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A flat Friedmann–Robertson–Walker universe dominated by a cosmological constant ( Λ ) and cold dark matter (CDM) has been the working model preferred by cosmologists since the discovery of cosmic acceleration 1 , 2 . However, tensions of various degrees of significance are known to be present among existing datasets within the Λ CDM framework 3 – 11 . In particular, the Lyman-α forest measurement of the baryon acoustic oscillations (BAO) by the Baryon Oscillation Spectroscopic Survey 3 prefers a smaller value of the matter density fraction Ω M than that preferred by cosmic microwave background (CMB). Also, the recently measured value of the Hubble constant, H 0  = 73.24 ± 1.74 km s −1  Mpc −1 (ref. 12 ), is 3.4 σ higher than the 66.93 ± 0.62 km s −1  Mpc −1 inferred from the Planck CMB data 7 . In this work, we investigate whether these tensions can be interpreted as evidence for a non-constant dynamical dark energy. Using the Kullback–Leibler divergence 13 to quantify the tension between datasets, we find that the tensions are relieved by an evolving dark energy, with the dynamical dark energy model preferred at a 3.5 σ significance level based on the improvement in the fit alone. While, at present, the Bayesian evidence for the dynamical dark energy is insufficient to favour it over Λ CDM, we show that, if the current best-fit dark energy happened to be the true model, it would be decisively detected by the upcoming Dark Energy Spectroscopic Instrument survey 14 . Recent observations reveal tension between various cosmological probes. Assuming dark energy to be non-constant, depending on redshift, may relieve this tension. The Dark Energy Spectroscopic Instrument survey will be able to confirm this result.

We investigate the statistics of the available Pantheon+ dataset. Noticing that the χ2 value for the best-fit ΛCDM model to the real data is small, we quantify how significant its smallness is by calculating the distribution of χ2 values for the best-fit ΛCDM model fit to mock Pantheon+-like datasets, using the provided covariance matrix. We further investigate the distribution of the residuals of the Pantheon+ dataset with respect to the best-fit ΛCDM model, and notice that they scatter less than would be expected from the covariance matrix but find no significant kurtosis. These results point to the conclusion that the Pantheon+ covariance matrix is over-estimated. One simple interpretation of these results is a ∼7% overestimation of errors on SN distance moduli in Pantheon+ data. When the covariance matrix is reduced by subtracting an intrinsic scatter term from the diagonal terms of the covariance matrix, the best-fit χ2 for the ΛCDM model achieves a normal value of 1580 and no deviation from ΛCDM is detected. We further quantify how consistent the ΛCDM model is with respect to the modified data with the subtracted covariance matrix using model-independent reconstruction techniques such as the iterative smoothing method. We find that the standard model is consistent with the data. There are a number of potential explanations for this smallness of the χ2, such as a Malmquist bias at high redshift, or accounting for systematic uncertainties by adding them to the covariance matrix, thus approximating systematic uncertainties as statistical ones.

We introduce the concept of a one-way, broadband information package, the Cosmic Illuminating Gift, intended to provide distant intelligences with fundamental empirical data about the Universe. Unlike previous messaging to extraterrestrial intelligences (METI) that emphasized greetings or cultural identity, the Gift aims to transmit unbiased, universally interpretable information that recipients could not otherwise obtain due to their distinct spacetime position and epoch. By emphasizing raw observations, rather than human interpretations or cosmological models, the Gift aspires to serve as a neutral and enduring resource. A central assumption of the project is that any potential recipients are likely to possess a level of intelligence and technological sophistication far beyond our own. Accordingly, the content and encoding of the Gift are not designed to “teach” fundamentals, but to deliver compact, logically structured packets that such civilizations could decode even at extremely low signal-to-noise levels. This perspective shifts the challenge from brute-force transmission to ensuring that photons arrive in spectrally quiet windows and that the format is unmistakably artificial and distinguishable from astrophysical backgrounds. We outline strategies for content selection, encoding, and transmission that reflect this assumption. Practical implementation is feasible with current or near-term infrastructure, and future advances will only improve the quality of subsequent Gifts. Ultimately, the endeavor is unique among scientific projects in that it anticipates no feedback or measurable result within the span of our civilization’s timeline. Its significance lies instead in the act of contribution itself: offering a durable, universal dataset as a gesture of intellectual solidarity across cosmic distances.

