Nils Schöneberg, Guillermo Franco Abellán, Andrea Pérez Sánchez, Samuel J. Witte, c Vivian Poulin, Julien Lesgourgues

Despite the remarkable success of the $\Lambda$Cold Dark Matter ($\Lambda$CDM) cosmological model, a growing discrepancy has emerged (currently measured at the level of $\sim 4-6 \sigma$) between the value of the Hubble constant $H_0$ measured using the local distance ladder and the value inferred using the cosmic microwave background and galaxy surveys. While a vast array of $\Lambda$CDM extensions have been proposed to explain these discordant observations, understanding the (relative) success of these models in resolving the tension has proven difficult -- this is a direct consequence of the fact that each model has been subjected to differing, and typically incomplete, compilations of cosmological data. In this review, we attempt to make a systematic comparison of sixteen different models which have been proposed to resolve the $H_0$ tension (spanning both early- and late-Universe solutions), and quantify the relative success of each using a series of metrics and a vast array of data combinations. Owing to the timely appearance of this article, we refer to this contest as the ''$H_0$ Olympics''; the goal being to identify which of the proposed solutions, and more broadly which underlying mechanisms, are most likely to be responsible for explaining the observed discrepancy (should unaccounted for systematics not be the culprit). This work also establishes a foundation of tests which will allow the success of novel proposals to be meaningful ''benchmarked''.

Pedro da Silveira Ferreira, Miguel Quartin

An observer in relative motion to the Cosmic Microwave Background (CMB) rest frame is sensitive to both aberration and Doppler effects. Both effects introduce similar but non-identical off-diagonal couplings in the spherical harmonic coefficients. The CMB temperature dipole may have additional contributions from an intrinsic component, which in turn produces different aberration and Doppler couplings. Moreover, the standard conversion from intensity measurements into temperature also introduces spurious Doppler-like couplings. In order to learn about the intrinsic dipole it is therefore important to measure both aberration and Doppler couplings in an independent manner while also removing the spurious contributions from unit conversion, which are degenerate with the dipole. Here we present a pipeline to measure the Doppler and aberration signal independently from each other and from the dipole itself. We also consider realistic beaming, noise and mask effects. Our pipeline results in independent and unbiased estimators which have uncertainties only ~20% larger than the simple theoretical expectations. We discuss the achievable precision in each measurement for Planck 2018, and also forecast them for future ground-based experiments with the Simons Observatory and CMB-S4. An alternative pipeline is presented in order to cross-check results and improve robustness.

Daniel Baumann, Carlos Duaso Pueyo, Austin Joyce, Hayden Lee, Guilherme L. Pimentel

We extend the cosmological bootstrap to correlators involving massless particles with spin. In de Sitter space, these correlators are constrained both by symmetries and by locality. In particular, the de Sitter isometries become conformal symmetries on the future boundary of the spacetime, which are reflected in a set of Ward identities that the boundary correlators must satisfy. We solve these Ward identities by acting with weight-shifting operators on scalar seed solutions. Using this weight-shifting approach, we derive three- and four-point correlators of massless spin-1 and spin-2 fields with conformally coupled scalars. Four-point functions arising from tree-level exchange are singular in particular kinematic configurations, and the coefficients of these singularities satisfy certain factorization properties. We show that in many cases these factorization limits fix the structure of the correlators uniquely, without having to solve the conformal Ward identities. The additional constraint of locality for massless spinning particles manifests itself as current conservation on the boundary. We find that the four-point functions only satisfy current conservation if the s, t, and u-channels are related to each other, leading to nontrivial constraints on the couplings between the conserved currents and other operators in the theory. For spin-1 currents this implies charge conservation, while for spin-2 currents we recover the equivalence principle from a purely boundary perspective. For multiple spin-1 fields, we recover the structure of Yang-Mills theory. Finally, we apply our methods to slow-roll inflation and derive a few phenomenologically relevant scalar-tensor three-point functions.

Philip D. Mannheim

Since particles obey wave equations, in general one is not free to postulate that particles move on the geodesics associated with test particles. Rather, for this to be the case one has to be able to derive such behavior starting from the equations of motion that the particles obey, and to do so one can employ the eikonal approximation. To see what kind of trajectories might occur we explore the domain of support of the propagators associated with the wave equations. For a minimally coupled massless scalar field the domain of support in curved space is shown to not be restricted to the light cone, while for a conformally coupled massless scalar field the curved space domain is only restricted to the light cone if it propagates in a conformal to flat background. Consequently, eikonalization does not in general lead to null geodesics for curved space massless rays even though it does lead to straight line trajectories in flat spacetime. Equal remarks apply to the massless conformal invariant Maxwell equations. However, for massive particles one does obtain standard geodesic behavior this way, since they do not propagate on the light cone to begin with. Thus depending on how big the curvature actually is, in principle, even if not necessarily in practice, the standard null-geodesic-based gravitational bending formula and the general behavior of propagating light rays are in need of modification in regions with high enough curvature. We show that relativistic eikonalization has an intrinsic light-front structure, and show that eikonalization in a theory with local conformal symmetry leads to trajectories that are only globally conformally symmetric. Propagation of massless particles off the light cone is also manifest in a conformal invariant scalar field propagator in two spacetime dimensions. It takes support both on and inside the light cone, even if the geometry is conformal to flat.

