Hubble Tension Research Articles

No-go guide for the Hubble tension: Late-time or local-scale new physics

No-go guide for the Hubble tension: Late-time or local-scale new physics

Hints of New Physics for the Hubble Tension: Violation of Cosmological Principle

Discrepancy between the measurements of Hubble constant H 0 from the cosmic microwave background and the local distance ladder is the most serious challenge to the standard ΛCDM model. Recent research has pointed out that it might be related with the violation of cosmological principle. Here, we investigate the impact of dipole–monopole correction on the constraints of H 0 utilizing the dipole-fitting method based on the ΛCDM model and cosmography method. Our results show that the dipole–monopole correction can reduce the constraints of H 0 from a larger value consistent with SH0ES results to a smaller value consistent with Planck results. This finding can effectively alleviate the Hubble tension. Through making redshift tomography and model-independent analyses, we confirm that our findings are independent of the redshift and cosmological model. In addition, the theoretical prediction of H(z)/(1 + z) reconstructed by the constraints of the ΛCDM model with the dipole correction is in agreement with baryon acoustic oscillation (BAO) measurements, including five Dark Energy Spectroscopic Instrument BAOs within the 1σ range except a data point at z = 0.51. Our research suggests that the Hubble tension originates from new physics beyond the standard ΛCDM model, which might lead to a violation of the cosmological principle.

Neutron Stars constraints on a late G transition

It has been suggested recently that the Hubble tension could be eliminated by a sharp, ∼10% increase of the effective gravitational constant at z∼0.01. This would decrease the luminosities of type 1a supernovae in just the needed amount to explain the larger value of the Hubble parameter. In the present paper we call attention to a dramatic effect of such transition on neutron stars. A neutron star that existed at z=0.01 would contract, conserving the baryon mass but undergoing a mass reduction. We computed neutron star models, with a realistic equation of state, and obtained that this reduction is typically 0.04M⊙. This amounts to an energy of 7×1052 erg. The transition will affect all neutron stars that formed along the history of each galaxy prior to the transition. Given the large number of neutron stars per galaxy, the liberated energy is huge. An estimate of the expected fluxes of neutrinos and x-rays yields values exceeding observational upper limits, thus rendering the late G transition scenario non-viable.

Updated Cosmological Constraints in Extended Parameter Space with Planck PR4, DESI Baryon Acoustic Oscillations, and Supernovae: Dynamical Dark Energy, Neutrino Masses, Lensing Anomaly, and the Hubble Tension

We present updated constraints on cosmological parameters in a 12-parameter model, extending the standard six-parameter ΛCDM by including dynamical dark energy (DE; w 0, w a ), the sum of neutrino masses (∑m ν ), the effective number of non-photon radiation species (N eff), the lensing amplitude scaling (A lens), and the running of the scalar spectral index (α s ). For cosmic wave background (CMB) data, we use the Planck Public Release (PR) 4 (2020) HiLLiPoP and LoLLiPoP likelihoods, Planck PR4+Atacama Cosmology Telescope (ACT) DR6 lensing, and Planck 2018 low-ℓ TT likelihoods, along with DESI DR1 baryon acoustic oscillations (BAO) and Pantheon+ and DESY5 uncalibrated Type Ia supernovae (SNe) likelihoods. Key findings are the following: (i) Contrary to DESI results, CMB+BAO+Pantheon+ data include a cosmological constant within 2σ, while CMB+BAO+DESY5 excludes it at over 2σ, indicating the dynamical nature of DE is not yet robust. Potential systematics in the DESY5 sample may drive this exclusion. (ii) Some data combinations show a 1σ+ detection of nonzero ∑m ν , indicating possible future detection. We also provide a robust upper bound of ∑m ν ≲ 0.3 eV (95% confidence limit (CL)). (iii) With CMB+BAO+SNe, A lens = 1 is included at 2σ (albeit not at 1σ), indicating no significant lensing anomaly in this extended cosmology with Planck PR4 likelihoods. (iv) The Hubble tension persists at 3.2 to 3.9σ, suggesting these simple extensions do not resolve it. (v) The S 8 tension with Dark Energy Survey Year 3 weak lensing is reduced to 1.4σ, likely due to additional parameters and the Planck PR4 likelihoods.

