Cosmic Microwave Background Data Research Articles

Measuring the reionization optical depth without large-scale CMB polarization

We study the possibility of measuring the optical depth at reionization τ without relying on large-scale cosmic microwave background (CMB) polarization. Our analysis is driven by the need to obtain competitive measurements that can validate the state-of-the-art constraints on this parameter, widely based on E-mode polarization measurements at ℓ≤30. This need is partially motivated by the typical concerns regarding anomalies observed in the Planck large-scale CMB data as well as by the remarkable fact that, excluding these latter, τ consistently exhibits correlations with anomalous parameters, such as Alens and Ωk, suggesting that slightly higher values of the optical depth at reionization could significantly alleviate or even eliminate anomalies. Within the Λ cold dark matter model, our most constraining result is τ=0.080±0.012, obtained by combining Planck temperature and polarization data at ℓ>30, the Atacama Cosmology Telescope (ACT) and Planck measurements of the lensing potential, baryon acoustic oscillations (BAOs), and type-Ia supernova data from the Pantheon+catalog. Notably, using only ACT temperature, polarization, and lensing data in combination with BAOs and supernovae, we obtain τ=0.076±0.015, which is entirely independent of Planck. The relative precision of these results is approaching the constraints based on large-scale CMB polarization (τ=0.054±0.008). Despite the overall agreement, we report a slight 1.8σ shift toward larger values of τ. We also test how these results change by extending the cosmological model. While in many extensions they remain robust, in general, obtaining precise measurements of τ may become significantly more challenging. Published by the American Physical Society 2024

High-accuracy emulators for observables in ΛCDM, Neff, Σmν, and w cosmologies

Abstract We use the emulation framework CosmoPower to construct and publicly release neural network emulators of cosmological observables, including the Cosmic Microwave Background (CMB) temperature and polarization power spectra, matter power spectrum, distance-redshift relation, baryon acoustic oscillation (BAO) and redshift-space distortion (RSD) observables, and derived parameters. We train our emulators on Einstein-Boltzmann calculations obtained with high-precision numerical convergence settings, for a wide range of cosmological models including ΛCDM, wCDM, ΛCDM+Neff, and ΛCDM+Σmν. Our CMB emulators are accurate to better than 0.5% out to ℓ = 104 which is sufficient for Stage-IV data analysis, and our P(k) emulators reach the same accuracy level out to k = 50 Mpc−1, which is sufficient for Stage-III data analysis. We release the emulators via an online repository (CosmoPower Organisation), which will be continually updated with additional extended cosmological models. Our emulators accelerate cosmological data analysis by orders of magnitude, enabling cosmological parameter extraction analyses, using current survey data, to be performed on a laptop. We validate our emulators by comparing them to class and camb and by reproducing cosmological parameter constraints derived from Planck TT, TE, EE, and CMB lensing data, as well as from the Atacama Cosmology Telescope Data Release 4 CMB data, Dark Energy Survey Year-1 galaxy lensing and clustering data, and Baryon Oscillation Spectroscopic Survey Data Release 12 BAO and RSD data.

The quest for CMB signatures of conformal cyclic cosmology

Circles of low-variance and Hawking points in the Cosmic Microwave Background (CMB), resulting from black hole mergers and black hole evaporation, respectively, in a previous cycle of the universe, have been predicted as possible evidence for the Conformal Cyclic Cosmology model (CCC) introduced by R. Penrose. We present a high-resolution search for such low-variance circles in the Planck and WMAP CMB data, and introduce HawkingNet, our machine learning open-source software based on a ResNet18 algorithm, to search for Hawking points in the CMB.We find that spots consisting of a few unusually bright (high-temperature) or dark (low-temperature) pixels, erroneously lead to regions with many low-variance circles, and consequently sets of near-concentric low-variance circles, when applying the search criteria used in previous work [1]. After removing those spots from the data, no statistically significant low-variance circles can be found.Concerning Hawking points, also no statistically significant evidence is found when using a Gaussian temperature amplitude model over ∼ 1° opening angle and after accounting for spots of unusual brightness.That the unusual spots in the data are themselves remnants of Hawking points is not supported by low-variance and/or low-temperature circles around them.The absence of such statistically-significant distinct features in the currently available CMB data does not disprove the CCC model, but implies that higher resolution CMB data and/or refined CCC based predictions are needed to pursue the search for CCC signatures further.

