Static Spherically Symmetric Kerr-Schild Metrics and Implications for the Classical Double Copy

We discuss the physical interpretation of stress-energy tensors that source static spherically symmetric Kerr-Schild metrics. We find that the sources of such metrics with no curvature singularities or horizons do not simultaneously satisfy the weak and strong energy conditions. Sensible stress-energy tensors usually satisfy both of them. Under most circumstances these sources are not perfect fluids and contain shear stresses. We show that for these systems the classical double copy associates the electric charge density to the Komar energy density. In addition, we demonstrate that the stress-energy tensors are determined by the electric charge density and their conservation equations.Comment: 11 page

Loop-Induced Stochastic Bias at Small Wavevectors

Primordial non-Gaussianities enhanced at small wavevectors can induce a power spectrum of the galaxy overdensity that differs greatly from that of the matter overdensity at large length scales. In previous work, it was shown that "squeezed" three-point and "collapsed" four-point functions of the curvature perturbation $\zeta$ can generate these non-Gaussianities and give rise to so-called scale-dependent and stochastic bias in the galaxy overdensity power spectrum. We explore a third way to generate non-Gaussianities enhanced at small wavevectors: the infrared behavior of quantum loop contributions to the four-point correlations of $\zeta$. We show that these loop effects lead to stochastic bias, which can be observable in the context of quasi-single field inflation.Comment: 10 pages, 4 figure

An Estimate of the Inclusive Branching Ratio to B_c in Ξ_(bbq) Decay

We estimate the branching ratio for the inclusive decays Ξ_(bbq) → B^((∗))_c+X_(c,s,q) to be approximately 1%. Our estimate is performed using non-relativistic potential quark model methods that are appropriate if the bottom and charm quarks are heavy compared to the strong interaction scale. Here the superscript (∗) denotes that we are summing over spin zero B_c and spin one B^∗_c mesons and the subscript q denotes a light quark. Our approach treats the two bottom quarks in the baryon Ξ_(bbq) as a small color anti-triplet. This estimate for the inclusive branching ratio to B_c and B^∗_c mesons also holds for decays of the lowest lying T_(bbqq) tetraquark states, provided they are stable against strong and electromagnetic decay

Deep-learning based measurement of planetary radial velocities in the presence of stellar variability

We present a deep-learning based approach for measuring small planetary radial velocities in the presence of stellar variability. We use neural networks to reduce stellar RV jitter in three years of HARPS-N sun-as-a-star spectra. We develop and compare dimensionality-reduction and data splitting methods, as well as various neural network architectures including single line CNNs, an ensemble of single line CNNs, and a multi-line CNN. We inject planet-like RVs into the spectra and use the network to recover them. We find that the multi-line CNN is able to recover planets with 0.2 m/s semi-amplitude, 50 day period, with 8.8% error in the amplitude and 0.7% in the period. This approach shows promise for mitigating stellar RV variability and enabling the detection of small planetary RVs with unprecedented precision.Comment: Draft, unsubmitted, 10 pages, 8 figure

Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms

We prove that every mapping torus of any free group endomorphism is residually finite. We show how to use a not yet published result of E. Hrushovski to extend our result to arbitrary linear groups. The proof uses algebraic self-maps of affine spaces over finite fields. In particular, we prove that when such a map is dominant, the set of its fixed closed scheme points is Zariski dense in the affine space.Comment: 18 page

The Immirzi Parameter as an Instanton Angle

The Barbero-Immirzi parameter is a one parameter quantization ambiguity underpinning the loop approach to quantum gravity that bears tantalizing similarities to the theta parameter of gauge theories such as Yang-Mills and QCD. Despite the apparent semblance, the Barbero-Immirzi field has resisted a direct topological interpretation along the same lines as the theta-parameter. Here we offer such an interpretation. Our approach begins from the perspective of Einstein-Cartan gravity as the symmetry broken phase of a de Sitter gauge theory. From this angle, just as in ordinary gauge theories, a theta-term emerges from the requirement that the vacuum is stable against quantum mechanical tunneling. The Immirzi parameter is then identified as a combination of Newton's constant, the cosmological constant, and the theta-parameter.Comment: 24 page