DESI observations and the Hubble tension in light of modified recombination

DESI observations and the Hubble tension in light of modified recombination

Cascading Dark Energy

The standard cosmological model is in the midst of a stress test, thanks to the tension between supernova-based measurements of the Hubble constant H 0 and inferences of its values from cosmic microwave background (CMB) anisotropies. Numerous explanations for the present-day cosmic acceleration require the presence of a new fundamental scalar field, as do early dark energy solutions to the Hubble tension. This raises the possibility that multiple fields cooperatively contribute to the dark energy component in bursts throughout cosmic time due to distinct initial conditions and couplings. Here, this cascading dark energy scenario is illustrated through a realization that effectively reduces to a two-field model, with two epochs in which dark energy is cosmologically significant. The model is compared to measurements of the CMB and baryon acoustic oscillations, as well as both PANTHEON and SH0ES observations of Type Ia supernovae. Neglecting the linear perturbations, it is found that this scenario ameliorates the Hubble tension, improving over purely late-time models of dark energy and the agreement between the galaxy survey measurements of baryon acoustic oscillations.

2D BAO vs. 3D BAO: Solving the Hubble Tension with Bimetric Cosmology

Ordinary 3D Baryon Acoustic Oscillations (BAO) data are model-dependent, requiring the assumption of a cosmological model to calculate comoving distances during data reduction. Throughout the present-day literature, the assumed model is ΛCDM. However, it has been pointed out in several recent works that this assumption can be inadequate when analyzing alternative cosmologies, potentially biasing the Hubble constant (H0) low, thus contributing to the Hubble tension. To address this issue, 3D BAO data can be replaced with 2D BAO data, which are only weakly model-dependent. The impact of using 2D BAO data, in combination with alternative cosmological models beyond ΛCDM, has been explored for several phenomenological models, showing a promising reduction in the Hubble tension. In this work, we accommodate these models in the theoretically robust framework of bimetric gravity. This is a modified theory of gravity that exhibits a transition from a (possibly) negative cosmological constant in the early universe to a positive one in the late universe. By combining 2D BAO data with cosmic microwave background and type Ia supernovae data, we find that the inverse distance ladder in this theory yields a Hubble constant of H0=(71.0±0.9)km/s/Mpc, consistent with the SH0ES local distance ladder measurement of H0=(73.0±1.0)km/s/Mpc. Replacing 2D BAO with 3D BAO results in H0=(68.6±0.5)km/s/Mpc from the inverse distance ladder. We conclude that the choice of BAO data significantly impacts the Hubble tension, with ordinary 3D BAO data exacerbating the tension, while 2D BAO data provide results consistent with the local distance ladder.

Reheating Constraints and the H0 Tension in Quintessential Inflation

In this work, we focus on two important aspects of modern cosmology: reheating and Hubble constant tension within the framework of a unified cosmic theory, namely the quintessential inflation connecting the early inflationary era and late-time cosmic acceleration. In the context of reheating, we use instant preheating and gravitational reheating, two viable reheating mechanisms when the evolution of the universe is not affected by an oscillating regime. After obtaining the reheating temperature, we analyze the number of e-folds and establish its relationship with the reheating temperature. This allows us to connect, for different quintessential inflation models (in particular for models coming from super-symmetric theories such as α-attractors), the reheating temperature with the spectral index of scalar perturbations, thereby enabling us to constrain its values. In the second part of this article, we explore various alternatives to address the H0 tension. From our perspective, this tension suggests that the simple Λ-Cold Dark Matter model, used as the baseline by the Planck team, needs to be refined in order to reconcile its results with the late-time measurements of the Hubble constant. Initially, we establish that quintessential inflation alone cannot mitigate the Hubble tension by solely deviating from the concordance model at low redshifts. The introduction of a phantom fluid, capable of increasing the Hubble rate at the present time, becomes a crucial element in alleviating the Hubble tension, resulting in a deviation from the Λ-Cold Dark Matter model only at low redshifts. On a different note, by utilizing quintessential inflation as a source of early dark energy, thereby diminishing the physical size of the sound horizon close to the baryon–photon decoupling redshift, we observe a reduction in the Hubble tension. This alternative avenue, which has the same effect of a cosmological constant changing its scale close to the recombination, sheds light on the nuanced interplay between the quintessential inflation and the Hubble tension, offering a distinct perspective on addressing this cosmological challenge.

