Cosmin Ilie, Caleb Levy, Jacob Pilawa, Saiyang Zhang

Dark Matter (DM) can be trapped by the gravitational field of any star, since collisions with nuclei in dense environments can slow down the DM particle below the escape velocity ($v_{esc}$) at the surface of the star. If captured, the DM particles can self annihilate, and, therefore, provide a new source of energy for the star. We investigate this phenomenon for capture of DM particles with mass ($m_X$) heavier than $100$ GeV by the first generation of stars (Pop III stars), by using the recently developed multiscatter capture formalism. Pop III stars are particularly good DM captors, since they form in DM rich environments, at the center of $~\sim 10^6 M_\odot$ DM minihalos, at redshifts $z~\sim 15$. Assuming a DM-proton scattering cross section ($\sigma)$ at the deepest current exclusion limits provided by the XENON1T experiment, we find that captured DM annihilations at the core of Pop III stars can lead, via the Eddington limit, to upperbounds in stellar masses that can be as low as a few $M_\odot$ if the ambient DM density ($\rho_X$) at the location of the Pop III star is sufficiently high. Conversely, when Pop III stars are identified, one can use their observed mass ($M_\star$) to place bounds on $\rho_X \sigma$. Using adiabatic contraction to estimate the ambient DM density in the environment surrounding Pop III stars, we place projected upper limits on $\sigma$, for $M_\star$ in the $100-1000 M_\odot$ range, and find bounds that are competitive with, or deeper than, those provided by the most sensitive current direct detection experiments. Most intriguingly, we find that each of the Pop III stars considered could be used to probe below the "neutrino floor," and identify the corresponding necessary ambient DM density.

Kyu-Hyun Chae, Federico Lelli, Harry Desmond, Stacy S. McGaugh, Pengfei Li, James M. Schombert

The Strong Equivalence Principle (SEP) distinguishes General Relativity from other viable theories of gravity. The SEP demands that the internal dynamics of a self-gravitating system under free-fall in an external gravitational field should not depend on the external field strength. We test the SEP by investigating the external field effect (EFE) in Milgromian dynamics (MOND), proposed as an alternative to dark matter in interpreting galactic kinematics. We report a detection of this EFE using galaxies from the Spitzer Photometry and Accurate Rotation Curves (SPARC) sample together with estimates of the large-scale external gravitational field from an all-sky galaxy catalog. Our detection is threefold: (1) the EFE is individually detected at $8\sigma$ to $11\sigma$ in "golden" galaxies subjected to exceptionally strong external fields, while it is not detected in exceptionally isolated galaxies, (2) the EFE is statistically detected at more than $4\sigma$ from a blind test of 153 SPARC rotating galaxies, giving a mean value of the external field consistent with an independent estimate from the galaxies' environments, and (3) we detect a systematic downward trend in the weak gravity part of the radial acceleration relation at the right acceleration predicted by the EFE of the MOND modified gravity. Tidal effects from neighboring galaxies in the $\Lambda$CDM context are not strong enough to explain these phenomena. They are not predicted by existing $\Lambda$CDM models of galaxy formation and evolution, adding a new small-scale challenge to the $\Lambda$CDM paradigm. Our results point to a breakdown of the SEP, supporting modified gravity theories beyond General Relativity.

Tobias Westphal, Hans Hepach, Jeremias Pfaff, Markus Aspelmeyer

We demonstrate gravitational coupling between two gold spheres of approximately 1mm radius and 90mg mass. By periodically modulating the source mass position at a frequency f=12.7mHz we generate a time-dependent gravitational acceleration at the location of the test mass, which is measured off resonance in a miniature torsional balance configuration. Over an integration time of 350 hours the test mass oscillator enables measurements with a systematic accuracy of 4E-11m/s^2 and a statistical precision of 4E-12m/s^2. This is sufficient to resolve the gravitational signal at a minimal surface distance of 400mum between the two masses. We observe both linear and quadratic coupling, consistent in signal strength with a time-varying 1/r gravitational potential. Contributions of non-gravitational forces could be kept to less than 10% of the observed signal. We expect further improvements to enable the isolation of gravity as a coupling force for objects well below the Planck mass. This opens the way for precision tests of gravity in a new regime of isolated microscopic source masses.

A. A. Eremko, L. Brizhik, V. M. Loktev

The Dirac equation with the Coulomb potential is studied. It is shown that there exists a new invariant in addition to the known Dirac and Johnson-Lippman ones. The solution of the Dirac equation, using the generalized invariant, and explicit expressions for the bispinors corresponding to the three sets of the invariants, their eigenvalues and quantum numbers are obtained. The general solution of the Dirac equation with the Coulomb potential is shown to contain free parameters, whose variation transforms one particular solution into any other and controls spatial electron probability amplitude and spin polarization. The electron probability densities and spin polarizations are obtained in the general form and calculated explicitly for some electron states in the hydrogen-like energy spectrum. The spatial distributions of these characteristics are shown to depend essentially on the invariant set, demonstrating physical difference of the states corresponding to different invariants.

