Recent cosmological observations, including the latest Dark Energy Spectroscopic Instrument (DESI) data releases DR1 and DR2, have renewed interest in the possibility that dark energy may exhibit dynamical behavior rather than being a strict cosmological constant. In this work, we perform a fully model-independent reconstruction of the quintessence scalar field potential using Gaussian Process regression and current Hubble measurements. Instead of assuming a specific functional form for the scalar field potential, we reconstruct the quintessence potential and the corresponding kinetic energy directly from observational data. Our analysis is based on Hubble parameter measurements obtained from cosmic chronometers and the latest high-precision DESI DR2 baryon acoustic oscillation (BAO) data, together with Type Ia supernova data from the Pantheon+ compilation. Gaussian Processes provide a nonparametric and model-independent framework that allows the data to guide the reconstruction. We employ two covariance functions, namely the squared exponential and the Matern (ν= 9/2) kernels, in order to assess the sensitivity of the reconstruction to the kernel choice. We further explore the impact of background cosmological assumptions by considering different priors on the matter density and spatial curvature. Finally, we compare the reconstructed scalar field potential with two theoretically motivated benchmark models: a power law potential and an exponential potential. We find that both models remain consistent with the reconstructed potential within the inferred confidence intervals.

Recent DESI data suggest that dark energy may be evolving and motivate the use of model-independent diagnostics such as Om(z) and probes of the equation of state (EoS) of dark energy, w(z). Traditional reconstructions of w(z) rely on differentiating the expansion history, h(z)=H(z)/H_0, which amplifies noise and systematic uncertainties. In this work, we introduce a new diagnostic, the w_0-probe, which is constructed from Om(z), and which enables a direct determination of the current EoS from h(z) without any additional differentiation. While retaining the null-test capability of Om(z) for ΛCDM, the w_0-probe also provides a direct estimate of w_0 – the current EoS of dark energy. We demonstrate that this reconstruction of w_0 is robust for any smooth underlying w(z). We apply this method to Gaussian-process (GP) reconstructions of h(z) using current SNe Ia+BAO+CMB data. Both Om(z) and the w_0-probe exclude ΛCDM at the 95% confidence level (C.L.), with the latter favouring w_0≃-0.62 ± 0.03 at 95% C.L. To mitigate potential over-constraining from GP priors, we additionally analyze χ^2-limited reconstructions with likelihoods exceeding the 95% CPL threshold. The w_0-probe obtained from these high-likelihood samples again predominantly excludes ΛCDM and yields w_0∈(-0.8,-0.5) at z→ 0, demonstrating the robustness of our results. The w_0-probe therefore provides a simple, model-independent, and robust diagnostic of the current EoS of dark energy.

Recent data from DESI Year 2 BAO, Planck CMB, and various supernova compilations suggest a preference for evolving dark energy, with hints that the equation of state may cross the phantom divide line (w = -1). While this behavior is seen in both parametric and non-parametric reconstructions, comparing reconstructions that support such behavior (such as the best fit of CPL) with those that maintain w>-1 (like the best fit algebraic quintessence) is not straightforward, as they differ in flexibility and structure, and are not necessarily nested within one another. Thus, the question remains as to whether the crossing behavior that we observe, suggested by the data, truly represents a dark energy model that crosses the phantom divide line, or if it could instead be a result of data fluctuations and the way the data are distributed. We investigate the likelihood of this possibility. For this analysis we perform 1,000 Monte Carlo simulations based on a fiducial algebraic quintessence model. We find that in 3.2 % of cases, CPL with phantom crossing not only fits better, but exceeds the real-data χ^2 improvement. This Monte Carlo approach quantifies to what extent statistical fluctuations and the specific distribution of the data could fool us into thinking the phantom divide line is crossed, when it is not. Although evolving dark energy remains a robust signal, and crossing w=-1 a viable phenomenological solution that seems to be preferred by the data, its precise behavior requires deeper investigation with more precise data.