Constraints on cosmological models from quasars calibrated with type Ia supernova by a Gaussian process

Abstract In this paper, we use quasars calibrated from type Ia supernova (SN Ia) to constrain cosmological models. We consider three different X-ray luminosity (LX) - ultraviolet luminosity (LUV) relations of quasars, i.e. the standard LX − LUV relation and two redshift-evolutionary relations (Type I and Type II) respectively constructed from copula and considering a redshift correction to the luminosity of quasars. Only in the case of the Type I relation, quasars can always provide effective constraints on the ΛCDM model. Furthermore, we show that, when the observational Hubble data (OHD) are added, the constraints on the absolute magnitude M of SN Ia and the Hubble constant H0 can be obtained. In the ΛCDM model, the OHD measurements plus quasars with the Type I relation yields M =$-19.321^{+0.085}_{-0.076}$, which is in good agreement with the measurement from SH0ES (M = −19.253 ± 0.027), and H0 = 70.80 ± 3.6 km s−1 Mpc−1, falling between the measurements from SH0ES and the Planck cosmic microwave background radiation data.

Parameter space of leptogenesis in polynomial inflation

Polynomial inflation is a very simple and well motivated scenario. A potential with a concave “almost” saddle point at field value ϕ = ϕ 0 fits well the cosmic microwave background (CMB) data and makes testable predictions for the running of the spectral index and the tensor to scalar ratio. In this work we analyze leptogenesis in the polynomial inflation framework. We delineate the allowed parameter space giving rise to the correct baryon asymmetry as well as being consistent with data on neutrino oscillations. To that end we consider two different reheating scenarios. (i) If the inflaton decays into two bosons, the reheating temperature can be as high as  T rh ∼ 1014 GeV without spoiling the flatness of the potential, allowing vanilla N 1 thermal leptogenesis to work if  T rh > M 1 where N 1 is the lightest right-handed neutrino and  M 1 its mass. Moreover, if the dominant decay of the inflaton is into Higgs bosons of the Standard Model, we find that rare three-body inflaton decays into a Higgs boson plus one light and one heavy neutrino allow leptogenesis even for T rh < M 1 if the inflaton mass is of order 1012 GeV or higher; in the polynomial inflation scenario this requires ϕ 0 ≳ 2.5 MP . This novel mechanism of non-thermal leptogenesis is quite generic, since the coupling leading to the three-body final state is required in the type I see-saw mechanism. (ii) If the inflaton decays into two fermions, the flatness of the potential implies a lower reheating temperature. In this case inflaton decay to two N 1  still allows successful non-thermal leptogenesis if  ϕ 0 ≳ 0.1 MP and T rh ≳ 106 GeV.

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.

Searching for local features in primordial power spectrum using genetic algorithms

Abstract We present a novel methodology for exploring local features directly in the primordial power spectrum using a genetic algorithm (GA) pipeline coupled with a Boltzmann solver and Cosmic Microwave Background data (CMB). After testing the robustness of our pipeline using mock data, we apply it to the latest CMB data, including Planck 2018 and CamSpec PR4. Our model-independent approach provides an analytical reconstruction of the power spectra that best fits the data , with the unsupervised machine learning algorithm exploring a functional space built off simple ‘grammar’ functions. We find significant improvements upon the simple power-law behaviour, by Δχ2 ≲ −21, consistently with more traditional model-based approaches. These best-fits always address both the low-ℓ anomaly in the TT spectrum and the residual high-ℓ oscillations in the TT, TE and EE spectra. The proposed pipeline provides an adaptable tool for exploring features in the primordial power spectrum in a model-independent way, providing valuable hints to theorists for constructing viable inflationary models that are consistent with the current and upcoming CMB surveys.

