Accurate and efficient modeling of the dynamics of binary black holes (BBHs) is crucial to their detection and parameter estimation through gravitational waves, with both LIGO/Virgo and LISA. General BBH configurations will have misaligned spins and eccentric orbits, eccentricity being particularly relevant at early times. Modeling these systems is both analytically and numerically challenging. Even though the 1.5 post-Newtonian (PN) order is Liouville integrable, numerical work has demonstrated chaos at 2PN order, which impedes the existence of an analytic solution. In this article we revisit integrability at both 1.5PN and 2PN orders. At 1.5PN, we construct four (out of five) action integrals. At 2PN, we show that the system is indeed integrable—but in a perturbative sense—by explicitly constructing five mutually commuting constants of motion. Because of the KAM theorem, this is consistent with the past numerical demonstration of chaos. Our method extends to higher PN orders, opening the door for a fully analytical solution to the generic eccentric, spinning BBH problem.

Degenerate higher-order scalar-tensor (DHOST) theories are considered the most general class of scalar-tensor theories with an additional scalar field. DHOST theories modify the laws of gravity even at galaxy clusters scale hence affecting the weak lensing, x-ray, and Sunyaev-Zel’dovich observables. We derive the theoretical expression for the lensing convergence $\kappa$ and the pressure profile $P$ of clusters in the framework of DHOST theories and quantify how much they deviate from their general relativity counterparts. We argue that combined measurements of $\kappa$, $P$, and of the electron number density $n_e$ can constrain both the cluster parameters and some effective parameters of the DHOST theory. We carry on a Fisher matrix forecasts analysis to investigate whether this is indeed the case considering different scenarios for the spatial resolution and errors on the measured quantities.

We perform a covariant $1+3$ split of the Newton-Cartan equations. The resulting 3-dimensional system of equations, called the $1+3$-Newton-Cartan equations, is structurally equivalent to the $1+3$-Einstein equations. In particular it features the momentum constraint, and a choice of adapted coordinates corresponds to a choice of shift vector. We show that these equations reduce to the classical Newton equations without the need for special Galilean coordinates. The solutions to the $1+3$-Newton-Cartan equations are equivalent to the solutions of the classical Newton equations if space is assumed to be compact or if fall-off conditions at infinity are assumed. We then show that space expansion arises as a fundamental field in Newton-Cartan theory, and not by construction as in the classical formulation of Newtonian cosmology. We recover the Buchert-Ehlers theorem for the general expansion law in Newtonian cosmology.

We consider $f(R)$ gravity theories in the presence of a scalar field minimally coupled to gravity with a self-interacting potential in ($2+1$)-dimensions. Without specifying the form of the $f(R)$ function, we first obtain an exact black hole solution dressed with scalar hair with the scalar charge to appear in the $f(R)$ function and we discuss its thermodynamics. This solution at large distances gives a hairy Bañados, Teitelboim, and Zanelli (BTZ) black hole, and it reduces to the BTZ black hole when the scalar field decouples. In a pure $f(R)$ gravity supported by the scalar field, we find an exact hairy black hole similar to the BTZ black hole with phantom hair and an analytic $f(R)$ form and discuss its thermodynamics.

We give a detailed account of the Hamiltonian Gotay-Nester-Hinds (GNH) analysis of the parametrized unimodular extension of the Holst action. The purpose of the paper is to derive, through the clear geometric picture furnished by the GNH method, a simple Hamiltonian formulation for this model and explain why it is difficult to arrive at it in other approaches. We will also show how to take advantage of the field equations to anticipate the simple form of the constraints that we find in the paper.

Space-based gravitational-wave (GW) detectors, including LISA, Taiji and TianQin, are able to detect mHz GW signals produced by mergers of supermassive black hole binaries, which opens a new window for GW astronomy. In this article, we numerically estimate the potential capabilities of the future networks of multiple space-based detectors using Bayesian analysis. We modify the public package bilby and employ the sampler pymultinest to analyze the simulated data of the space-based detector networks, and investigate their abilities for source localization and testing the parity symmetry of gravity. In comparison with the case of an individual detector, we find detector networks can significantly improve the source localization. While for constraining the parity symmetry of gravity, we find that detector networks and an individual detector follow the similar constraints on the parity-violating energy scale $M_{\mathrm{PV}}$. Similar analysis can be applied to other potential observations of various space-based GW detectors.