Axion baryogenesis puts a new spin on the Hubble tension

We show that a rotating axion field that makes a transition from a matterlike equation of state to a kinationlike equation of state around the epoch of recombination can significantly ameliorate the Hubble tension, i.e., the discrepancy between the determinations of the present-day expansion rate H0 from observations of the cosmic microwave background on one hand and type Ia supernovae on the other. We consider a specific, UV-complete model of such a rotating axion and find that it can relax the Hubble tension without exacerbating tensions in determinations of other cosmological parameters, in particular the amplitude of matter fluctuations S8. We subsequently demonstrate how this rotating axion model can also generate the baryon asymmetry of our Universe, by introducing a coupling of the axion field to right-handed neutrinos. This baryogenesis model predicts heavy neutral leptons that are most naturally within reach of future lepton colliders, but in finely tuned regions of parameter space may also be accessible at the high-luminosity LHC and the beam dump experiment SHiP. Published by the American Physical Society 2024

The model of the local Universe in the framework of the second-order perturbation theory

Abstract Recently, we constructed the specific solution to the second-order cosmological perturbation theory, around any Friedmann–Lema\^itre–Robertson–Walker (FLRW) background filled with dust matter and a positive cosmological constant. In this paper, we use the {\it Cosmicflows-4} (CF4) sample of galaxies from the Extragalactic Distance Database to constrain this metric tensor. We obtain an approximation to the local matter distribution and geometry. We numerically solve for null geodesics for randomly distributed mock sources and compare this model with the Lema\^itre-Hubble constant inferred from the observations under the assumption of perfect isotropy and homogeneity. We conclude on effects of realistic inhomogeneities on the luminosity distance in the context of the Hubble tension and discuss limitations of our approach.

Investigating the Hubble tension and σ 8 discrepancy in f(Q) cosmology

In this study, we incorporated a three-parameter family, of the metric incompatible modification of standard general relativity ω models into the Boltzmann code MGCLASS at both the background and perturbation levels, in order to conduct a Bayesian study employing probes that include the cosmic microwave background (CMB), baryon acoustic oscillations (BAO), weak lensing (WL), alone or its correlation with galaxy clustering (3×2pt) and growth measurements f σ 8, for each submodel. Our analysis focused on the impact of the Hubble tension in H 0 and the discrepancy in σ 8 resulting from the inclusion of our model's parameters, namely M, α and β. We find that none of the sub models, considered alone or combined, were able of alleviating the Hubble tension with only reducing it to 3 σ in the least constraining, highest degree of freedom case while we found that the σ 8 discrepancy, already strongly mitigated on WL linear scales, especially when we let all our model's parameters as free, appears again when considering the more constraining 3×2pt probe. Among the parameters considered, we found that β, acting in scaling both the gravitational and the Hubble parameter, had the most impact in reducing the discrepancy, with data preferring far from ΛCDM alike values, before the combination with fσ 8 constrain it back to its general relativity values.

