Dark Matter Model Research Articles

Quantum model of galactic halos with an Navarro-Frenk-White dark matter profile

A quantum model of a cold dark matter galactic halo is developed. The model requires specifying the mass and radius of the halo as well as its density profile. The structure of the halo resulting from the theory is predicted and its physical properties are determined. Verification of these theoretical predictions by observations is proposed and discussed. The model is constructed by analytically solving the governing equation and using its time-independent solutions to determine the internal structure of a galactic halo with an Navarro-Frenk-White cold dark matter density profile. The governing equation that is the basis of the developed theory is derived from the irreducible representations of the extended Galilean group. The method of finding the solutions is analytical, even though an Navarro-Frenk-White density profile is used in the calculations. The theory predicts a halo with a core composed of free dark matter particles that move randomly with frequent collisions. It also predicts an envelope in which the particles are confined to their orbits, which are quantized. Except in the close vicinity of the core, the population of the orbits remains fixed, and physical reasons for the nonexistence of quantum jumps between these orbits are presented. A quantum model of a galactic cold dark matter halo with a given Navarro-Frenk-White density profile is constructed. It predicts a quantum structure of the halo that is significantly different than any previously known dark matter model. The quantum model naturally accounts for dark matter being collisionless, and it predicts that dark matter can only emit radiation of one fixed frequency. The values of this frequency are computed for dark matter particles of different masses. A potential observational verification of the theory is also discussed.

Euclid preparation

In this paper we investigate the impact of lensing magnification on the analysis of Euclid’s spectroscopic survey using the multipoles of the two-point correlation function for galaxy clustering. We determine the impact of lensing magnification on cosmological constraints as well as the expected shift in the best-fit parameters if magnification is ignored. We considered two cosmological analyses: (i) a full-shape analysis based on the Λ cold dark matter (CDM) model and its extension w0waCDM and (ii) a model-independent analysis that measures the growth rate of structure in each redshift bin. We adopted two complementary approaches in our forecast: the Fisher matrix formalism and the Markov chain Monte Carlo method. The fiducial values of the local count slope (or magnification bias), which regulates the amplitude of the lensing magnification, have been estimated from the Euclid Flagship simulations. We used linear perturbation theory and modelled the two-point correlation function with the public code coffe. For a ΛCDM model, we find that the estimation of cosmological parameters is biased at the level of 0.4–0.7 standard deviations, while for a w0waCDM dynamical dark energy model, lensing magnification has a somewhat smaller impact, with shifts below 0.5 standard deviations. For a model-independent analysis aimed at measuring the growth rate of structure, we find that the estimation of the growth rate is biased by up to 1.2 standard deviations in the highest redshift bin. As a result, lensing magnification cannot be neglected in the spectroscopic survey, especially if we want to determine the growth factor, one of the most promising ways to test general relativity with Euclid. We also find that, by including lensing magnification with a simple template, this shift can be almost entirely eliminated with minimal computational overhead.

Cosmic insights from galaxy clusters: Exploring magnification bias on sub-millimetre galaxies

Context. Magnification bias, an observational effect of gravitational lensing in the weak regime, allows the cosmological model to be tested through angular correlations of sources at different redshifts. This effect has been observed in various contexts, particularly with sub-millimetre galaxies (SMGs), offering valuable astrophysical and cosmological insights. Aims. The study aims to investigate the magnification bias effect exerted by galaxy clusters on SMGs and its implications for astrophysical and cosmological parameters within the Λ-CDM model. Methods. Magnification bias was explored by quantifying the cross-correlation function, which we then utilised to derive constraints on cosmological and astrophysical parameters with a Markov chain Monte Carlo algorithm. Two distinct galaxy cluster samples were used to assess result robustness and understand the influence of sample characteristics. Results. Cluster samples show higher cross-correlation values than galaxies, with an excess at larger scales suggesting contributions from additional large-scale structures. The parameters obtained, while consistent with those of galaxies, are less constrained due to broader redshift distributions and limited cluster statistics. Results align with weak lensing studies, hinting at slightly lower σ8 and Ωm values than Planck’s cosmic microwave background data, emphasising the need for enhanced precision and alternative low-redshift universe tests. Conclusions. While this method yields constraints that are compatible with the Λ-CDM model, its limitations include broader redshift distributions and a limited number of lenses, resulting in less constrained parameters compared to previous galaxy studies. Nonetheless, our study underscores the potential of using galaxy clusters as lenses for magnification bias studies, capitalising on their elevated masses and thus providing a promising avenue to test current cosmology theories. Further progress can be made by expanding the lens sample size.

