the 8h -1 Mpc scales to which S 8 is sensitive. We expect improved constraints with upcoming high-resolution CMB and galaxy lensing and future galaxy clustering data, where we will further assess if axions can restore cosmic concordance.

Implications for Primordial Black Holes from Cosmological Constraints on Scalar-induced Gravitational Waves

Sufficiently large scalar perturbations in the early universe can create overdense regions that collapse into primordial black holes (PBHs). This process is accompanied by the emission of scalar-induced gravitational waves that behave like an extra radiation component, thus contributing to the relativistic degrees of freedom (N eff). We show that the cosmological constraints on N eff can be used to pose stringent limits on PBHs created from this particular scenario as well as the relevant small-scale curvature perturbation (). We show that the combination of cosmic microwave background (CMB), baryon acoustic oscillation, and Big Bang nucleosynthesis data sets can exclude supermassive PBHs with peak mass M • ∈ [5 × 105, 5 × 1010] M ⊙ as the major component of dark matter, while the detailed constraints depend on the shape of the PBHs’ mass distribution. A future CMB mission such as CMB-S4 can greatly broaden this constraint window to M • ∈ [8 × 10−5, 5 × 1010] M ⊙, covering substellar masses. These limits on PBHs correspond to a tightened constraint on on scales of k ∈ [10, 1022] Mpc−1, much smaller than those probed by direct CMB and large-scale structure power spectra.

Cosmological Parameters from Planck Data in SU(2)CMB, Their Local ΛCDM Values, and the Modified Photon Boltzmann Equation

AbstractA review of the spatially flat cosmological model SU(2)CMB, minimally induced by the postulate that the cosmic microwave background (CMB) is subject to an SU(2) rather than a U(1) gauge principle, is given. Cosmological parameter values, which are determined from the Planck CMB power spectra at small angular scales, are compared to their values in spatially flat ΛCDM from both local and global extractions. As a global model SU(2)CMB leans toward local ΛCDM cosmology and is in tension with some global ΛCDM parameter values. Spectral antiscreening / screening effects in SU(2)CMB radiance are presented within the Rayleigh– Jeans regime in dependence on temperature and frequency. Such radiance anomalies can cause CMB large‐angle anomalies. Therefore, it is pointed out how SU(2)CMB modifies the Boltzmann equation for the perturbations of the photon phase space distribution at low redshift and why this requires to the solve the ℓ‐hierarchy on a comoving momentum grid (q‐grid) for all z.

Fitting Power Spectrum of Scalar Perturbations for Primordial Black Hole Production during Inflation

A simple phenomenological fit for the power spectrum of scalar (curvature) perturbations during inflation is proposed to analytically describe slow roll of inflaton and formation of primordial black holes (PBH) in the early universe, in the framework of single-field models. The fit is given by a sum of the power spectrum of slow-roll inflation, needed for a viable description of the cosmic microwave background (CMB) radiation in agreement with Planck/BICEP/Keck measurements, and the log-normal (Gaussian) fit for the power spectrum enhancement (peak) needed for efficient PBH production, in the leading (model-independent) approximation. The T-type α-attractor models are used to get the simple CMB power spectrum depending upon the e-folds as the running variable. The location and height of the peak are chosen to yield the PBH masses in the asteroid-size window allowed for the whole (current) dark matter. We find the restrictions on the peak width.

Excess of lensing amplitude in the Planck CMB power spectrum

Precise measurements of the Planck cosmic microwave background (CMB) angular power spectrum (APS) at small angles have stimulatedaccurate statistical analyses of the lensing amplitude parameter A L. To confirm if it satisfies the value expected by the flat-ΛCDM concordance model, i.e. A L = 1,we investigate the spectrum difference obtained as the difference of the measured Planck CMB APS and the Planck best-fitΛCDM APS model. To know if this residual spectrum corresponds to statistical noise or if it has a hidden signature that can be accounted forwith a larger lensing amplitude A L > 1,we apply the Ljung-Box statistical test and find, with high statistical significance, that the spectrum difference is not statistical noise.This spectrum difference is then analysed in detail using simulated APS, based on the Planck ΛCDM best-fit model, where thelensing amplitude is a free parameter.We explore different binnations of the multipole order ℓ and look for the best-fit lensing amplitude parameter that accountsfor the spectrum difference in a χ 2 procedure.We find that there is an excess of signal that is well explained by a ΛCDM APS with a non-null lensing amplitude parameter A lens, with values in the interval [0.10,0.29] at 68% confidence level.Furthermore, the lensing parameter in the Planck APS should be 1 + A lens > 1 at ∼ 3σ of statistical confidence.Additionally, we perform statistical tests that confirm the robustness of this result.Important to say that this excess of lensing amplitude, not accounted in the Planck's flat-ΛCDM model, could have an impacton the theoretical expectation of large-scale structures formation once the scales where it was detected correspond to these matterclustering processes.