Rafael C. Nunes, Eleonora Di Valentino

It has been intensively discussed if modifications in the dynamics of the Universe at late times is able or not to solve the $H_0$ tension. On the other hand, it has also been argued that the $H_0$ tension is actually a tension on the supernova absolute magnitude $M_B$. In this work, we robustly constraint $M_B$ using Pantheon Supernovae Ia (SN) sample, Baryon Acoustic Oscillations (BAO), and Big Bang Nucleosynthesis (BBN) data, and assess the $M_B$ tension by comparing three theoretical models, namely the standard $\Lambda$CDM, the wCDM and a non-gravitational interaction (IDE) between dark energy (DE) and dark matter (DM). We find that the IDE model can solve the $M_B$ tension with a coupling different from zero at 95\% CL, confirming the results obtained using a $H_0$ prior.

Ashok K. Singal

We determine here peculiar motion of the Solar system, first time from the $m-z$ Hubble diagram of quasars. Observer's peculiar motion causes a systematic shift in the $m-z$ plane between sources lying along the velocity vector and those in the opposite direction, providing a measure of the peculiar velocity. Accordingly, from a sample of $\sim 1.2 \times 10^5$ mid-infrared quasars with measured spectroscopic redshifts, we arrive at a peculiar velocity $\sim 22$ times larger than that from the CMBR dipole, but direction matching within $\sim 2\sigma$. Previous findings from number count, sky brightness or redshift dipoles observed in samples of distant AGNs or SNe Ia too had yielded values two to ten times larger than the CMBR value, %but this by far is the largest value arrived at for the peculiar motion, though the direction in all cases agreed with the CMBR dipole. Since a genuine solar peculiar velocity cannot vary from one dataset to the other, an order of magnitude, statistically significant, discordant dipoles, might imply that we may instead have to look for some other cause for the genesis of these dipole, including that of the CMBR. At the same time, a common direction for all these dipoles, determined from completely independent surveys by different groups employing different techniques, might indicate that these dipoles are not resulting from some systematics in the observations or in the data analysis, but could instead suggest a preferred direction in the Universe due to an inherent anisotropy, which, in turn, would be against the Cosmological Principle (CP), the most basic tenet of the modern cosmology.

Gia Dvali

We present certain universal bounds on the capacity of quantum information storage and on the time scale of its retrieval for a generic quantum field theoretic system. The capacity, quantified by the microstate entropy, is bounded from above by the surface area of the object measured in units of a Goldstone decay constant. The Goldstone bosons are universally present due to the spontaneous breaking of Poincare and internal symmetries by the information-storing object. Applied to a black hole, the bound reproduces the Bekenstein-Hawking entropy. However, the relation goes beyond gravity. The minimal time-scale required for retrieving the quantum information from a system is equal to its volume measured in units of the same Goldstone scale. For a black hole this reproduces the Page time as well as the quantum break-time. The same expression for the information retrieval time is shared by non-gravitational saturated states in gauge theories, including QCD. The saturated objects exhibit some universal signatures such as the emission of ultra-soft radiation. Similar bounds apply to non-relativistic many-body systems.

James Bonifacio

The eigenvalues of the Laplace-Beltrami operator and the integrals of products of eigenfunctions must satisfy certain consistency conditions on compact Riemannian manifolds. These consistency conditions are derived by using spectral decompositions to write quadruple overlap integrals in terms of products of triple overlap integrals in multiple ways. In this paper, we show how these consistency conditions imply bounds on the Laplacian eigenvalues and triple overlap integrals of closed hyperbolic manifolds, in analogy to the conformal bootstrap bounds on conformal field theories. We find an upper bound on the gap between two consecutive nonzero eigenvalues of the Laplace-Beltrami operator in terms of the smaller eigenvalue, an upper bound on the smallest eigenvalue of the rough Laplacian on symmetric, transverse-traceless, rank-2 tensors, and bounds on integrals of products of eigenfunctions and eigentensors. Our strongest bounds involve numerically solving semidefinite programs and are presented as exclusion plots. We also prove the analytic bound $\lambda_{i+1} \leq 1/2+3 \lambda_i+\sqrt{\lambda_i^2+2 \lambda_i+1/4}$ for consecutive nonzero eigenvalues of the Laplace-Beltrami operator on closed orientable hyperbolic surfaces. We give examples of genus-2 surfaces that nearly saturate some of these bounds. To derive the consistency conditions, we make use of a transverse-traceless decomposition for symmetric tensors of arbitrary rank.