arXiv subjects

Stephon Alexander

Publications and source records attributed to Stephon Alexander.

At least 55 records · Page 3Linked to original sources

arXiv2023

An Inner Product for 4D Quantum Gravity and the Chern-Simons-Kodama State

We demonstrate that reality conditions for the Ashtekar connection imply a non-trivial measure for the inner product of gravitational states in the polarization where the Ashtekar connection is diagonal, and we express the measure as the determinant of a certain first-order differential operator. This result opens the possibility to perform a non-perturbative analysis of the quantum gravity scalar product. In this polarization, the Chern-Simons-Kodama state, which solves the constraints of quantum gravity for a certain factor ordering, and which has de Sitter space as a semiclassical limit, is perturbatively non-normalizable with respect to the naive ve inner product. Our work reopens the question of whether this state might be normalizable when the correct non-perturbative inner product and choice of integration contour are taken into account. As a first step, we perform a semi-classical treatment of the measure by evaluating it on the round three-sphere, viewed as a closed spatial slice of de Sitter. The result is a simple, albeit divergent, infinite product that might serve as a regulator for a more complete treatment of the problem. Additionally, our results suggest deep connections between the problem of computing the norm of the CSK state in quantum gravity and computing the Chern-Simons partition function for a complex group.

hep-th↗

arXiv2023

Towards A Direct Detection of the Spin of Dark Matter

We investigate the contribution of higher spin particles in the signal of direct detection experiments searching for dark matter. We consider a bosonic or fermionic higher spin dark matter (HSDM) candidate which interacts with the Standard Model via a dark U(1) mediator. For a particular subclass of interactions, spin-polarized targets may be used for spin determination: The angular dependence of scatterings can distinguish integer (spin-$s$) vs. half-integer (spin-$s + 1/2$), while the recoil energy dependence of the signal determines $s$. We consider also the signal of a supersymmetric higher spin dark sector, which suggests a characteristic signal (''SUSY Rilles'') for directional direct detection.

hep-ph↗

arXiv2023

Pure gauge theory for the gravitational spin connection

The gravitational spin connection appears in gravity as a non-Abelian gauge field for the Lorentz group $SO(3,1)$, which is non-compact. The action for General Relativity is linear in the field strength associated to the spin connection, and its equation of motion corresponds to the standard metricity constraint. Consequently, the zero-torsion spin connection is never realized as an independent degree of freedom and is determined by the vierbein field. In this work, we take a different perspective and consider a pure Yang-Mills theory for the spin connection coupled to Dirac fermions, resulting in the former being a dynamical field. After discussing various approaches towards managing the pathologies associated with non-compact gauge theories, we compute the tree-level amplitude for fermion scattering via a spin connection exchange. In contrast to integrating out torsion in the presence of fermions, the model induces a chiral four-Fermi like term that involves a right-right current interaction, which is not present in the Standard Model.

gr-qc↗

arXiv2023

Parity-Violating Trispectrum from Chern-Simons Gravity

We show that dynamical Chern-Simons (dCS) gravity imprints a parity-violating signal in primordial scalar perturbations. Specifically, we find that, after dCS amplifies one graviton helicity due to a tachyonic instability, the graviton-mediated correlation between two pairs of scalars develops a parity-odd component. This correlation, the primordial scalar trispectrum, is then transferred to the corresponding curvature correlator and thus is imprinted in both LSS and the CMB. We find that the parity-odd piece has roughly the same amplitude as its parity-even counterpart, scaled linearly by the degree of gravitational circular polarization $Π_{\rm circ} \sim \sqrt{\varepsilon}[H^2/(M_{\rm Pl} f)] \leq 1$, with $\varepsilon$ the slow-roll parameter, $H$ the inflationary Hubble scale, $f$ the dCS decay constant, and the upper bound saturated for purely circularly-polarized gravitons. We also find that, in the collapsed limit, the ratio of the two trispectra contains direct information about the graviton's spin. In models beyond standard inflationary dCS, e.g. those with multiple scalar fields or superluminal scalar sound speed, there can be a large enhancement factor $F \gtrsim 10^6$ to the trispectrum. We find that an LSS survey that contains $N_{\rm modes}$ linear modes would place an $nσ$ constraint on $Π_{\rm circ}r$ of $\sim 0.04\ (n/3)(10^6/F)(10^6/N_{\rm modes})^{1/2}$ from the parity-odd galaxy trispectrum, for tensor-to-scalar ratio $r$. We also forecast for several spectroscopic and 21-cm surveys. This constraint implies that, for high-scale single-field inflation parameters, LSS can probe very large dCS decay constants $f \lesssim 4\times 10^9\ {\rm GeV}(3/n)(F/10^6)\left(N_{\rm modes}/10^6\right)^{1/2}$. Our result is the first example of a massless particle yielding a parity-odd scalar trispectrum through spin-exchange.