In this analysis we apply a model-independent framework to test the flat ΛCDM cosmology using simulated SNIa data from the upcoming Legacy Survey of Space and Time (LSST) and combined with simulated Dark Energy Spectroscopic Instrument (DESI) five-years Baryon Acoustic Oscillations (BAO) data. We adopt an iterative smoothing technique to reconstruct the expansion history from SNIa data, which, when combined with BAO measurements, facilitates a comprehensive test of the Universe's curvature and the nature of dark energy. The analysis is conducted under four different mock fiducial cosmologies: two curvatures (Ω k ,0 = 0 and 0.1) and two models of dark energy: a cosmological constant Λ and the phenomenologically emergent dark energy. We forecast that our reconstruction technique can constrain cosmological parameters, such as the curvature ( k ,0) and c/ H 0 r d , with spread due to the SNIa uncertainties up to ±4% and ±0.1 respectively, without assuming any form of dark energy.

Gravitationally lensed supernovae (glSNe) are a powerful tool for exploring the realms of astronomy and cosmology. Time-delay measurements and the lens modeling of glSNe can provide a robust and independent method for constraining the expansion rate of the Universe. The study of the light curves of unresolved glSNe presents a unique opportunity for using small telescopes to investigate these systems. We investigate diverse observational strategies for the initial detection of glSNe using the 7-Dimensional Telescope (7DT). This multitelescope system is composed of twenty 50 cm telescopes. We implement different observing strategies on a subset of 5807 strong-lensing systems and candidates identified within the Dark Energy Camera Legacy Survey (DECaLS), as reported in various publications. Our simulations under ideal observing conditions indicate the maximum expected annual detection rates for various glSN types (type Ia and core-collapse (CC)) using the 7DT target-observing mode in the r band at a depth of 22.04 mag as follows: 7.46 events for type Ia, 2.49 for type Ic, 0.8 for type IIb, 0.52 for type IIL, 0.78 for type IIn, 3.75 for type IIP, and 1.15 for type Ib. Furthermore, in the case of medium-band filter observations (m6000) at a depth of 20.61 in the Wide-field Time-domain Survey (WTS) program, the predicted detection rate for glSNe Ia is 2.53 yr^-1. These initially detected systems will be followed-up with observations with more powerful telescopes, and we therefore applied a model-independent approach to forecast the ability of measuring H_0 using a Gaussian process from type Ia supernovae (SNe Ia) data and time-delay distance information derived from glSN systems, which include both Ia and CC types. We forecast that the expected detection rate of glSN systems can achieve a precision of $2.7%$ in estimating the H_0.

In this study, we use a flexible parametrization of the equation of state of dark energy to explore its possible evolution with datasets from the Dark Energy Spectroscopic Instrument (DESI), Planck cosmic microwave background (CMB), and either the 5-year Dark Energy Survey (DES) or the Pantheon+ (PP) supernova (SN) compilation. This parametrization, called transitional dark energy (TDE), allows for rapid changes in the equation of state but also changes like that in the Chevallier-Polarski-Linder (CPL) w0-wa parametrization. We find a 3.86 preference for evolving dark energy over ACDM with the DES SN dataset and a weaker 2.46 preference when using the PP dataset. This corroborates the finding of the DESI Collaboration, who found that their baryon acoustic oscillation data preferred evolving dark energy when fit with the CPL parametrization of the equation of state. Our analysis reveals no significant outliers in the DESI data around the TDE best-fit, while the data is asymmetrically distributed around the ACDM best-fit model such that the measured distances are on average smaller. The DESI and SN data both prefer an expansion history that implies a higher dark energy density around z = 0.5 than in the Planck-ACDM model, with the inferred equation of state being greater than -1 around z = 0 and close to or below -1 at z > 0.5. We show that when the expansion rate is greater than that in the Planck-ACDM model (around z = 0.5), the growth rate calculated assuming General Relativity is suppressed relative to the PlanckACDM model, and it rebounds as the expansion rate differences between the models become smaller closer to the present time. We derive an approximate analytic expression for the growth rate differences to understand this behavior quantitatively. The resulting flattening of the f sigma(8)(z) curve compared to the ACDM model could be an independent signature of the temporal evolution of dark energy.