Hunting WIMPs with LISA: correlating dark matter and gravitational wave signals

The thermal freeze-out mechanism in its classical form is tightly connected to physics beyond the Standard Model around the electroweak scale, which has been the target of enormous experimental efforts. In this work we study a dark matter model in which freeze-out is triggered by a strong first-order phase transition in a dark sector, and show that this phase transition must also happen close to the electroweak scale, i.e. in the temperature range relevant for gravitational wave searches with the LISA mission. Specifically, we consider the spontaneous breaking of a U(1)′ gauge symmetry through the vacuum expectation value of a scalar field, which generates the mass of a fermionic dark matter candidate that subsequently annihilates into dark Higgs and gauge bosons. In this set-up the peak frequency of the gravitational wave background is tightly correlated with the dark matter relic abundance, and imposing the observed value for the latter implies that the former must lie in the milli-Hertz range. A peculiar feature of our set-up is that the dark sector is not necessarily in thermal equilibrium with the Standard Model during the phase transition, and hence the temperatures of the two sectors evolve independently. Nevertheless, the requirement that the universe does not enter an extended period of matter domination after the phase transition, which would strongly dilute any gravitational wave signal, places a lower bound on the portal coupling that governs the entropy transfer between the two sectors. As a result, the predictions for the peak frequency of gravitational waves in the LISA band are robust, while the amplitude can change depending on the initial dark sector temperature.

Deep Hubble Space Telescope Photometry of Large Magellanic Cloud and Milky Way Ultrafaint Dwarfs: A Careful Look into the Magnitude–Size Relation

We present deep Hubble Space Telescope photometry of 10 targets from Treasury Program GO-14734, including six confirmed ultrafaint dwarf (UFD) galaxies, three UFD candidates, and one likely globular cluster. Six of these targets are satellites of, or have interacted with, the Large Magellanic Cloud (LMC). We determine their structural parameters using a maximum-likelihood technique. Using our newly derived half-light radius (r h ) and V-band magnitude (M V ) values in addition to literature values for other UFDs, we find that UFDs associated with the LMC do not show any systematic differences from Milky Way UFDs in the magnitude–size plane. Additionally, we convert simulated UFD properties from the literature into the M V –r h observational space to examine the abilities of current dark matter (DM) and baryonic simulations to reproduce observed UFDs. Some of these simulations adopt alternative DM models, thus allowing us to also explore whether the M V –r h plane could be used to constrain the nature of DM. We find no differences in the magnitude–size plane between UFDs simulated with cold, warm, and self-interacting DM, but note that the sample of UFDs simulated with alternative DM models is quite limited at present. As more deep, wide-field survey data become available, we will have further opportunities to discover and characterize these ultrafaint stellar systems and the greater low surface-brightness universe.

Forecasts for Galaxy Formation and Dark Matter Constraints from Dwarf Galaxy Surveys

The abundance of faint dwarf galaxies is determined by the underlying population of low-mass dark matter (DM) halos and the efficiency of galaxy formation in these systems. Here, we quantify potential galaxy formation and DM constraints from future dwarf satellite galaxy surveys. We generate satellite populations using a suite of Milky Way (MW)–mass cosmological zoom-in simulations and an empirical galaxy–halo connection model, and assess sensitivity to galaxy formation and DM signals when marginalizing over galaxy–halo connection uncertainties. We find that a survey of all satellites around one MW-mass host can constrain a galaxy formation cutoff at peak virial masses of M50=108M⊙ at the 1σ level; however, a tail toward low M50 prevents a 2σ measurement. In this scenario, combining hosts with differing bright satellite abundances significantly reduces uncertainties on M50 at the 1σ level, but the 2σ tail toward low M50 persists. We project that observations of one (two) complete satellite populations can constrain warm DM models with m WDM ≈ 10 keV (20 keV). Subhalo mass function (SHMF) suppression can be constrained to ≈70%, 60%, and 50% that in cold dark matter (CDM) at peak virial masses of 108, 109, and 1010 M ⊙, respectively; SHMF enhancement constraints are weaker (≈20, 4, and 2 times that in CDM, respectively) due to galaxy–halo connection degeneracies. These results motivate searches for faint dwarf galaxies beyond the MW and indicate that ongoing missions like Euclid and upcoming facilities including the Vera C. Rubin Observatory and Nancy Grace Roman Space Telescope will probe new galaxy formation and DM physics.