Alleviating the Hubble tension using the Barrow holographic dark energy cosmology with Granda–Oliveros IR cut-off

ABSTRACT In this study, we investigate the Barrow holographic dark energy (BHDE) model with the Granda–Oliveros(G–O) infrared (IR) cut-off in the presence of neutrino masses, utilizing the latest observational data to address the Hubble tension. The GO cut-off is defined as $L_{\mathrm{ IR}}=(\alpha H^2 + \beta \dot{H})^{-1/2}$. We place constraints on the total neutrino mass $\sum m_{\nu }$ using data from Type Ia supernovae (SN) Pantheon, cosmic chronometers (CC), cosmic microwave background (CMB), Baryon Acoustic Oscillation (BAO) data sets, and Planck Lensing. Specifically, the comprehensive CMB + BAO + CC + Pantheon data set provides a total neutrino mass of $0.118\, \text{eV}$. The parameters for the Barrow-GO model are determined to be $\Delta = 0.0055^{+0.0086}_{-0.0086}$, $\alpha = 0.997^{+0.060}_{-0.060}$, and $\beta = 0.598^{+0.080}_{-0.080}$, showing good agreement with previous studies. One of the key findings of this study is the model’s ability to alleviate the Hubble tension, as evidenced by the comparison of $H_0$ measurements. Specifically, the tension value for the combination of data set (CMB + BAO + CC + Pantheon + Lensing) is $1.5\sigma$ with the Planck 2018 and $1.4\sigma$ with R22. These results underscore the importance of multi-data set integration in refining constraints on neutrino properties and highlight the model’s efficacy in probing fundamental aspects of neutrino physics. Our results demonstrate that the BHDE model with the GO cut-off can effectively address the Hubble tension, offering a coherent framework that reconciles local and cosmological measurements of the Hubble constant.

Sound horizon independent constraints on early dark energy: the role of supernova data

We assess the consistency of cosmological models that alter the size of the sound horizon at last scattering to resolve the Hubble tension with data from ACT + Planck CMB lensing, Big Bang Nucleosynthesis, and supernova data from Pantheon or Pantheon+. We use early dark energy (EDE) as an example model but conclude that the results could apply to other similar models. We constrain ΛCDM and EDE with these data finding that while they can constrain ΛCDM very tightly, EDE opens up the parameter space significantly and allows H 0 > 72 km s-1Mpc-1. We combine these data with measurements from ACT + Planck TT650TEEE CMB primary anisotropy and galaxy baryon acoustic oscillations, and find that overall, EDE fits these data better than ΛCDM at ≈ 2σ. However, the fit to specifically the sound-horizon-independent measurements is worse for EDE than ΛCDM. We assess this increase in χ 2 coming from the sound-horizon-independent measurements and find that the best-fit model is still consistent with a random statistical fluctuation even with H 0 values around 72 km s-1Mpc-1. Finally, we find that supernova data play an important role in constraining EDE-like models with higher preferred values of Ω m , as preferred by Pantheon+, reducing the allowed parameter space for H 0 values greater than 70 km s-1Mpc-1.

Evaluating extensions to LCDM: an application of Bayesian model averaging and selection

We present a powerful and innovative statistical framework to address key cosmological questions about the universe's fundamental properties, performing Bayesian model averaging (BMA) and model selection. Utilizing this framework, we systematically explore extensions beyond the standard ΛCDM model, considering a varying curvature density parameter ΩK, a spectral index ns = 1 and a varying n run, a constant dark energy equation of state (EOS) w 0CDM and a time-dependent one w 0 w aCDM. We also assess cosmological data against a varying effective number of neutrino species N eff. Our analysis incorporates data from various combinations of cosmic microwave background (CMB) data from the latest Planck PR4 analysis, CMB lensing from Planck 2018, baryonic acoustic oscillations (BAO), and the Bicep-KECK 2018 results.We reinforce the standard ΛCDM model statistical preference when combining CMB data withCMB lensing, BAO, and Bicep-KECK 2018 data against the K-ΛCDM model anddns /d ln k-ΛCDM with a probability > 80%. Whenevaluating the dark energy EOS, we find that this dataset does not exhibit a strong preferencebetween the standard ΛCDM model and the constant dark energy EOS model w 0CDM,with a model posterior probability distribution of approximately ≈ 40%:60% in favour of w 0CDM, while the time-varying dark energy EOS model only holds below 1%probability. We find a similar result also when considering the N eff-ΛCDM model, with asplit probability almost 50%-50% from both our datasets.Overall, our application of BMA reveals that including model uncertainty in these cases does notsignificantly impact the Hubble tension, showcasing BMA's robustness and utility in cosmologicalmodel evaluation.