Probing the physics of reionization using kinematic Sunyaev–Zeldovich power spectrum from current and upcoming cosmic microwave background surveys

ABSTRACT The patchiness in the reionization process alters the statistics of cosmic microwave background (CMB), with the kinematic Sunyaev–Zeldovich (kSZ) effect in the CMB temperature power spectrum being a notable consequence. In this work, we aim to explore the potential of future kSZ power spectrum measurements in inferring the details of the reionization process. In this pursuit, we capitalize on the recent developments in foreground mitigation techniques using the Cross-Internal Linear Combination (Cross-ILC) technique, which enables robust detection of the kSZ power spectrum with signal-to-noise ratio roughly 20σ–30σ in this decade by South pole Telescope (SPT-3G) and Simons Observatory (SO); and ≥80σ by CMB-S4 – substantially improving on the recent evidence for kSZ binned at ℓ = 3000 using SPT-SZ + SPTpol surveys. We use a fiducial kSZ power spectrum along with realistic error bars expected from the above technique for SPT-3G, SO, and CMB-S4 to constrain the parameter space for a physical model of reionization. We find that with the improved error bars it will be possible to place stringent constraints on reionization using solely the Cross-ILC recovered SPT-3G kSZ without imposing any prior on τ in the Bayesian inference. Notably, high-fidelity kSZ measurements from CMB-S4 coupled with τ measurements through LiteBIRD will enable unprecedented constraint on the midpoint of reionization with an error bar of ∼0.25 and the duration of reionization with an error bar at ∼0.21 exclusively using CMB data. This study highlights the need to capture kSZ power spectrum on a broad range of multipoles to gain insights into the inhomogeneous reionization era.

21 cm intensity mapping cross-correlation with galaxy surveys: Current and forecasted cosmological parameters estimation for the SKAO

ABSTRACT We present a comprehensive set of forecasts for the cross-correlation signal between 21 cm intensity mapping and galaxy redshift surveys. We focus on the data sets that will be provided by the SKAO for the 21 cm signal, DESI and Euclid for galaxy clustering. We build a likelihood which takes into account the effect of the beam for the radio observations, the Alcock–Paczynski effect, a simple parametrization of astrophysical nuisances, and fully exploit the tomographic power of such observations in the range z = 0.7–1.8 at linear and mildly non-linear scales (k &amp;lt; 0.25h Mpc−1). The forecasted constraints, obtained with Monte Carlo Markov Chains techniques in a Bayesian framework, in terms of the six base parameters of the standard ΛCDM model, are promising. The predicted signal-to-noise ratio for the cross-correlation can reach ∼50 for z ∼ 1 and k ∼ 0.1h Mpc−1. When the cross-correlation signal is combined with current Cosmic Microwave Background (CMB) data from Planck, the error bar on $\Omega _{\rm c}\, h^2$ and H0 is reduced by factors 3 and 6, respectively, compared to CMB only data, due to the measurement of matter clustering provided by the two observables. The cross-correlation signal has a constraining power that is comparable to the autocorrelation one and combining all the clustering measurements a sub-per cent error bar of 0.33 per cent on H0 can be achieved, which is about a factor 2 better than CMB only measurements. Finally, as a proof of concept, we test the full pipeline on the real data measured by the MeerKat collaboration (Cunnington et al. 2022) presenting some (weak) constraints on cosmological parameters.

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

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. 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 Lambda cold dark matter model. 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. 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 $ and $ values than Planck 's cosmic microwave background data, emphasising the need for enhanced precision and alternative low-redshift universe tests. While this method yields constraints that are compatible with the Lambda cold dark matter 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.

Exploring modified gravity: constraints on the μ and Σ parametrization with WMAP, ACT, and SPT