Quasars could serve as standard candles if the relation between their ultraviolet (UV) and X-ray luminosities can be accurately calibrated. Previously, we developed a model-independent method to calibrate quasar standard candles using the distance–redshift relation reconstructed from Type Ia supernovae (SNe Ia) at z < 2 using Gaussian process regression. Interestingly, we found that the calibrated quasar standard candle data set preferred a deviation from ΛCDM at redshifts above z > 2. One possible interpretation of these findings is that the calibration parameters of the quasar UV and X-ray luminosity relationship evolves with redshift. In order to test the redshift dependence of the quasar calibration in a model-independent manner, we divided the quasar sample whose redshift overlaps with the redshift coverage of Pantheon+ SNe Ia compilation into two subsamples: a low-redshift quasar subsample and a high-redshift quasar subsample. Assuming all the quasar samples are reliable, our results show that there is about a 4 σ inconsistency between the quasar parameters inferred from the subsamples without considering evolution. This inconsistency suggests the possibility of considering redshift evolution for the relationship between the quasars’ UV and X-ray luminosities. We then test an explicit parameterization of the redshift evolution of the quasar calibration parameters via γ ( z ) = γ _0 + γ _1 (1 + z ) and β ( z ) = β _0 + β _1 (1 + z ). Combining this redshift-dependent calibration relationship with the distance–redshift relationship reconstructed from the Pantheon+ supernova compilation, we find the high-redshift subsample and low-redshift subsample become consistent at the 2 σ level, which means that the parameterized form of γ ( z ) and β ( z ) works well at describing the evolution of the quasar calibration parameters.

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.

Absolute distances from strong lensing can anchor Type Ia Supernovae (SNe Ia) at cosmological distances giving a model-independent inference of the Hubble constant ( H _0 ). Future observations could provide strong lensing time-delay distances with source redshifts up to z ≃ 4, which are much higher than the maximum redshift of SNe Ia observed so far. In order to make full use of time-delay distances measured at higher redshifts, we use quasars as a complementary cosmic probe to measure cosmological distances at redshifts beyond those of SNe Ia and provide a model-independent method to determine H _0 . In this work, we demonstrate a model-independent, joint constraint of SNe Ia, quasars, and time-delay distances from strong lensed quasars. We first generate mock data sets of SNe Ia, quasar, and time-delay distances based on a fiducial cosmological model. Then, we calibrate the quasar parameters model independently using Gaussian process (GP) regression with mock SNe Ia data. Finally, we determine the value of H _0 model-independently using GP regression from mock quasars and time-delay distances from strong lensing systems. As a comparison, we also show the H _0 results obtained from mock SNe Ia in combination with time-delay lensing systems whose redshifts overlap with SNe Ia. Our results show that quasars at higher redshifts show great potential to extend the redshift coverage of SNe Ia and thus enable the full use of strong lens time-delay distance measurements from ongoing cosmic surveys and improve the accuracy of the estimation of H _0 from 2.1% to 1.3% when the uncertainties of the time-delay distances are 5% of the distance values.

This is the second in a series of papers in which we use JWST MIRI multiband imaging to measure the warm dust emission in a sample of 31 multiply imaged quasars, to be used as a probe of the particle nature of dark matter. We present measurements of the relative magnifications of the strongly lensed warm dust emission in a sample of 9 systems. The warm dust region is compact and sensitive to perturbations by populations of halos down to masses $\sim 10^6$ M$_{\odot}$. Using these warm dust flux-ratio measurements in combination with 5 previous narrow-line flux-ratio measurements, we constrain the halo mass function. In our model, we allow for complex deflector macromodels with flexible third and fourth-order multipole deviations from ellipticity, and we introduce an improved model of the tidal evolution of subhalos. We constrain a WDM model and find an upper limit on the half-mode mass of $10^{7.6} M_\odot$ at posterior odds of 10:1. This corresponds to a lower limit on a thermally produced dark matter particle mass of 6.1 keV. This is the strongest gravitational lensing constraint to date, and comparable to those from independent probes such as the Ly$\alpha$ forest and Milky Way satellite galaxies.

Gaussian processes have been widely used in cosmology to reconstruct cosmological quantities in a model-independent way. However, the validity of the adopted mean function and hyperparameters, and the dependence of the results on the choice have not been well explored. In this paper, we study the effects of the underlying mean function and the hyperparameter selection on the reconstruction of the distance moduli from type Ia supernovae. We show that the choice of an arbitrary mean function affects the reconstruction: a zero mean function leads to unphysical distance moduli and the best-fit LCDM to biased reconstructions. We propose to marginalize over a family of mean functions and over the hyperparameters to effectively remove their impact on the reconstructions. We further explore the validity and consistency of the results considering different kernel functions and show that our method is unbiased.