Aspects of Everpresent Λ. Part II. Cosmological tests of current models

This paper investigates Everpresent Λ, a stochastic dark energy model motivated by causal set theory and unimodular gravity, and confronts it with two key observational data sets, Supernova Ia (SN Ia) and Cosmic Microwave Background (CMB) data. A key feature of this model is that Λ fluctuates over time and on average the magnitude of its fluctuations is of the order of the dominant energy density (be it radiation or matter) for the given epoch. In particular, we focus on a phenomenological implementation of Everpresent Λ known as Model 1. The random fluctuations in Everpresent Λ realizations are generated using seed numbers, and we find that for a small fraction of seeds Model 1 is capable of producing realizations that fit SN Ia data better than ΛCDM. We further investigate what features distinguish these realizations from the more general behaviour, and find that the “good” realizations have relatively small fluctuations at low redshifts (z < 1.5), which do not closely track the matter density. We find that Model 1 struggles to improve on ΛCDM at describing the CMB data. However, by suppressing the values of Λ near the last scattering surface, as suggested in [1], we find a large improvement in the best fit of the model, though still with a χ 2 value much larger than that of ΛCDM. We also study the allowed variation of the dark energy density by the CMB constraints in a more model-independent manner, and find that some variation (especially prior to recombination) is possible and in fact can lead to improvement over ΛCDM and reduce the Hubble tension, in line with some early dark energy proposals. However, for the kinds of variations considered, the favoured fluctuations are smaller in magnitude than is typical in current Everpresent Λ models.

Higgs inflation via a metastable standard model potential, generalised renormalisation frame prescriptions and predictions for primordial gravitational waves

Higgs Inflation via a metastable Standard Model Higgs Potential is possible if the effective Planck mass in the Jordan frame increases after inflation ends. Here we consider the predictions of this model independently of the dynamics responsible for the Planck mass transition. The classical predictions are the same as for conventional Higgs Inflation. The quantum corrections are dependent upon the conformal frame in which the effective potential is calculated. We generalise beyond the usual Prescription I and II renormalisation frame choices to include intermediate frames characterised by a parameter α. We find that the model predicts a well-defined correlation between the values of the scalar spectral index ns and tensor-to-scalar ratio r. For values of ns varying between the 2-σ Planck observational limits, we find that r varies between 0.002 and 0.005 as ns increases, compared to the classical prediction of 0.003. Therefore significantly larger or smaller values of r are possible, which are correlated with larger or smaller values of ns . In addition, the model can be compatible with the larger values of ns predicted by Early Dark Energy solutions to the Hubble tension, with correspondingly larger values of r. The model can be tested via the detection of primordial gravitational waves by the next generation of CMB polarisation experiments.

Estimation of the Hubble constant using Gaussian process regression and viable alternatives

A well-known problem in cosmology is the ‘Hubble tension’ problem, i.e. different estimates for the Hubble constant H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} are not concordant with each other. This work investigates different statistical methods for estimating this value using cosmic chronometer, type Ia supernova and baryonic acoustic data. We start by making use of methods already established in the literature for this purpose, namely Gaussian process regression and Markov chain Monte Carlo (MCMC) methods based on the concordance Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document}CDM model. We also consider two novel approaches; the first makes use of non-parametric MCMC inference on the hyperparameters of a Gaussian process kernel, independently of any cosmological model. The second approach is Student’s t-process regression, which is a generalised version of Gaussian process regression that makes use of the multivariate Student’s t-distribution instead of the multivariate Gaussian distribution. We also consider variants of these two methods which account for heteroscedasticity within the data. A comparison of the different approaches is made. In particular, the model-independent techniques investigated mostly agree with predictions based on the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document}CDM model. Moreover, Gaussian process regression is highly sensitive to the prior specification, while Student’s t-process regression and the heteroscedastic variants of both methods are more robust to this. Student’s t-process regression and both heteroscedastic models suggest a lower value of the Hubble constant. Across all the estimates obtained for the Hubble constant within this work, the median value is H^0med=68.85±1.67\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{H}_0^{med} = 68.85 \\pm 1.67$$\\end{document} km s-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document} Mpc-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document}.