ABSTRACT The cosmic acceleration problem remains one of the most significant challenges in cosmology. One of the proposed solutions to this problem is the modification of gravity on large scales. In this paper, we explore the well-known μ–Σ parametrization scenarios and confront them with observational data, including the cosmic microwave background (CMB) radiation from the Wilkinson Microwave Anisotropy Probe (WMAP), Atacama Cosmology Telescope (ACT), and South Pole Telescope (SPT), as well as large-scale structure data from the Sloan Digital Sky Survey (SDSS; baryon acoustic oscillation + redshift-space distortion) and Pantheon supernova (SN) catalogue. We employ a Bayesian framework to constrain the model parameters and discuss the implications of our results on the viability of modified gravity theories. Our analysis reveals the strengths and limitations of the μ–Σ parametrization and provides valuable insights into the nature of gravity on cosmological scales. From the joint analysis of the ACT + WMAP + SDSS + SN, we find μ0 − 1 = 0.02 ± 0.19 and Σ0 − 1 = 0.021 ± 0.068 at 68 per cent confidence level (CL). In light of the SPT + WMAP + SDSS + SN, we find μ0 − 1 = 0.07 ± 0.18 and $\Sigma _0 -1 = -0.009^{+0.078}_{-0.11}$ at 68 per cent CL. In all the analyses carried out, we do not find any deviations from the theory of general relativity. Our results represent an observational update on the well-known μ–Σ parametrization in view of current CMB data, independent of and competitive with the constraints obtained with the Planck data.

Early dark energy constraints with late-time expansion marginalization

Early dark energy (EDE) is an extension to the ΛCDM model that includes an additional energy density contribution near recombination. The model was proposed to reduce the tension between the measurements of the Hubble constant H 0 from the cosmic microwave background (CMB) and from the local cosmic distance ladder. Some analyses in the recent literature have shown intriguing hints for EDE. However, this model increases the tension in the derived clustering of galaxies (as measured by the so-called S 8 parameter) between CMB and large scale structure (LSS) measurements. This new tension limits the contribution of EDE during recombination, and thus its effect on the Hubble tension. In this work, we investigate whether the inclusion of a general, smooth late-time dark energy modification can increase back the EDE contribution when LSS data is included in the analysis. In order to generalize the late expansion with respect to the ΛCDM model, we substitute the cosmological constant by a late dark energy fluid model with a piecewise constant equation of state w(z) in redshift bins. We show that, when analysing this generalized model with combinations of CMB, LSS and type Ia supernovae data from several experiments no significant changes on S 8 and EDE parameter constraints is found. The contribution to the EDE fraction constraint with late-time expansion marginalization is f EDE = 0.067+0.019 -0.027 using 3 redshift bins, with similar results for 5 and 10 redshift bins. This work shows that in order to solve simultaneously the Hubble and S 8 tensions, one needs a mechanism for increasing the clustering of matter at late times different from a simple change in the background evolution of late dark energy.

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.

12 × 2 pt combined probes: pipeline, neutrino mass, and data compression

With the rapid advance of wide-field surveys it is increasingly important to perform combined cosmological probe analyses. We present a new pipeline for simulation-based multi-probe analyses, which combines tomographic large-scale structure (LSS) probes (weak lensing and galaxy clustering) with cosmic microwave background (CMB) primary and lensing data. These are combined at the C ℓ-level, yielding 12 distinct auto- and cross-correlations. The pipeline is based on UFalconv2, a framework to generate fast, self-consistent map-level realizations of cosmological probes from input lightcones, which is applied to the CosmoGridV1 N-body simulation suite. It includes a non-Gaussian simulation-based covariance for the LSS tracers, several data compression schemes, and a neural network emulator for accelerated theoretical predictions. We validate the pipeline by comparing the simulations to these predictions, and our derived constraints to earlier analyses. We apply our framework to a simulated 12×2 pt tomographic analysis of KiDS, BOSS, and Planck, and forecast constraints for a ΛCDM model with a variable neutrino mass. We find that, while the neutrino mass constraints are driven by the CMB data, the addition of LSS data helps to break degeneracies and improves the constraint by up to 35%. For a fiducial Mν  = 0.15 eV, a full combination of the above CMB+LSS data would enable a 3σ constraint on the neutrino mass. We explore data compression schemes and find that MOPED outperforms PCA and is made robust using the derivatives afforded by our automatically differentiable emulator. We also study the impact of an internal lensing tension in the CMB data, parametrized by AL , on the neutrino mass constraint, finding that the addition of LSS to CMB data including all cross-correlations is able to mitigate the impact of this systematic. UFalconv2 and a MOPED compressed Planck CMB primary + CMB lensing likelihood are made publicly available.[UFalconv2: https://cosmology.ethz.ch/research/software-lab/UFalcon.html, compressed Planck CMB primary + CMB lensing likelihood: https://github.com/alexreevesy/planck_compressed.]

