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We propose a new intuitive metric for evaluating the tension between two experiments, and apply it to several data sets. While our metric is non-optimal, if evidence of tension is detected, this evidence is robust and easy to interpret. Assuming a flat $Lambda$CDM cosmological model, we find that there is a modest $2.2sigma$ tension between the DES Year 1 results and the ${it Planck}$ measurements of the Cosmic Microwave Background (CMB). This tension is driven by the difference between the amount of structure observed in the late-time Universe and that predicted from fitting the ${it Planck}$ data, and appears to be unrelated to the tension between ${it Planck}$ and local esitmates of the Hubble rate. In particular, combining DES, Baryon Acoustic Oscillations (BAO), Big-Bang Nucleosynthesis (BBN), and supernovae (SNe) measurements recovers a Hubble constant and sound horizon consistent with ${it Planck}$, and in tension with local distance-ladder measurements. If the tension between these various data sets persists, it is likely that reconciling ${it all}$ current data will require breaking the flat $Lambda$CDM model in at least two different ways: one involving new physics in the early Universe, and one involving new late-time Universe physics.
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Quantifying the concordance between different cosmological experiments is important for testing the validity of theoretical models and systematics in the observations. In earlier work, we thus proposed the Surprise, a concordance measure derived from the relative entropy between posterior distributions. We revisit the properties of the Surprise and describe how it provides a general, versatile, and robust measure for the agreement between datasets. We also compare it to other measures of concordance that have been proposed for cosmology. As an application, we extend our earlier analysis and use the Surprise to quantify the agreement between WMAP 9, Planck 13 and Planck 15 constraints on the $Lambda$CDM model. Using a principle component analysis in parameter space, we find that the large Surprise between WMAP 9 and Planck 13 (S = 17.6 bits, implying a deviation from consistency at 99.8% confidence) is due to a shift along a direction that is dominated by the amplitude of the power spectrum. The Planck 15 constraints deviate from the Planck 13 results (S = 56.3 bits), primarily due to a shift in the same direction. The Surprise between WMAP and Planck consequently disappears when moving to Planck 15 (S = -5.1 bits). This means that, unlike Planck 13, Planck 15 is not in tension with WMAP 9. These results illustrate the advantages of the relative entropy and the Surprise for quantifying the disagreement between cosmological experiments and more generally as an information metric for cosmology.
The determination of the Hubble constant has been a central goal in observational astrophysics for nearly 100 years. Extraordinary progress has occurred in recent years on two fronts: the cosmic distance ladder measurements at low redshift and cosmic microwave background (CMB) measurements at high redshift. The CMB is used to predict the current expansion rate through a best-fit cosmological model. Complementary progress has been made with baryon acoustic oscillation (BAO) measurements at relatively low redshifts. While BAO data do not independently determine a Hubble constant, they are important for constraints on possible solutions and checks on cosmic consistency. A precise determination of the Hubble constant is of great value, but it is more important to compare the high and low redshift measurements to test our cosmological model. Significant tension would suggest either uncertainties not accounted for in the experimental estimates, or the discovery of new physics beyond the standard model of cosmology. In this paper we examine in detail the tension between the CMB, BAO, and cosmic distance ladder data sets. We find that these measurements are consistent within reasonable statistical expectations, and we combine them to determine a best-fit Hubble constant of 69.6+/-0.7 km/s/Mpc. This value is based upon WMAP9+SPT+ACT+6dFGS+BOSS/DR11+H_0/Riess; we explore alternate data combinations in the text. The combined data constrain the Hubble constant to 1%, with no compelling evidence for new physics.
A Large Quasar Group (LQG) of particularly large size and high membership has been identified in the DR7QSO catalogue of the Sloan Digital Sky Survey. It has characteristic size (volume^1/3) ~ 500 Mpc (proper size, present epoch), longest dimension ~ 1240 Mpc, membership of 73 quasars, and mean redshift <z> = 1.27. In terms of both size and membership it is the most extreme LQG found in the DR7QSO catalogue for the redshift range 1.0 <= z <= 1.8 of our current investigation. Its location on the sky is ~ 8.8 deg north (~ 615 Mpc projected) of the Clowes & Campusano LQG at the same redshift, <z> = 1.28, which is itself one of the more extreme examples. Their boundaries approach to within ~ 2 deg (~ 140 Mpc projected). This new, huge LQG appears to be the largest structure currently known in the early universe. Its size suggests incompatibility with the Yadav et al. scale of homogeneity for the concordance cosmology, and thus challenges the assumption of the cosmological principle.
Current cosmological data exhibit a tension between inferences of the Hubble constant, $H_0$, derived from early and late-universe measurements. One proposed solution is to introduce a new component in the early universe, which initially acts as early dark energy (EDE), thus decreasing the physical size of the sound horizon imprinted in the cosmic microwave background (CMB) and increasing the inferred $H_0$. Previous EDE analyses have shown this model can relax the $H_0$ tension, but the CMB-preferred value of the density fluctuation amplitude, $sigma_8$, increases in EDE as compared to $Lambda$CDM, increasing tension with large-scale structure (LSS) data. We show that the EDE model fit to CMB and SH0ES data yields scale-dependent changes in the matter power spectrum compared to $Lambda$CDM, including $10%$ more power at $k = 1~h$/Mpc. Motivated by this observation, we reanalyze the EDE scenario, considering LSS data in detail. We also update previous analyses by including $Planck$ 2018 CMB likelihoods, and perform the first search for EDE in $Planck$ data alone, which yields no evidence for EDE. We consider several data set combinations involving the primary CMB, CMB lensing, SNIa, BAO, RSD, weak lensing, galaxy clustering, and local distance-ladder data (SH0ES). While the EDE component is weakly detected (3$sigma$) when including the SH0ES data and excluding most LSS data, this drops below 2$sigma$ when further LSS data are included. Further, this result is in tension with strong constraints imposed on EDE by CMB and LSS data without SH0ES, which show no evidence for this model. We also show that physical priors on the fundamental scalar field parameters further weaken evidence for EDE. We conclude that the EDE scenario is, at best, no more likely to be concordant with all current cosmological data sets than $Lambda$CDM, and appears unlikely to resolve the $H_0$ tension.
We demonstrate that creation of dark-matter particles at a constant rate implies the existence of a cosmological term that decays linearly with the Hubble rate. We discuss the cosmological model that arises in this context and test it against observations of the first acoustic peak in the cosmic microwave background (CMB) anisotropy spectrum, the Hubble diagram for supernovas of type Ia (SNIa), the distance scale of baryonic acoustic oscillations (BAO) and the distribution of large scale structures (LSS). We show that a good concordance is obtained, albeit with a higher value of the present matter abundance than in the Lambda CDM model. We also comment on general features of the CMB anisotropy spectrum and on the cosmic coincidence problem.
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