In this paper, we propose a method to reconstruct the curvaton potential from a scale-dependent non-Gaussianity parameter $f_{\mathrm{NL}}$. We exemplify our method, devising a weakly self-interacting curvaton model that produces a scale-dependent $f_{\mathrm{NL}}$ that crosses zero twice and is bounded from below and above. We identify the higher value of crossing with the cosmic microwave background (CMB) pivot scale, making the lower value fall within important structure formation scales. In addition, our curvaton model satisfies the observational constraints and leads to a $k$-dependent $f_{\mathrm{NL}}$ that can explain the CMB dipolar modulation. Our procedure can be straightforwardly extended to reconstruct the curvaton potential instead from the $g_{\mathrm{NL}}$ parameter.

The Neutron star Interior Composition Explorer (NICER) is currently observing the x-ray pulse profiles emitted by hot spots on the surface of rotating neutron stars allowing for an inference of their radii with unprecedented precision. A critical ingredient in the pulse profile model is an analytical formula for the oblate shape of the star. These formulas require a fitting over a large ensemble of neutron star solutions, which cover a wide set of equations of state, stellar compactnesses and rotational frequencies. However, this procedure introduces a source of systematic error, as (i) the fits do not describe perfectly the surface of all stars in the ensemble and (ii) neutron stars are described by a single equation of state, whose influence on the surface shape is averaged out during the fitting procedure. Here we perform a first study of this systematic error, finding evidence that it is subdominant relative to the statistical error in the radius inference by NICER. We also find evidence that the formula currently used by NICER can be used in the inference of the radii of rapidly rotating stars, outside of the formula’s domain of validity. Moreover, we employ an accurate enthalpy-based method to locate the surface of numerical solutions of rapidly rotating neutron stars and a new highly accurate formula to describe their surfaces. These results can be used in applications that require an accurate description of oblate surfaces of rapidly rotating neutron stars.

We evolve high-mass disks of mass $15–50M_{\odot }$ orbiting a $50M_{\odot }$ spinning black hole in the framework of numerical relativity. Such high-mass systems could be an outcome during the collapse of rapidly rotating very massive stars. The massive disks are dynamically unstable to the so-called one-armed spiral-shape deformation with the maximum fractional density perturbation of $\delta \rho /\rho \gtrsim 0.1$, and hence, high-amplitude gravitational waves are emitted. The waveforms are characterized by an initial high-amplitude burst with the frequency of $\sim 40–50\mathrm{Hz}$ and the maximum amplitude of $(1–10)\times {10}^{-22}$ at the hypothetical distance of 100 Mpc and by a subsequent low-amplitude quasiperiodic oscillation. We illustrate that the waveforms in our models with a wide range of the disk mass resemble that of GW190521. We also point out that gravitational waves from rapidly rotating very massive stars can be the source for 3rd-generation gravitational-wave detectors for exploring the formation process of rapidly spinning high-mass black holes of mass $\sim 50–100M_{\odot }$ in an early universe.

Equation of state (EOS) insensitive relations, so-called universal relations, between the neutron star (NS) compactness, its multipolar tidal deformability coefficients, and between the tidal parameters for binary systems are essential to break degeneracies in gravitational wave data analysis. Here, we validate and recalibrate these universal relations using a large set of almost 2 million phenomenological EOSs that are consistent with current observations. In doing so, we extend universal relations to a larger region of the EOS parameter space, most notably to softer EOSs and larger compactnesses. We show that waveform models that neglect higher-than-leading-order tidal deformations of the NSs accumulate as much as 3.5 radians of dephasing from 20 Hz to merger. We also perform a full Bayesian parameter estimation of the GW170817 data, and we compare the NS radius constraints produced using universal relations from the literature and the updated fits we propose here. We find that the new fits yield a NS radius that is smaller by about 500 meters. This difference is less than the statistical uncertainty on the radius at the signal-to-noise ratio of GW170817, but it is significantly larger than the precision anticipated for next-generation detectors.

We present results on the search for the coalescence of compact binary mergers using convolutional neural networks and the LIGO/Virgo data, corresponding to the O2 observation period. Two-dimensional images in time and frequency are used as input, and two sets of neural networks are trained separately for low mass ($0.2-2.0{\mathrm{M}}_{\odot }$) and high mass ($25-100{\mathrm{M}}_{\odot }$) compact binary coalescence events. We explored neural networks trained with input information from a single or a pair of interferometers, indicating that the use of information from pairs leads to an improved performance. A scan over the full O2 data set using the convolutional neural networks for detection demonstrates that the performance is compatible with that from canonical pipelines using matched filtering techniques, opening the possibility for an online implementation in future observation periods. No additional events with significant signal-to-noise ratio are found in the O2 data.