astro-ph.CO↗

arXiv2023

Addressing the Hubble and $S_8$ Tensions with a Kinetically Mixed Dark Sector

We present a kinetically mixed dark sector (KMIX) model to address the Hubble and $S_8$ tensions. Inspired from string theory, our model includes two fields: an axion, which plays a role similar to the scalar field in early dark energy models, and a dilaton. This theory differs from other axio-dilaton models aimed at the Hubble tension in that there is necessarily kinetic mixing between the two fields which allows for efficient energy transfer from the axion into the dilaton which has $w\approx1$. As a direct consequence of these dynamics, we find the model does not need to resort to a fine-tuned potential to solve the Hubble tension and naturally accommodates a standard axion potential. Furthermore, the axion will necessarily makeup a small (fuzzy) fraction of $Ω_{\rm cdm}$ once it begins to oscillate at the bottom of its potential and will suppress the growth of perturbations on scales sensitive to $S_8$. Interestingly, the scale of the potential for the dilaton has to be small, $\lesssim \mathcal{O}(10~{\rm meV})^4$, suggesting the possibility for a connection to dark energy. Implementing the dynamics for the background and perturbations in a modified Boltzmann code we calculate the CMB and matter power spectra for our theory. Exploring the parameter space of our model, we find regions which can accommodate a $\sim 10\%$ increase in $H_0$ from the Planck inferred value and $S_8$ values that are consistent with large-scale structure constraints.

astro-ph.CO↗

arXiv2023

Black Hole Superradiance in Dynamical Chern-Simons Gravity

Black hole superradiance provides a window into the dynamics of light scalar fields and their interactions close to a rotating black hole. Due to the rotation of the black hole, the amplitude of the scalar field becomes magnified, leading to a "black hole bomb" effect. Recent work has demonstrated that rotating black holes in dynamical Chern-Simons gravity possess unique structures, the "Chern-Simons caps," which may influence the behavior of matter near the black hole. Motivated by the presence of these caps, we study superradiance in dynamical Chern-Simons gravity in the context of a slowly rotating black hole. We find that additional modes are excited and contribute to the superradiance beyond what is expected for a Kerr black hole. Studying the superradiant spectrum of perturbations, we find that the Chern-Simons contributions give rise to small corrections to the angular dependence of the resulting scalar cloud. Finally, we comment on potential observable consequences and future avenues for investigation.

gr-qc↗

arXiv2022

An Exact Fermionic Chern-Simons-Kodama State in Quantum Gravity

The Chern-Simons-Kodama (CSK) state is an exact, non-perturbative wave function in the Ashtekar formulation of classical General Relativity. In this work, we find a generalized fermionic CSK state by solving the extended gravitational and fermionic Hamiltonian constraints of the Wheeler-DeWitt equation exactly. We show that this new state reduces to the original Kodama state upon symmetry reduction to FRW coordinates with perturbative fermionic corrections, making contact with the Hartle-Hawking and Vilenkin wave functions of the universe in cosmology. We also find that when both torsion and fermions are non-vanishing, the wave function possesses a finite amplitude to evade the Big Bang curvature singularity.

gr-qc↗

arXiv2022

Chern-Simons Gravity and Neutrino Self-Interactions

Dynamical Chern-Simons gravity (dCS) is a four-dimensional parity-violating extension of general relativity. Current models predict the effect of this extension to be negligible due to large decay constants $f$ close to the scale of grand unified theories. Here, we present a construction of dCS allowing for much smaller decay constants, ranging from sub-eV to Planck scales. Specifically, we show that if there exists a fermion species with strong self-interactions, the short-wavelength fermion modes form a bound state. This bound state can then undergo dynamical symmetry breaking and the resulting pseudoscalar develops Yukawa interactions with the remaining long-wavelength fermion modes. Due to this new interaction, loop corrections with gravitons then realize a linear coupling between the pseudoscalar and the gravitational Chern-Simons term. The strength of this coupling is set by the Yukawa coupling constant divided by the fermion mass. Therefore, since self-interacting fermions with small masses are ideal, we identify neutrinos as promising candidates. For example, if a neutrino has a mass $m_ν\lesssim {\rm meV}$ and the Yukawa coupling is order unity, the dCS decay constant can be as small as $f \sim 10^3 m_ν\lesssim {\rm eV}$. We discuss other potential choices for fermions.