Changing CO bands in near-IR spectra of CP Cephei

ABSTRACT We present time-series near-infrared spectra for the classical Cepheid, CP Cephei, from the Astrophysical Research Consortium 3.5-m telescope and near-infrared spectrograph, TripleSpec, at Apache Point Observatory, NM, USA. Spectral observations were made at nine points through the minimum and partway up the ascending portion of the optical light curve for the star. Carbon monoxide (CO) was detected in absorption in the 2.3-$\mu$m region for each observation. We measured the strength of CO absorption using the 2-0 band head in the feature for each observation and confirm that the CO varies with pulsation. We show that these measurements follow the $(J-K)$ colour curve, confirming that temperature drives the destruction of CO. By obtaining convolved filter magnitudes from the spectral data we found that the effect of the CO feature on K magnitudes is small, unlike the CO feature in the mid-infrared at 4.5 $\mu$m. The dissociation of CO in the near-infrared spectra tracks with the effect seen in the mid-infrared photometric measurements of a similar Galactic Cepheid. Confirmation of the varying CO feature illustrates the need for further investigations into the related mid-infrared period–colour–metallicity relation in order to address the impact of Cepheid metallicities on the Hubble tension.

Exploring the Hubble tension with a late time Modified Gravity scenario

We investigate a modified cosmological model aimed at addressing the Hubble tension, considering revised dynamics in the late Universe. The model introduces a parameter c affecting the evolution equations, motivated by a modified Poisson algebra inspired by effective Loop Quantum Cosmology. Our analysis includes diverse background datasets such as Cosmic Chronometers, Pantheon+ Type Ia Supernovae (with and without the SH0ES calibration), SDSS, DESY6 and DESI Baryon Acoustic Oscillations, and background information of the Cosmic Microwave Background. We find that the model alleviates the Hubble tension in most of the dataset combinations, with cases reducing discrepancies to below 1σ when including SH0ES. However, the model exhibits minimal improvement in the overall fit when compared to ΛCDM, and Bayesian evidence generally favors the standard model. Theoretical foundations support this approach as a subtle adjustment to low-redshift dynamics, suggesting potential for further exploration into extensions of ΛCDM. Despite challenges in data fitting, our findings underscore the promise of small-scale modifications in reconciling cosmological tensions.

Testing the coupling of dark radiations in light of the Hubble tension

We are studying the effects of Self-Interacting dark radiation (SIdr) on the evolution of the universe. Our main focus is on the cosmic microwave background (CMB) and how SIdr could potentially help resolve the Hubble tension. We are looking into different scenarios by mixing SIdr with Free-Streaming dark radiation (FSdr) or not to determine whether SIdr can indeed contribute to solving the Hubble tension. We find that SIdr alone can increase the Hubble constant (H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document}) to 70.1-1.6+1.3,km/s/Mpc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$70.1_{-1.6}^{+1.3}, \ ext {km/s/Mpc}$$\\end{document} with a value of Neff=3.27-0.31+0.23\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_\ extrm{eff}=3.27_{-0.31}^{+0.23}$$\\end{document}. However, including FSdr disfavors the existence of SIdr N~si≈0.37\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ilde{N}}_\ extrm{si}\\approx 0.37$$\\end{document}. Even though the Hubble constant is increased compared to the predicted value, it entails Neff=3.52±0.25\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_\ extrm{eff}=3.52\\pm 0.25$$\\end{document}. Finally, we implement the Fisher method for future experiments and a 7.64σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$7.64\\sigma $$\\end{document} measurement of N~si\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ilde{N}}_\ extrm{si}$$\\end{document} will be obtained when combing data from Planck, AliCPT, and CMB-S4.