Models with singlet fields coupling to the Higgs can enable a strongly first-order electroweak phase transition, of interest for baryogenesis and gravity waves. We improve on previous attempts to self-consistently solve for the bubble wall properties—wall speed $v_w$ and shape—in a highly predictive class of models with $Z_2$-symmetric singlet potentials. A new algorithm is implemented to determine $v_w$ and the wall profiles throughout the singlet parameter space in the case of subsonic walls, focusing on models with strong enough phase transitions to satisfy the sphaleron washout constraint for electroweak baryogenesis. We find speeds as low as $v_w\cong 0.1$ in our scan over parameter space, and the singlet must be relatively light to have a subsonic wall, $m_s\lesssim 135\mathrm{GeV}$.

Usually considered a background for experimental searches for the hypothetical neutrinoless double beta decay process, two-neutrino double beta decay nevertheless provides a complementary probe of physics beyond the Standard Model. In this paper we investigate how the presence of a sterile neutrino, coupled to the Standard Model either via a left-handed or right-handed current, affects the energy distribution and angular correlation of the outgoing electrons in two-neutrino double beta decay. We pay particular attention on the behavior of the energy distribution at the kinematic end point and we estimate the current limits on the active-sterile mixing and effective right-handed coupling using current experimental data as a function of the sterile neutrino mass. We also investigate the sensitivities of future experiments. Our results complement the corresponding constraints on sterile neutrinos from single beta decay measurements in the 0.1–10 MeV mass range.

We calculate the mass difference between the $\mathrm{\Upsilon }$ and ${\eta }_b$ and the $\mathrm{\Upsilon }$ leptonic width from lattice QCD using the highly improved staggered quark formalism for the $b$ quark and including $u$, $d$, $s$ and $c$ quarks in the sea. We have results for lattices with lattice spacing as low as 0.03 fm and multiple heavy quark masses, enabling us to map out the heavy quark mass dependence and determine values at the $b$ quark mass. Our results are $M_{\mathrm{\Upsilon }}-M_{{\eta }_b}=57.5(2.3)(1.0)\mathrm{MeV}$ (where the second uncertainty comes from neglect of quark-line disconnected correlation functions) and decay constants, $f_{{\eta }_b}=724(12)\mathrm{MeV}$ and $f_{\mathrm{\Upsilon }}=677.2(9.7)\mathrm{MeV}$, giving $\mathrm{\Gamma }(\mathrm{\Upsilon }\to e^{+}{e}^{-})=1.292(37)(3)\mathrm{keV}$. The hyperfine splitting and leptonic width are both in good agreement with experiment, and provide the most accurate lattice QCD results to date for these quantities by some margin. At the same time results for the time moments of the vector-vector correlation function can be compared to values for the $b$ quark contribution to $\sigma (e^{+}{e}^{-}\to \text{hadrons})$ determined from experiment. Moments 4–10 provide a 2% test of QCD and yield a $b$ quark contribution to the anomalous magnetic moment of the muon of $0.300(15)\times {10}^{-10}$. Our results, covering a range of heavy quark masses, may also be useful to constrain QCD-like composite theories for beyond the Standard Model physics.

In this work, we investigate how the details of the quark-gluon interaction vertex affect the quantitative description of chiral symmetry breaking through the gap equation for quarks. We start from two gluon propagator models widely used in literature and constructed in direct connection with our gradually improved understanding of infrared quantum chromodynamics coupled with its exact one-loop limit. The gap equation is then solved by employing a variety of vertex Ansätze, which have been constructed in order to implement some of the key aspects of quantum chromodynamics, namely, multiplicative renormalizability of the quark propagator, gauge invariance, matching with perturbation theory in the weak coupling regime, independence from unphysical kinematic singularities as well as manifestly correct transformation properties under charge conjugation and parity operations. On general grounds, all truncation schemes exhibit the same qualitative and quantitative pattern of chiral symmetry breaking, ensuring the overall robustness of this approach and its potentially reliable description of the hadron spectrum and properties.