hep-ph↗

arXiv2022

Torsion and the Probability of Inflation

We revisit the problem of the "probability of inflation" from the point of view of the Einstein-Cartan theory, where torsion can be present off-shell even in the absence of spinorial currents. An informal estimate suggests that the barrier for tunneling from "nothing" into a classical universe becomes thinner and lower, should torsion be present even if only off-shell. This is confirmed by a detailed calculation, where the usual assumptions are re-evaluated and repurposed in our situation. Interestingly some approximations used in the literature (such as the WKB approximation) are not needed in general, and in particular in our case. When we consider wave packets centered around zero torsion, however, the conclusion depends crucially how these are built. With a Klein-Gordon current prescription for the measure and probability, for small torsion variance, σ_c, we recover the plane wave results. Nonetheless, for large σc, higher order corrections could reverse this conclusion.

gr-qc↗

arXiv2022

The Chern-Simons Caps for Rotating Black Holes

We study the dynamical Chern-Simons gravity as an effective quantum field theory, and discuss a broad range of its parameter space where the theory is valid. Within that validity range, we show that slowly rotating black holes acquire novel geometric structures due to the gravitational dynamical Chern-Simons term. In particular, the rotating black hole solutions get endowed with two, cap-like domains, emanating from the north and south poles in the standard Boyer-Lindquist coordinates. The domains extend out to a distance that is approximately a few percent of the black hole's size. The cap-like domains have an unusual equation of state, pointing to non-standard dynamics within the caps. In particular, the focusing condition for geodesics is violated in those domains. This in turn implies that the Hawking-Penrose singularity theorem cannot be straightforwardly applied to hypothetical probe matter placed within the Chern-Simons caps.

hep-th↗

arXiv2021

Domain Adaptation for Simulation-Based Dark Matter Searches Using Strong Gravitational Lensing

Clues to the identity of dark matter have remained surprisingly elusive, given the scope of experimental programs aimed at its identification. While terrestrial experiments may be able to nail down a model, an alternative, and equally promising, method is to identify dark matter based on astrophysical or cosmological signatures. A particularly sensitive approach is based on the unique signature of dark matter substructure on galaxy-galaxy strong lensing images. Machine learning applications have been explored in detail for extracting just this signal. With limited availability of high quality strong lensing data, these approaches have exclusively relied on simulations. Naturally, due to the differences with the real instrumental data, machine learning models trained on simulations are expected to lose accuracy when applied to real data. This is where domain adaptation can serve as a crucial bridge between simulations and real data applications. In this work, we demonstrate the power of domain adaptation techniques applied to strong gravitational lensing data with dark matter substructure. We show with simulated data sets of varying complexity, that domain adaptation can significantly mitigate the losses in the model performance. This technique can help domain experts build and apply better machine learning models for extracting useful information from strong gravitational lensing data expected from the upcoming surveys.

astro-ph.CO↗

arXiv2021

Gravity waves in parity-violating Copernican Universes

In recent work minimal theories allowing the variation of the cosmological constant by means of a balancing torsion, have been proposed. It was found that such theories contain parity violating homogeneous and isotropic solutions, due to a torsion structure called the Cartan spiral staircase. Their dynamics are controlled by Euler and Pontryagin quasi-topological terms in the action. Here we show that such theories predict a dramatically different picture for gravitational wave fluctuations in the parity violating branch. If the dynamics are ruled solely by the Euler-type term, then linear tensor mode perturbations are entirely undetermined, hinting at a new type of gauge invariance. The Pontryagin term not only permits for phenomenologically sounder background solutions (as found in previous literature), but for realistic propagation of gravitational wave modes. We discuss the observational constraints and predictions of these theories.

gr-qc↗

arXiv2021

The Physics of Machine Learning: An Intuitive Introduction for the Physical Scientist

This article is intended for physical scientists who wish to gain deeper insights into machine learning algorithms which we present via the domain they know best, physics. We begin with a review of two energy-based machine learning algorithms, Hopfield networks and Boltzmann machines, and their connection to the Ising model. This serves as a foundation to understand the phenomenon of learning more generally. Equipped with this intuition we then delve into additional, more "practical," machine learning architectures including feedforward neural networks, convolutional neural networks, and autoencoders. We also provide code that explicitly demonstrates training a neural network with gradient descent.