The Nancy Grace Roman Space Telescope is capable of delivering an unprecedented all-sky, high-spatial resolution, multi-epoch infrared map to the astronomical community. This opportunity arises in the midst of numerous ground- and space-based surveys that will provide extensive spectroscopy and imaging together covering the entire sky (such as Rubin/LSST, Euclid, UNIONS, SPHEREx, DESI, SDSS-V, GALAH, 4MOST, WEAVE, MOONS, PFS, UVEX, NEO Surveyor, etc.). Roman can uniquely provide uniform high-spatial-resolution ( 0.1 arcsec) imaging over the entire sky, vastly expanding the science reach and precision of all of these near-term and future surveys. This imaging will not only enhance other surveys, but also facilitate completely new science. By imaging the full sky over two epochs, Roman can measure the proper motions for stars across the entire Milky Way, probing 100 times fainter than Gaia out to the very edge of the Galaxy. Here, we propose NANCY: a completely public, all-sky survey that will create a high-value legacy dataset benefiting innumerable ongoing and forthcoming studies of the universe. NANCY is a pure expression of Roman's potential: it images the entire sky, at high spatial resolution, in a broad infrared bandpass that collects as many photons as possible. The majority of all ongoing astronomical surveys would benefit from incorporating observations of NANCY into their analyses, whether these surveys focus on nearby stars, the Milky Way, near-field cosmology, or the broader universe.

One of the frontiers for advancing what is known about dark matter lies in using strong gravitational lenses to characterize the population of the smallest dark matter haloes. There is a large volume of information in strong gravitational lens images - the question we seek to answer is to what extent we can refine this information. To this end, we forecast the detectability of a mixed warm and cold dark matter scenario using the anomalous flux ratio method from strong gravitational lensed images. The halo mass function of the mixed dark matter scenario is suppressed relative to cold dark matter but still predicts numerous low-mass dark matter haloes relative to warm dark matter. Since the strong lensing signal receives a contribution from a range of dark matter halo masses and since the signal is sensitive to the specific configuration of dark matter haloes, not just the halo mass function, degeneracies between different forms of suppression in the halo mass function, relative to cold dark matter, can arise. We find that, with a set of lenses with different configurations of the main deflector and hence different sensitivities to different mass ranges of the halo mass function, the different forms of suppression of the halo mass function between the warm dark matter model and the mixed dark matter model can be distinguished with 40 lenses with Bayesian odds of 30:1.

We make the case that there can be no low-redshift solution to the ${H}_{0}$ tension. To robustly answer this question, we use a very flexible parametrization for the dark energy equation of state such that every cosmological distance still allowed by data exists within this prior volume. To then answer whether there exists a satisfactory solution to the ${H}_{0}$ tension within this comprehensive parametrization, we constrained the parametric form using different partitions of the Planck cosmic microwave background, SDSS-IV/eBOSS DR16 baryon acoustic oscillation, and Pantheon supernova datasets. When constrained by just the cosmic microwave background dataset, there exists a set of equations of state which yields high ${H}_{0}$ values, but these equations of state are ruled out by the combination of the supernova and baryon acoustic oscillation datasets. In other words, the constraint from the cosmic microwave background, baryon acoustic oscillation, and supernova datasets together does not allow for high ${H}_{0}$ values and converges around an equation of state consistent with a cosmological constant. Thus, since this very flexible parametrization does not offer a solution to the ${H}_{0}$ tension, there can be no solution to the ${H}_{0}$ tension that adds physics at only low redshifts. This is directly related to the expansion history of the Universe and its geometrical properties and would include models beyond those parametrized by $w(z)$.

We look at the distribution of the Bayesian evidence for mock realizations of supernova and baryon acoustic oscillation data. The ratios of Bayesian evidence of different models are often used to perform model selection. The significance of these Bayes factors is 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 data set, a model's evidence lies outside the distribution of evidence that result when the same fiducial model that generates the data sets 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 data set. Thus, we have demonstrated that the significance of Bayes factors needs to be calculated for each unique data set.