A Population III–Generated Dust Screen at z ∼ 16

The search for alternative cosmological models is largely motivated by the growing discordance between the predictions of ΛCDM and the ever-improving observations, such as the disparity in the value of H 0 measured at low and high redshifts. One model in particular, known as the R h = ct universe, has been highly successful in mitigating or removing all of the inconsistencies. In this picture, however, the anisotropies in the cosmic microwave background (CMB) would have emerged at a redshift z ∼ 16, rather than via fluctuations in the recombination zone at z ∼ 1080. We demonstrate here that a CMB created in the early universe, followed by scattering through a Population III–generated dust screen, is consistent with all of the current data. Indeed, the Planck measurements provide a hint of an ∼2%–4% frequency dependence in the CMB power spectrum, which would be naturally explained as a variation in the optical depth through the dust but not a Thomson scattering–dominated recombination environment. Upcoming measurements should be able to easily distinguish between these two scenarios, e.g., via the detection of recombination lines at z ∼ 1080, which would completely eliminate the dust-reprocessing idea.

Argument for the radiation-dominated behavior of matter fields in the preinflationary era

We investigate the leading-order behavior of matter fields in the preinflationary era using the semiclassical approximation. Many inflationary models assume without supporting arguments that the Universe was radiation dominated prior to inflation, leading to modifications of cosmological observables, such as the cosmic microwave background power spectrum. In previous work, we demonstrated that conformally coupled scalar fields do have a radiationlike contribution to the stress-energy tensor at sufficiently early times. In this work, we extend these arguments to apply to massless spin-1 fields and massive or massless spin-$\frac{1}{2}$ fields. We find massless spin-1 fields always have a radiationlike contribution. For spin-$\frac{1}{2}$ fields, we find the contribution at early times is radiationlike assuming this is the dominant contribution to the stress-energy tensor.

Cannibal dark matter decoupled from the standard model: Cosmological constraints

An internally thermalized dark matter (DM) with only gravitational interaction with the standard model (SM) particles at low temperatures, may undergo number-changing self-scatterings in the early Universe, eventually freezing out to the observed DM abundance. If these reactions, such as a $3 \rightarrow 2$ process, take place when the DM is non-relativistic, DM cannibalizes itself to cool much slower than standard non-relativistic matter during the cannibal phase. As shown in earlier studies, if the cannibal phase takes place during the matter-dominated epoch, there are very strong constraints from structure formation. Considering scenarios in which the cannibal phase freezes out in the radiation-dominated epoch instead, we show that cannibal DM decoupled from the SM can be viable, consistent with all present cosmological constraints. To this end, we solve the coupled evolution equations of the DM temperature and density, and determine its abundance for different DM self-couplings. We then evaluate the constraints on these parameters from the cosmic-microwave background power spectrum, the big-bang nucleosynthesis limits on the relativistic degrees of freedom, the Lyman-$\alpha$ limits on the DM free-streaming length and the theoretical upper bound on the $3 \rightarrow 2$ annihilation rate from $S-$matrix unitarity. We find that depending upon the DM self-couplings, a scalar cannibal DM with mass in the range of around 80 eV to 700 TeV can make up the observed DM density and satisfy all the constraints, when the initial DM temperature ($T_{\rm DM}$) is lower than the SM one ($T_{\rm SM}$), with $T_{\rm SM}/9100 \lesssim T_{\rm DM} \lesssim \,T_{\rm SM}/1.1$.

Observational imprints of our lost twin anti-universe

We consider observational consequences of the entanglement between our universe and a hypothetical twin anti-universe in the third quantization scheme of the canonical quantum gravity in order to make such a scenario falsifiable. Based on our recent and unique investigations we select some special form of the interuniversal interaction which allows the entanglement entropy of the pair of universes to diverge at the critical points of their classical evolution where the specific behaviour of the Hubble parameter plays the key role. We find that the modification of the cosmic microwave background (CMB) power spectrum due to the entanglement with our twin anti-universe for such models is enlarged for small modes k and small multipole numbers l. Our specific form of the interaction is then constrained by the Planck satellite data giving the interaction coupling constant bound to be lambda _olesssim {mathcal {O}}(10^{-56}),text {s}^{-3} which is small, but not negligible compared to the inflationary contribution. Some other coupling functions which allow more critical points are also briefly commented on in the context of their observational effect on CMB and other prospective observational data.