Minkowski Functionals in 𝖲𝖮(3) for the spin-2 CMB polarisation field

The study of the angular power spectrum of Cosmic Microwave Background (CMB) anisotropies, both in intensity and in polarisation, has led to the tightest constraints on cosmological parameters. However, this statistical quantity is not sensitive to any deviation from Gaussianity and statistical isotropy in the CMB data. Minkowski Functionals (MFs) have been adopted as one of the most powerful statistical tools to study such deviations, since they characterise the topology and geometry of the field of interest. In this paper, we extend the application of MFs to CMB polarisation data by introducing a new formalism, where we lift the spin 2 polarisation field to a scalar function in a higher-dimensional manifold: the group of rotations of the sphere, SO(3). Such a function is defined as f = Q cos(2ζ) - U sin(2ζ). We analytically obtain the expected values for the MFs of f in the case of Gaussian isotropic polarisation maps. Furthermore, we present a new pipeline which estimates these MFs from input HEALPix polarisation maps. We apply it to CMB simulations in order to validate the theoretical results and the methodology. The pipeline is to be included in the publicly available Python package Pynkowski .

Patchy screening of the CMB from dark photons

We study anisotropic (patchy) screening induced by the resonant conversion of cosmic microwave background (CMB) photons into dark-sector massive vector bosons (dark photons) as they cross non-linear large scale structure (LSS). Resonant conversion takes place through the kinetic mixing of the photon with the dark photon, one of the simplest low energy extensions to the Standard Model. In the early Universe, resonant conversion can occur when the photon plasma mass, obtained as the photon propagates through the ionized interstellar and intergalactic media, matches the dark photon mass. After the epoch of reionization, resonant conversion occurs mainly in the ionized gas that occupies virialized dark matter halos, for a range of dark photon masses between 10-13 eV ≲ m A' ≲ 10-11 eV. This leads to new CMB anisotropies that are correlated with LSS, which we refer to as patchy dark screening, in analogy with anisotropies from Thomson screening. Its unique frequency dependence allows it to be distinguished from the blackbody CMB. In this paper, we use a halo model approach to predict the imprint of dark screening on the CMB temperature and polarization anisotropies, as well as their correlation with LSS. We then examine the two- and three-point correlation functions of the dark-screened CMB, as well as correlation functions between CMB and LSS observables, to project the sensitivity of future measurements to the kinetic mixing parameter and dark photon mass. We demonstrate that an analysis with existing CMB data can improve upon current constraints on the kinetic mixing parameter by two orders of magnitude with the two-point correlation functions, while data from upcoming CMB experiments and LSS surveys can further improve the reach by another order of magnitude with two- and three-point correlation functions.

Warm Dark matter constraints from the joint analysis of CMB, Ly α, and global 21 cm data

ABSTRACT With the help of our previously built MCMC (Markov chain Monte Carlo)-based parameter estimation package cosmoreionmc, we investigate in detail the potential of 21 cm global signal, when combined with cosmic microwave background (CMB) and observations related to the Quasar (QSO) absorption spectra, to constraint the mass of warm dark matter (WDM) particle. For the first time, we simultaneously vary all the free parameters (mass of WDM particle, cosmological parameters, and astrophysical parameters) in a joint analysis with CMB, observations related to the QSO absorption spectra and 21 cm global signal, to address the long-overlooked issue of the possible degeneracies between the dark matter particle mass mX and cosmological/astrophysical parameters. From the existing CMB and QSO absorption spectra data, we can rule out mX &amp;lt; 2.8 keV at 95 per cent confidence level. Including a mock 21 cm global signal in the redshift range z = 25−5 expected to be observed with upcoming instruments designed for global signal, the forecasted constraint is found to be much tighter mX &amp;gt; 7.7 keV, assuming that the true dark matter model is the usual cold dark matter. In case the mock 21 cm signal is constructed for dark matter particles having mX = 7 keV, our forecasts indicate that (mX/keV)−1 is in the range [0.1, 0.2] (95  per cent confidence level). This implies that the future 21 cm data should allow detection of the WDM particle mass if mX ∼ 7 keV.