We investigate the statistics of the available Pantheon+ dataset. Noticing that the \\(\\chi^2\\) value for the best-fit \\(\\Lambda\\)CDM model to the real data is small, we quantify how significant its smallness is by calculating the distribution of \\(\\chi^2\\) values for the best-fit \\(\\Lambda\\)CDM model fit to mock Pantheon+-like datasets, using the provided covariance matrix. We further investigate the distribution of the residuals of the Pantheon+ dataset with respect to the best-fit \\(\\Lambda\\)CDM model, and notice that they scatter less than would be expected from the covariance matrix but find no significant kurtosis. These results point to the conclusion that the Pantheon+ covariance matrix is over-estimated. One simple interpretation of these results is a \\(\\sim\\)7\\% overestimation of errors on SN distance moduli in Pantheon+ data. When the covariance matrix is reduced by subtracting an intrinsic scatter term from the diagonal terms of the covariance matrix, the best-fit \\(\\chi^2\\) for the \\(\\Lambda\\)CDM model achieves a normal value of 1580 and no deviation from \\(\\Lambda\\)CDM is detected. We further quantify how consistent the \\(\\Lambda\\)CDM model is with respect to the modified data with the subtracted covariance matrix using model-independent reconstruction techniques such as the iterative smoothing method. We find that the standard model is consistent with the data. There are a number of potential explanations for this smallness of the \\(\\chi^2\\), such as a Malmquist bias at high redshift, or accounting for systematic uncertainties by adding them to the covariance matrix, thus approximating systematic uncertainties as statistical ones.

We look at the distribution of the Bayesian evidence for mock realizations of supernova and baryon acoustic oscillation data. The ratios of Bayesian evidences of different models are often used to perform model selection. The significance of these Bayes factors are then interpreted using scales such as the Jeffreys or Kass \\& Raftery scale. First, we demonstrate how to use the evidence itself to validate the model, that is to say how well a model fits the data, regardless of how well other models perform. The basic idea is that if, for some real dataset a model's evidence lies outside the distribution of evidences that result when the same fiducial model that generates the datasets is used for the analysis, then the model in question is robustly ruled out. Further, we show how to assess the significance of a hypothetically computed Bayes factor. We show that the range of the distribution of Bayes factors can greatly depend on the models in question and also the number of data points in the dataset. Thus, we have demonstrated that the significance of Bayes factors needs to be calculated for each unique dataset.

We introduce a generalised form of an emergent dark energy model with one degree of freedom for the dark energy sector that has the flexibility to include both \\(\\Lambda\\)CDM model as well as the Phenomenologically Emergent Dark Energy (PEDE) model proposed by Li & Shafieloo (2019) as two of its special limits. The free parameter for the dark energy sector, namely \\(\\Delta\\), has the value of \\(0\\) for the case of the \\(\\Lambda\\) and \\(1\\) for the case of PEDE. Fitting the introduced parametric form to Planck CMB data and most recent \\(H_0\\) results from local observations of Cepheids and Supernovae, we show that the \\(\\Delta=0\\) associated with the \\(\\Lambda\\)CDM model would fall out of 4\\(\\sigma\\) confidence limits of the derived posterior of the \\(\\Delta\\) parameter. Moreover, \\(H_0\\) tensions will be alleviated with emergent dark energy model and this model can satisfy the combination of Planck CMB data and local \\(H_0\\) observations with \\(\\Delta{\\rm{DIC}}\\,=\\,-2.88\\) compared with \\(\\LCDM\\) model.