GammaBayes: a Bayesian pipeline for dark matter detection with CTA

We present GammaBayes, a Bayesian Python package for dark matter detection with the Cherenkov Telescope Array (CTA).GammaBayes takes as input the CTA measurements of gamma rays and a user-specified dark-matter particle model.It outputs the posterior distribution for parameters of the dark-matter model including the velocity-averaged cross section for dark-matter self interactions 〈σv〉 and the dark-matter mass mχ .It also outputs the Bayesian evidence, which can be used for model selection.We demonstrate GammaBayes using 525 hours of simulated data, corresponding to 108 observed gamma-ray events.The vast majority of this simulated data consists of noise, but 100000 events arise from the annihilation of scalar singlet dark matter with mχ = 1 TeV.We recover the dark matter mass within a 95% credible interval of mχ ∼ 0.96–1.07 TeV.Meanwhile, the velocity averaged cross section is constrained to 〈σv〉 ∼ 1.4–2.1 × 10-25 cm3 s-1 (95% credibility).This is equivalent to measuring the number of dark-matter annihilation events to be NS ∼ 1.1-0.2 +0.2 × 105.The no-signal hypothesis 〈σv〉 = 0 is ruled out with about 5σ credibility.We discuss how GammaBayes can be extended to include more sophisticated signal and background models and the computational challenges that must be addressed to facilitate these upgrades.The source code is publicly available here.

Integrated study of dark matter and dark energy models

Dark matter and dark energy are used as two important concepts in cosmology to explain some of the observed phenomena in the universe. Dark matter is one of the most dominant constituents of the Universe, and it influences the structural formation of the Universe through gravity, including the formation and evolution of galaxies, clusters, and the large-scale structure of the Universe. Dark energy is believed to be one of the causes of the accelerated expansion of the Universe, and its presence explains the observed phenomenon of the accelerating rate of expansion of the Universe. Although their existence has not been directly observed, people understand through the study of the structure and evolution of the universe that they play an important role in the universe. This paper first introduces the background knowledge of dark matter and its related properties and explains the reasons why three types of models, namely WIMP, axion, and sterile neutrino, are candidates for dark matter in the light of existing observations. The paper then discusses the relevant properties of dark energy and analyses the mainstream dark energy models. For the cosmological constant mode, the fine-tuning problem and cosmic coincidence problem it faces are analysed in detail. The evolution of the dark energy equation of state from the past >-1 to the present <-1 is then explained, and this is used to introduce the scalar field model involving dynamic, the Chaplygin gas model, the holographic dark energy model, and the interacting dark energy model.

Simple test with rotation curves for the multistate scalar field dark matter model

Simple test with rotation curves for the multistate scalar field dark matter model

Quantum collider probes of the fermionic Higgs portal

We explore the sensitivity of future hadron colliders to constrain the fermionic Higgs portal, with a focus on scenarios where the new fermions cannot be directly observed in exotic Higgs decays. This portal emerges in various models including twin-Higgs scenarios and dark matter models, posing significant challenges for collider tests. Working in an effective field theory (EFT), we determine the reach of the high-luminosity option of the Large Hadron Collider (HL-LHC), the high-energy upgrade of the LHC (HE-LHC) and a proposed Future Circular Collider (FCC) in probing the fermionic Higgs portal through off-shell and double-Higgs production. Notably, we find that quantum-enhanced indirect probes offer a better sensitivity than other direct Higgs measurements. We argue that this finding is valid in a wide class of ultraviolet realisations of the EFT. Our study presents a roadmap of a multifaceted search strategy for exploring the fermionic Higgs portal at forthcoming hadron machines.