We have developed a frequentist approach for model selection which determines the consistency between any cosmological model and the data using the distribution of likelihoods from the iterative smoothing method. Using this approach, we have shown how confidently we can conclude whether the data support any given model without comparison to a different one. In this current work, we compare our approach with the conventional Bayesian approach based on the estimation of the Bayesian evidence using nested sampling. We use simulated future Roman (formerly WFIRST)-like type Ia supernovae data in our analysis. We discuss the limits of the Bayesian approach for model selection and show how our proposed frequentist approach can perform better in the falsification of individual models. Namely, if the true model is among the candidates being tested in the Bayesian approach, that approach can select the correct model. If all of the options are false, then the Bayesian approach will select merely the least incorrect one. Our approach is designed for such a case and we can conclude that all of the models are false.

In this paper we explore the existing tensions in the local cosmological expansion rate, $H_0$, and amplitude of the clustering of large-scale structure at $8\, h^{-1}\mathrm{Mpc}$, $\sigma_8$, as well as models that claim to alleviate these tensions. We consider seven models: evolving dark energy ($w$CDM), extra radiation ($N_\mathrm{eff}$), massive neutrinos, curvature, primordial magnetic fields (PMF), self-interacting neutrino models, and early dark energy (EDE). We test these models against three data sets that span the full range of measurable cosmological epochs, have significant precision, and are well-tested against systematic effects: the Planck 2018 cosmic microwave background data, the Sloan Digital Sky Survey baryon acoustic oscillation scale measurements, and the Pantheon catalog of Type Ia supernovae. We use the recent SH0ES $H_0$ measurement and several measures of $\sigma_8$ (and its related parameter $S_8=\sigma_8\sqrt{\Omega_\mathrm{m}/0.3}$). We find that four models are above the "strong" threshold in Bayesian model selection, $w$CDM, $N_\mathrm{eff}$, PMF, and EDE. However, only EDE also relieves the $H_0$ tension in the full data sets to below 2$\sigma$. Contrarily, no model alleviates the $S_8/\sigma_8$ tension in the full data set, nor does better than $\Lambda$CDM in the combined case of both $H_0$ and $S_8/\sigma_8$ tensions.

Cosmic Probes of Fundamental Physics take two primary forms: Very high energy particles (cosmic rays, neutrinos, and gamma rays) and gravitational waves. Already today, these probes give access to fundamental physics not available by any other means, helping elucidate the underlying theory that completes the Standard Model. The last decade has witnessed a revolution of exciting discoveries such as the detection of high-energy neutrinos and gravitational waves. The scope for major developments in the next decades is dramatic, as we detail in this report.

In this paper we will list a few important goals that need to be addressed in the next decade, also taking into account the current discordances between the different cosmological probes, such as the disagreement in the value of the Hubble constant $H_0$, the $\sigma_8$--$S_8$ tension, and other less statistically significant anomalies. While these discordances can still be in part the result of systematic errors, their persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the necessity for new physics or generalisations beyond the standard model. In this paper, we focus on the $5.0\,\sigma$ tension between the {\it Planck} CMB estimate of the Hubble constant $H_0$ and the SH0ES collaboration measurements. After showing the $H_0$ evaluations made from different teams using different methods and geometric calibrations, we list a few interesting new physics models that could alleviate this tension and discuss how the next decade's experiments will be crucial. Moreover, we focus on the tension of the {\it Planck} CMB data with weak lensing measurements and redshift surveys, about the value of the matter energy density $\Omega_m$, and the amplitude or rate of the growth of structure ($\sigma_8,f\sigma_8$). We list a few interesting models proposed for alleviating this tension, and we discuss the importance of trying to fit a full array of data with a single model and not just one parameter at a time. Additionally, we present a wide range of other less discussed anomalies at a statistical significance level lower than the $H_0$--$S_8$ tensions which may also constitute hints towards new physics, and we discuss possible generic theoretical approaches that can collectively explain the non-standard nature of these signals.[Abridged]

We compute the distribution of likelihoods from the non-parametric iterative smoothing method over a set of mock Pantheon-like type Ia supernova datasets. We use this likelihood distribution to test whether typical dark energy models are consistent with the data and to perform parameter estimation. In this approach, the consistency of a model and the data is determined without the need for comparison with another alternative model. Simulating future WFIRST-like data, we study type II errors and show how confidently we can distinguish different dark energy models using this non-parametric approach.