Analyzing Earth's Position based on the Anisotropic Characteristics of Cosmic Microwave Background Radiation

This paper elaborates on the results of an exhaustive study regarding the Earth's position in the universe based on the Cosmic Microwave Background (CMB) radiation map, which is the latest discovery in modern astronomy. CMB radiation provides crucial insights into the early distribution of mass and energy in the universe. The aim of this research is to understand the theory and mechanisms behind the formation of polarity structures in the CMB and analyze their correlation with Earth's position in the overall structure of the universe. Intensity measurement data of CMB radiation published by COBE, WMAP, and Planck present temperature distribution data in coordinates in FITS (Flexible Image Transport System) format files. Subsequently, a spherical harmonic transformation is performed to obtain spherical harmonic coefficients a_lm as equations that represent dipole, quadrupole, octupole models, and various other multipole models. The analysis of the correlation in the temperature distribution of CMB radiation involves detailing various patterns found in the dipole, quadrupole, and octopole models, demonstrating quasi-symmetry characteristics with Earth at its center. An analysis of anisotropic CMB data yields an interesting hypothesis that the Earth's position plays a role in shaping the structure of the universe on a certain scale. Even more extremely, it can be said that Earth is at the center of the universe. This finding prompts profound contemplation about Earth's position in the structure of the cosmos, opening the door for further research in this field.

Investigating the accelerated expansion of the Universe through updated constraints on viable f(R) models within the metric formalism

ABSTRACT Modified theories of gravity encompass a class of f(R) models that seek to elucidate the observed late-time accelerated expansion of the universe. In this study, we examine a set of viable f(R) models (Hu–Sawicki: two cases, Satrobinsky, Tsujikawa, exponential and arcTanh models) in metric formalism, using recent cosmological data sets: type Ia supernovae data, cosmic chronometer observations, baryonic acoustic oscillations data, data from H ii starburst galaxies, local measurements of the Hubble parameter (H0), and cosmic microwave background radiation data. We re-parametrize the f(R) models using a distortion/deviation parameter (b) which is a measure of their deviation from the lambda-cold dark matter (ΛCDM) model. Taking into account the ‘Hubble tension,’ we perform the study both with and without a Gaussian prior for H0 from local measurements, following the standard statistical procedures for constraining parameters and comparing models. Our findings are as follows: (i) in many cases the f(R) models are strongly favoured over the standard ΛCDM model, (ii) the deviation parameter (b) significantly deviates from zero in several cases, (iii) the inclusion of local H0 not only increases the fitted value of H0 (as expected) but also affects the gap between predictions of f(R) models and the ΛCDM model, and (iv) the relevant quantities characterizing the (accelerated) expansion of the universe such as transition redshift and the equations-of-state parameters, obtained in our models, are consistent with those obtained in a model-independent way by others. Our investigation and results present a compelling case for pursuing further research on f(R) models with future observations to come.

The Hubble tension survey: A statistical analysis of the 2012–2022 measurements

ABSTRACT In order to investigate the potential Hubble tension, we compile a catalogue of 216 measurements of the Hubble–Lemaître constant H0 between 2012 and 2022, which includes 109 model-independent measurements and 107 ΛCDM model-based measurements. Statistical analyses of these measurements show that the deviations of the results with respect to the average H0 are far larger than expected from their error bars if they follow a Gaussian distribution. We find that xσ deviation is indeed equivalent in a Gaussian distribution to xeqσ deviation in the frequency of values, where xeq = 0.72x0.88. Hence, a tension of 5σ, estimated between the Cepheid-calibrated type Ia supernovae and cosmic microwave background (CMB) data, is indeed a 3σ tension in equivalent terms of a Gaussian distribution of frequencies. However, this recalibration should be independent of the data whose tension we want to test. If we adopt the previous analysis of data of 1976–2019, the equivalent tension is reduced to 2.25σ. Covariance terms due to correlations of measurements do not significantly change the results. None the less, the separation of the data into two blocks with H0 &amp;lt; 71 and H0 ≥ 71 km s−1 Mpc−1 finds compatibility with a Gaussian distribution for each of them without removing any outlier. These statistical results indicate that the underestimation of error bars for H0 remain prevalent over the past decade, dominated by systematic errors in the methodologies of CMB and local distance ladder analyses.