We investigate fluctuations of the net-baryon number density in hot hadronic matter. We discuss the interplay between chiral dynamics and repulsive interactions and their influence on the properties of these fluctuations near the chiral crossover. The chiral dynamics is modeled by the parity doublet Lagrangian that incorporates the attractive and repulsive interactions mediated via the exchange of scalar and vector mesons, respectively. The mean-field approximation is employed to account for chiral criticality. We focus on the qualitative properties and systematics of the cumulants of the net-baryon number density up to the sixth order. It is shown that the higher-order cumulants exhibit a substantial suppression in the vicinity of the chiral phase transition due to the presence of repulsive interactions. We find, however, that the characteristic properties of cumulants near the chiral crossover observed in lattice QCD results are entirely linked to the critical chiral dynamics and, in general, cannot be reproduced in phenomenological models, which account only for effective repulsive interactions via excluded-volume corrections or van der Waals–type interactions. Consequently, a description of the higher-order cumulants of the net-baryon density in the chiral crossover requires a self-consistent treatment of the chiral in-medium effects and repulsive interactions.

We discuss the violation of quark-flavor symmetry at high temperatures, induced from nonperturbative thermal loop corrections and axial anomaly, based on a three-flavor linear-sigma model including an $SU(3)$ flavor violation induced by $U(1{)}_A$ anomaly which we call an axial-anomaly induced-flavor breaking term. We employ a nonperturbative analysis following the Cornwall-Jackiw-Tomboulis formalism, and show that the model undergoes a chiral crossover with a pseudocritical temperature, consistently with lattice observations. We find following features regarding the flavor breaking eminent around and above the pseudocritical temperature: (i) up-and down-quark condensates drop faster than the strange quark’s toward the criticality, but still keep nonzero value even going far above the critical temperature; (ii) the introduced anomaly-related flavor-breaking effect acts as a catalyzer toward the chiral restoration, and reduces the amount of flavor breaking in the up, down and strange quark condensates; (iii) a dramatic deformation for the meson flavor mixing structure is observed, in which the anomaly-induced favor breaking is found to be almost irrelevant; (iv) the meson spectroscopy gets corrected by the net nonperturbative flavor breaking effects, where the scalar meson mass hierarchy (inverse mass hierarchy) is significantly altered by the presence of the anomaly-related flavor breaking; (v) the topological susceptibility significantly gets the contribution from the surviving strange quark condensate, which cannot be dictated by the chiral perturbation theory, and deviates from the dilute instanton gas prediction. There the anomaly-induced flavor breaking plays a role of the destructive interference for the net flavor violation, as in the flavor breaking in the quark condensates; (vi) the $U(1{)}_A$ breaking signaled by nonzero topological susceptibility is enhanced by the nonperturbative strange quark condensate, which may account for the tension in the effective restoration of the $U(1{)}_A$ symmetry currently observed on lattices with two flavors and $2+1$ flavors near the chiral limit. Our founding critical natures can be checked in the future lattice simulations, and will give some implications to the thermal history of QCD axion.

We introduce a half-filled Hamiltonian of spin-half lattice fermions that can be studied with the efficient meron-cluster algorithm in any dimension. As with the usual bipartite half-filled Hubbard models, the naïve $U(2)$ symmetry is enhanced to $SO(4)$. On the other hand, our model has a novel spin-charge flip ${\mathbb{Z}}_2^C$ symmetry which is an important ingredient of free massless fermions. In this work we focus on one spatial dimension and show that our model can be viewed as a lattice-regularized two-flavor chiral-mass Gross-Neveu model. Our model remains solvable in the presence of the Hubbard coupling $U$, which maps to a combination of Gross-Neveu and Thirring couplings in one dimension. Using the meron-cluster algorithm we find that the ground state of our model is a valence bond solid when $U=0$. From our field theory analysis, we argue that the valence bond solid forms inevitably because of an interesting frustration between spin and charge sectors in the renormalization group flow enforced by the ${\mathbb{Z}}_2^C$ symmetry. This state spontaneously breaks translation symmetry by one lattice unit, which can be identified with a ${\mathbb{Z}}_2^{\chi }$ chiral symmetry in the continuum. We show that increasing $U$ induces a quantum phase transition to a critical phase described by the $SU(2{)}_1$ Wess-Zumino-Witten theory. The quantum critical point between these two phases is known to exhibit a novel symmetry enhancement between spin and dimer. Here we verify the scaling relations of these correlation functions near the critical point numerically. Our study opens up the exciting possibility of numerical access to similar novel phase transitions in higher dimensions in fermionic lattice models using the meron-cluster algorithm.

Matter and dark matter are unified under the framework of $SU(6)\to SU(5)\times U(1{)}_N$. A dark-matter candidate is possible, not because it is stable, but because it has a very long lifetime, in analogy to that of the proton in theories of grand unification. A specific example is presented.