Renata Kallosh

This paper is dedicated to Mike Duff on the occasion of his 70th birthday. I discuss some issues of M-theory/string theory/supergravity closely related to Mike's interests. I describe a relation between STU black hole entropy, Cayley hyperdeterminant, Bhargava cube and a 3-qubit Alice, Bob, Charlie triality symmetry. I shortly describe my recent work with Gunaydin, Linde, Yamada on M-theory cosmology, inspired by the work of Duff with Ferrara and Borsten, Levay, Marrani et al. Here we have 7-qubits, a party including Alice, Bob, Charlie, Daisy, Emma, Fred, George. Octonions and Hamming error correcting codes are at the base of these models. They lead to 7 benchmark targets of future CMB missions looking for primordial gravitational wave from inflation. I also show puzzling relations between the fermion mass eigenvalues in these cosmological models, exceptional Jordan eigenvalue problem, and black hole entropy. The symmetry of our cosmological models is illustrated by beautiful pictures of a Coxeter projection of the root system of E7.

Cosmin Ilie, Caleb Levy, Jacob Pilawa, Saiyang Zhang

We show that the mere observation of the first stars (Pop III stars) in the universe can be used to place tight constraints on the strength of the interaction between dark matter and regular, baryonic matter. We apply this technique to a candidate Pop III stellar complex discovered with the Hubble Space Telescope at $z \sim 7$ and find bounds that are competitive with, or even stronger than, current direct detection experiments, such as XENON1T, for dark matter particles with mass ($m_X$) larger than about $100$ GeV. We also show that the discovery of sufficiently massive Pop III stars could be used to bypass the main limitations of direct detection experiments: the neutrino background to which they will be soon sensitive.

Ofer Lahav

The Cosmological Constant Lambda, a concept introduced by Einstein in 1917, has been with us ever since in different variants and incarnations, including the broader concept of Dark Energy. Current observations are consistent with a value of Lambda corresponding to about present-epoch 70% of the critical density of the Universe. This is causing the speeding up (acceleration) of the expansion of the Universe over the past 6 billion years, a discovery recognised by the 2011 Nobel Prize in Physics. Coupled with the flatness of the Universe and the amount of 30% matter (5% baryonic and 25% Cold Dark Matter), this forms the so-called Lambda-CDM standard model, which has survived many observational tests over about 30 years. However, there are currently indications of inconsistencies (`tensions' ) within Lambda-CDM on different values of the Hubble Constant and the clumpiness factor. Also, time variation of Dark Energy and slight deviations from General Relativity are not ruled out yet. Several grand projects are underway to test Lambda-CDM further and to estimate the cosmological parameters to sub-percent level. If Lambda-CDM will remain the standard model, then the ball is back in the theoreticians' court, to explain the physical meaning of Lambda. Is Lambda an alteration to the geometry of the Universe, or the energy of the vacuum? Or maybe it is something different, that manifests a yet unknown higher-level theory?

Juan Calderón Bustillo, Nicolas Sanchis-Gual, Alejandro Torres-Forné, José A. Font, Avi Vajpeyi, Rory Smith, Carlos Herdeiro, Eugen Radu, Samson H. W. Leong

Advanced LIGO-Virgo reported a short gravitational-wave signal (GW190521) interpreted as a quasi-circular merger of black holes, one populating the pair-instability supernova gap, forming a remnant black hole of $M_f\sim 142 M_\odot$ at a luminosity distance of $d_L \sim 5.3$ Gpc. With barely visible pre-merger emission, however, GW190521 merits further investigation of the pre-merger dynamics and even of the very nature of the colliding objects. We show that GW190521 is consistent with numerically simulated signals from head-on collisions of two (equal mass and spin) horizonless vector boson stars (aka Proca stars), forming a final black hole with $M_f = 231^{+13}_{-17}\,M_\odot$, located at a distance of $d_L = 571^{+348}_{-181}$ Mpc. The favoured mass for the ultra-light vector boson constituent of the Proca stars is $\mu_{\rm V}= 8.72^{+0.73}_{-0.82}\times10^{-13}$ eV. This provides the first demonstration of close degeneracy between these two theoretical models, for a real gravitational-wave event. Confirmation of the Proca star interpretation, which we find statistically slightly preferred, would provide the first evidence for a long sought dark matter particle.