cond-mat.dis-nn↗

arXiv2021

Cosmic Filament Spin from Dark Matter Vortices

The recent observational evidence for cosmic filament spin on megaparsec scales (Wang et al, Nature Astronomy 5, 839-845 (2021)) demands an explanation in the physics of dark matter. Conventional collisionless cold particle dark matter is conjectured to generate cosmic filament spin through tidal torquing, but this explanation requires extrapolating from the quasi-linear regime to the non-linear regime. Meanwhile no alternative explanation exists in the context of ultra-light (e.g., axion) dark matter, and indeed these models would naively predict zero spin for cosmic filaments. In this Letter we study cosmic filament spin in theories of ultra-light dark matter, such as ultra-light axions, and bosonic and fermionic condensates, such as superfluids and superconductors. These models are distinguished from conventional particle dark matter models by the possibility of dark matter vortices. We take a model agnostic approach, and demonstrate that a collection of dark vortices can explain the data reported in Wang et al. Modeling a collection of vortices with a simple two-parameter analytic model, corresponding to an averaging of the velocity field, we find an excellent fit to the data. We perform a Markov Chain Monte Carlo analysis and find constraints on the number of vortices, the dark matter mass, and the radius of the inner core region where the vortices are distributed, in order for ultra-light dark matter to explain spinning cosmic filaments.

astro-ph.CO↗

arXiv2021

Black hole and cosmological analysis of BF sequestered gravity

We study a minimal extension of a recently proposed modification of general relativity that draws on concepts from topological field theory to resolve aspects of the cosmological constant problem. In the original model, the field content of general relativity was augmented to include a gauge field and an adjoint-valued two-form without modifying the classical gravitational dynamics. Here we include a kinetic term for the gauge field which sources fluctuations of the cosmological constant. We then study spherically symmetric black holes and a simple homogeneous, isotropic cosmological model predicted by the extended theory. For the black hole case, we observe deviations near the event horizon as well as a ``charge"-like behavior induced by the gauge field. In the cosmological case, $\dot{H}$ is always positive and some solutions asymptote to a constant $H$.

gr-qc↗

arXiv2021

Strongly-Interacting Ultralight Millicharged Particles

We consider the implications of an ultra-light fermionic dark matter candidate that carries baryon number. This naturally arises if dark matter has a small charge under standard model baryon number whilst having an asymmetry equal and opposite to that in the visible universe. A prototypical model is a theory of dark baryons of a non-Abelian gauge group, i.e., a dark Quantum Chromo-Dynamics (QCD). For sub-eV dark baryon masses, the inner region of dark matter halos is naturally at 'nuclear density', allowing for the formation of exotic states of matter, akin to neutron stars. The Tremaine-Gunn lower bound on the mass of fermionic dark matter, i.e., the dark baryons, is violated by the strong short-range self-interactions, cooling via emission of light dark pions, and the Cooper pairing of dark quarks that occurs at densities that are high relative to the (ultra-low) dark QCD scale. We develop the astrophysics of these STrongly-interacting Ultra-light Millicharged Particles (STUMPs) utilizing the equation of state of dense quark matter, and find halo cores consistent with observations of dwarf galaxies. These cores are prevented from core-collapse by pressure of the 'neutron star', which suggests ultra-light dark QCD as a resolution to core-cusp problem of collisionless cold dark matter. The model is distinguished from ultra-light bosonic dark matter through direct detection and collider signatures, as well as by phenomena associated with superconductivity, such as Andreev reflection and superconducting vortices.

astro-ph.CO↗

arXiv2021

Decoding Dark Matter Substructure without Supervision

The identity of dark matter remains one of the most pressing questions in physics today. While many promising dark matter candidates have been put forth over the last half-century, to date the true identity of dark matter remains elusive. While it is possible that one of the many proposed candidates may turn out to be dark matter, it is at least equally likely that the correct physical description has yet to be proposed. To address this challenge, novel applications of machine learning can help physicists gain insight into the dark sector from a theory agnostic perspective. In this work we demonstrate the use of unsupervised machine learning techniques to infer the presence of substructure in dark matter halos using galaxy-galaxy strong lensing simulations.

astro-ph.CO↗

arXiv2021

The Autodidactic Universe

We present an approach to cosmology in which the Universe learns its own physical laws. It does so by exploring a landscape of possible laws, which we express as a certain class of matrix models. We discover maps that put each of these matrix models in correspondence with both a gauge/gravity theory and a mathematical model of a learning machine, such as a deep recurrent, cyclic neural network. This establishes a correspondence between each solution of the physical theory and a run of a neural network. This correspondence is not an equivalence, partly because gauge theories emerge from $N \rightarrow \infty $ limits of the matrix models, whereas the same limits of the neural networks used here are not well-defined. We discuss in detail what it means to say that learning takes place in autodidactic systems, where there is no supervision. We propose that if the neural network model can be said to learn without supervision, the same can be said for the corresponding physical theory. We consider other protocols for autodidactic physical systems, such as optimization of graph variety, subset-replication using self-attention and look-ahead, geometrogenesis guided by reinforcement learning, structural learning using renormalization group techniques, and extensions. These protocols together provide a number of directions in which to explore the origin of physical laws based on putting machine learning architectures in correspondence with physical theories.

hep-th↗