Secluded scalar dark matter and the muon anomalous magnetic moment

Abstract We consider a dark matter model with a singlet scalar, $\chi$, as our dark matter (DM) candidate which is secluded from the Standard Model (SM) and annihilates to the singlet scalar, $\phi$, via a contact interaction. 
The singlet scalar, $\phi$, has a leptophilic interaction with the SM leptons 
and may decay leptonically at tree level, and decays into a pair of photons at loop level. 
The focus in this work is to consider DM masses below 10 GeV. 
It is found a viable secluded region in the parameter space after imposing the observed 
relic density. There is a one-loop interaction between scalar dark matter and the atomic electron in this model. We then apply the available direct detection bounds from Xenon10, Xenon1T, and DarkSide on the DM-electron elastic scattering cross section. While the model can explain the muon anomalous magnetic moment, we put bounds from current and future lepton collider experiments.

The Observer and the General Centrality of Particles

According to the latest cosmological theories, the universe that began expanding with the Big Bang is a homogeneous and isotropic universe whose expansion continues to this day. According to cosmologists, based on this principle, the universe does not have a specific spatial center, and the special geometry considered for this viewpoint necessitates that any point in space can be considered the center of the universe. On the other hand, cosmologists consider the Big Bang as a point on a timeline, not a spatial occurrence. They state that our current best understanding of the origin and evolution of the universe is in line with the Standard Model of Cosmology (SMC), also known as the Lambda-Cold Dark Matter (ΛCDM) model. This model is based on two main theories of physics: General Relativity (GR) and the Standard Model of Particle Physics (SMPP). General Relativity is used to understand how the expansion of the universe is affected by the matter and energy within it, with gravity being the curvature of spacetime caused by the presence of mass and energy. Also, in this theory, a dimensionless quantity can be used to compare the time experienced by different observers in a gravitational field. This dimensionless quantity is often shown as the time dilation factor (Lorentz factor with the symbol γ, gamma). Alongside this theory, the Standard Model of Particle Physics describes the fundamental particles constituting matter and the three forces: electromagnetic, strong nuclear, and weak nuclear, governing the interactions of these particles. In this model, physicists often express time inversely as energy with the unit of giga-electron volts (GeV) and use it as a framework to understand the behavior of various particles in the early universe. Parallel to these theories, T-Consciousness Cosmology introduces the Spherical Cosmos Model (SCM). This model challenges the spatial centrality found in the standard cosmological model, which is based on the principle of isotropy. By doing so, SCM assigns a special place to the Milky Way galaxy, and consequently, to Earth, which is supported by results obtained from measurements and observations made from the depths of the cosmos. In this viewpoint, time is divided into Longitudinal Time and Transverse Time. The type of time defined in the theory of relativity as a four-dimensional intertwined spacetime is introduced here as an Entropic Time Force, which is a subcategory of Transverse Time. This challenges the definitions provided in SMPP or GR, raising questions about whether time should be considered a dimension or a quantity. T-Consciousness Cosmology states that the cosmos and every one of its components are subject to the Taheri Uncertainty Principle, and further considers them as virtual, by virtue of how they are defined by this principle. This principle can be examined from various angles, and in this discussion, it is approached from the perspective of time. On the other hand, the Taheri Uncertainty Principle segues to theories such as the Temporal Centrality of Particles, Time Continuity, and Time Uncertainty based on the special vantage point of the human observer, highlighting the fundamental role of humans in giving meaning to these concepts.