Motivated by the current status of the cosmological observations and significant tensions in the estimated values of some key parameters assuming the standard \\(\\)CDM model, we propose a simple but radical phenomenological emergent dark energy model where dark energy has no effective presence in the past and emerges at the later times. Theoretically, in this phenomenological dark energy model with zero degree of freedom (similar to a \\(\\)CDM model), one can derive that the equation of state of dark energy increases from \\(-23 ln\\, 10 -1\\) in the past to \\(-1\\) in the future. We show that by setting a hard-cut 2\\(\\) lower bound prior for the \\(H_0\\) that associates with \\(97.72\\%\\) probability from the recent local observations~riess2019large, this model can satisfy different combinations of cosmological observations at low and high redshifts (SNe Ia, BAO, Ly\\(\\) BAO and CMB) substantially better than the concordance \\(\\)CDM model with \\( ^2_bf -41.08\\) and \\(\\,DIC -35.38\\). If there are no substantial systematics in SN Ia, BAO or Planck CMB data and assuming reliability of the current local \\(H_0\\) measurements, there is a very high probability that with slightly more precise measurement of the Hubble constant our proposed phenomenological model rules out the cosmological constant with decisive statistical significance and is a strong alternative to explain combination of different cosmological observations. This simple phenomenologically emergent dark energy model can guide theoretically motivated dark energy model building activities.

We make use of model-independent statistical methods to assess the consistency of three different supernova compilations: Union3, Pantheon+ and DES 5-year supernovae. We expand the available model space of each, using Crossing Statistics, and test the compatibility of each dataset, against the other two. This is done using (I) a Flat \\(\\)CDM fitting to, and (II) Iterative Smoothing from, one particular dataset, and determining the level of deformation by required to fit the other two. This allows us to test the mutual consistency of the datasets both within the standard model and in the case of some extended model, motivated by features present in a particular dataset. We find that, in both these cases, the data are only consistent with the point in the parameter space corresponding to zero deformation, at around a \\(2\\) level, with the DES compilation showing the largest disagreement. However, all three datasets are still found to be consistent to within \\(1-2\\) for some subset of the extended model space implied by the deformations.

We search for super-imposed oscillations linearly or logarithmically spaced in Fourier wavenumbers \\(k\\) in Planck and South Pole Telescope (SPT-3G) 2018 temperature and polarization data. The SPT-3G temperature and polarization data provide a new window to test these oscillations at high multipoles beyond the Planck angular resolution and sensitivity. We consider linear and logarithmic oscillations with a constant amplitude, or with a power-law dependence or a Gaussian modulation, always in \\(k\\). These models correspond to three, four and five additional parameters beyond power-law primordial power spectrum for the templates considered, respectively. We find that each of the five models considered can provide an improved fit to Planck data, consistently with previous findings, and to SPT-3G data, always compared to power-law power spectrum. We find tighter constraints on the amplitude of the super-imposed oscillations from the combined Planck/SPT-3G data set than in each individual data sets. For linear oscillations, with the amplitude allowed to vary as a power-law in \\(k\\), as in the case of EFT, we find that the addition of SPT-3G data sets tighter constraints on the possibility that the amplitude increase at small scales. When the ranges of parameters which provide a better fit to Planck and SPT-3G data overlap, as in the case of Gaussian modulated oscillations, we find a larger \\(\\Delta \\chi^2 \\sim - 17.5 \\, (-14.7)\\) for logarithmic (linear) oscillations - in a combined Planck/SPT-3G data set than in each individual data sets. These findings will be further tested with upcoming CMB temperature and polarization measurements at high multipoles provided by ongoing ground experiments.

Previously we proposed a novel method to inspect the isotropy of the properties of gamma-ray bursts (GRBs) such as their duration, fluences and peak fluxes at various energy bands and different time scales, complementary to existing studies of spatial distribution of GRBs by other authors. The method was then applied on the Fermi GBM Burst Catalog containing 1591 GRBs and except one particular direction where we noticed some hints of violation from statistical isotropy, the rest of the data showed consistency with isotropy. In this work we apply our method with some minor modifications to the updated Fermi/GBM data sample containing 2266 GRBs, thus \\(\\sim 40\\) % larger. We also test two other major GRB catalogs, the BATSE Current GRB Catalog of the CGRO satellite containing \\(\\sim 2000\\) bursts and the Swift/BAT Gamma-Ray Burst Catalog containing \\(\\sim 1200\\) bursts. The new results using the updated data are consistent with our previous findings and no statistically significant anisotropic feature in the observed properties of these samples of all GRBs is found.