The Shell of the Cosmos

The Big Bang theory, widely accepted by cosmologists, explains the origin, expansion, and eventual fate of the universe. It was further developed by inflation theory, which solves issues like the horizon and flatness problems. This theory states that the Cosmic Microwave Background (CMB), a remnant of the Big Bang, permeates the entire universe. Cosmologists believe these photons were emitted during the recombination epoch, approximately 380,000 years after the Big Bang when the cosmos had a temperature of around 3,000 Kelvin. Additionally, the Lambda-Cold Dark Matter (ΛCDM) model addresses questions arising from observations of the cosmos, such as the existence of light elements like hydrogen, helium, lithium, and the anisotropy in the CMB, and eventually, the continuous expansion of space. In this model, dark energy, represented as the cosmological constant lambda (Λ), exerts negative pressure on empty space, counteracting the effects of gravity with a repulsive force. While the Standard Model of Particle Physics (SMPP) posits that the universe's matter originated from fundamental particles (quarks and leptons), it cannot explain the origin of these particles and how they came into existence, because general relativity and the SMPP cannot be integrated to explain matter production at the singularity point. T-Consciousness Cosmology introduces the ‘Spherical Cosmos Model’ (SCM) to answer questions about the cause of the explosion, expansion, and shape of the universe, the nature of ordinary matter and energy, dark matter and energy, the fate of the universe, the reason for the high density of objects in the depths of space, etc. In this model, the spherical cosmos has a shell called the ‘Shell of the Cosmos,’ made of Taheri Absolute Matter (TAM) that not only isolates it but also produces dark matter and dark energy, ordinary matter and ordinary energy, and finally space mesh from the inner surface to the inside of the cosmos since the birth of the universe. The Shell of this isolated sphere is currently expanding at a speed faster than the speed of light. In this perspective, dark matter and energy are the same space mesh that have been compressed to varying degrees. Dark energy, which is constantly being released from the Shell into the cosmos, unlike the standard model of cosmology, is one of the factors in the expansion of the isolated cosmos by creating positive pressure in it. Also in this model, the recombination epoch will always be located spherically at a certain distance from the Shell until the ultimate stage of Rebound. In other words, not only is the origin of the CMB not related to the past of the cosmos, but it also exists now, and given the vastness of the sphere and the position of the Earth within this sphere, we detect it in the microwave wavelength with a delay of several billion years. Therefore, the observed distant galaxies that have been attributed to the early epochs of the cosmos in the Big Bang model are currently being created by the Shell according to the Spherical Cosmos Model, and we are surrounded by particles and objects that are constantly being produced.

Structure formation with primordial black holes to alleviate early star formation tension revealed by JWST

This Letter explores the potential role of primordial black holes (PBHs) to address cosmological tensions as the presence of more massive than expected galaxies at high redshifts, as indicated by recent James Webb Space Telescope observations. Motivated by inflation models that enhance the power at scales beyond the observable range that produce PBHs with Schechter-like mass functions, we aim to explain the excess of high redshift galaxies via a modification of the Lambda cold dark matter power spectrum that consists in adding (i) a blue spectral index $n_b$ at $k_ piv =10/$Mpc and (ii) Poisson and isocurvature contributions from massive PBHs that only make up $0.5<!PCT!>$ of the dark matter. We simulated these models using the SWIFT code and find an increased abundance of high redshift galaxies in simulations that include PBHs. We compared these models to estimates from James Webb Space Telescope observations. Unlike the Lambda cold dark matter model, the inclusion of PBHs allowed us to reproduce the the observations with reasonable values for the star formation efficiency. Furthermore, the power spectra we adopted potentially produce PBHs that can serve as seeds for supermassive black holes with masses $7.57 odot

Freeze-in at stronger coupling

The predictivity of many nonthermal dark matter (DM) models is marred by the gravitational production background. Nevertheless, if the reheating temperature TR is low, the gravitationally produced relics can be diluted. We study the freeze-in dark matter production mechanism at temperatures below the dark matter mass. In this case, the coupling to the thermal bath has to be significant to account for the observed dark matter relic density. As a result, the direct DM detection experiments already probe such freeze-in models, excluding significant parts of parameter space. Published by the American Physical Society 2024

Cosmological parameters estimated from peculiar velocity–density comparisons: calibrating 2M++

ABSTRACT Cosmological parameters can be measured by comparing peculiar velocities with those predicted from a galaxy density field. Previous work has tested the accuracy of this approach with N-body simulations, but generally on idealized mock galaxy surveys. However, systematic biases may arise solely due to survey selection effects such as flux-limited samples, edge-effects, and complications due to the obscuration of the Galactic plane. In this work, we explore the impact of each of these effects individually as well as collectively using the semi-analytic models from numerical simulations to generate mock catalogues that mimic the 2M++ density field. We find the reconstruction and analysis methods used for our 2M++ mocks produce a value of fσ8 that is biased high by a factor 1.04 ± 0.01 compared to the true value. Moreover, a cosmic volume matching that of 2M++ has a cosmic variance uncertainty in fσ8 of $\sim 5~{{\ \rm per\ cent}}$. The systematic bias is a function of distance: it is unbiased close to the origin but is biased slightly high for distances in the range 100–180 h−1 Mpc. Correcting for this small bias, we find that recent peculiar velocity samples yield $f\sigma _8^{\textrm {lin}} = 0.362\pm 0.023$, a value that is in tension with the extrapolations from cosmic microwave background measurements. The predicted peculiar velocities from 2M++ have an error of 170 km s−1 that slowly increases with distance, exceeding 200 km s−1 only at distances of 180–200 h−1Mpc. Finally, the residual bulk flow speeds found in previous work are shown to be not in conflict with those expected in the Λ cold dark matter model.

Search for supersymmetry in final states with disappearing tracks in proton-proton collisions at s=13 TeV

A search is presented for charged, long-lived supersymmetric particles in final states with one or more disappearing tracks. The search is based on data from proton-proton collisions at a center-of-mass energy of 13 TeV collected with the CMS detector at the CERN LHC between 2016 and 2018, corresponding to an integrated luminosity of 137 fb−1. The search is performed over final states characterized by varying numbers of jets, b-tagged jets, electrons, and muons. The length of signal-candidate tracks in the plane perpendicular to the beam axis is used to characterize the lifetimes of wino- and Higgsino-like charginos produced in the context of the minimal supersymmetric standard model. The dE/dx energy loss of signal-candidate tracks is used to increase the sensitivity to charginos with a large mass and thus a small Lorentz boost. The observed results are found to be statistically consistent with the background-only hypothesis. Limits on the pair-production cross section of gluinos and squarks are presented in the framework of simplified models of supersymmetric particle production and decay, and for electroweakino production based on models of wino and Higgsino dark matter. The limits presented are the most stringent to date for scenarios with light third-generation squarks and a wino- or Higgsino-like dark matter candidate capable of explaining the observed dark matter relic density. © 2024 CERN, for the CMS Collaboration 2024 CERN

Impact of astrophysical effects on the dark matter mass constraint with 21 cm intensity mapping

ABSTRACT We present an innovative approach to constraining the non-cold dark matter model using a convolutional neural network (CNN). We perform a suite of hydrodynamic simulations with varying dark matter particle masses and generate mock 21 cm radio intensity maps to trace the dark matter distribution at z = 3 in the postreionization epoch. Our proposed method complements the traditional power-spectrum analysis. We compare the results of the CNN classification between the mock maps with different dark matter masses with those from the two-dimensional power spectrum of the differential brightness temperature map of 21 cm radiation. We find that the CNN outperforms the power spectrum. Moreover, we investigate the impact of baryonic physics on the dark matter model constraint, including star formation, self-shielding of H i gas, and ultraviolet background model. We find that these effects may introduce some contamination in the dark matter constraint, but they are insignificant compared to the system noise of the SKA instruments.

Probing dark matter with adaptive-optics based flux ratio anomalies: photometric and astrometric precision

ABSTRACT Strong gravitational lensing is a powerful probe of the distribution of matter on sub-kpc scales. It can be used to test the existence of completely dark sub-haloes surrounding galaxies, as predicted by the standard cold dark matter model, or to test alternative dark matter models. The constraining power of the method depends strongly on photometric and astrometric precision and accuracy. We simulate and quantify the capabilities of upcoming adaptive optics systems and advanced instruments on ground-based telescopes, focusing as an illustration on the Keck Telescope (OSIRIS + KAPA, LIGER + KAPA) and the Thirty Meter Telescope (TMT; IRIS + NFIRAOS). We show that these new systems will achieve dramatic improvements over current ones in both photometric and astrometric precision. Narrow line flux ratio errors below 2 per cent, and submilliarcsecond astrometric precision will be attainable for typical quadruply imaged quasars. With TMT, the exposure times required will be of order a few minutes per system, enabling the follow-up of 100–1000 systems expected to be discovered by the Rubin, Euclid, and Roman Telescopes.

Baryogenesis and dark matter in multiple hidden sectors

We explore a mechanism for producing the baryon asymmetry and dark matter in models with multiple hidden sectors that are Standard-Model-like but with varying Higgs mass parameters. If the field responsible for reheating the Standard Model and the exotic sectors carries an asymmetry, it can be converted into a baryon asymmetry using the standard sphaleron process. A hidden sector with positive Higgs mass squared can accommodate dark matter with its baryon asymmetry, and the larger abundance of dark matter relative to baryons is due to dark sphalerons being active all the way down the hidden sector QCD scale. This scenario predicts that dark matter is clustered in large dark nuclei and gives a lower bound on the effective relativistic degrees of freedom, ΔNeff≳0.05, which may be observable in the next-generation cosmic microwave background experiment CMB-S4. Published by the American Physical Society 2024