The minimal dark matter (MDM) scenario is a very simple framework of physics beyond the Standard Model (SM) to supplement the SM with a DM candidate. In this paper, we consider an ultraviolet completion of the scenario to an SO(10) grand unified theory, which is a well-motivated framework in light of the neutrino oscillation data. Considering various phenomenological constraints, such as the successful SM gauge coupling unification, the proton stability, and the direct/indirect DM detection constraints as well as the absolute electroweak vacuum stability, we have first singled out the minimal particle content of the MDM scenario at low energies. In addition to the SM particle content, our MDM scenario includes an ${\mathrm{SU}(2)}_L$ quintet scalar DM with a 9.4 TeV mass and three degenerate color-octet scalars with mass of 2 TeV. We then have found a way to embed the minimal particle content into SO(10) representations, in which a remnant $Z_2$ symmetry after the SO(10) symmetry breaking ensures the stability of the DM particle. The production cross section of the color-octet scalars at the Large Hadron Collider is found to be a few orders of magnitude below the current experimental bound.

Doubly heavy tetraquark states are the prime candidates for tightly bound exotic states. We present a systematic study of the mass spectra of the $S$-wave doubly heavy tetraquark states $QQ\overline{q}\overline{q}$ ($q=u$, $d$, $s$ and $Q=c$, $b$) with different quantum numbers $J^P=0^{+}$, $1^{+}$, and $2^{+}$ in the framework of the improved chromomagnetic interaction (ICMI) model. The parameters in the ICMI model are obtained by fitting the conventional hadron spectra and are used directly to predict the masses of the tetraquark states. For heavy quarks, the uncertainties of the parameters are obtained by comparing the masses of doubly and triply heavy baryons with those given by lattice QCD, QCD sum rules, and potential models. Several compact and stable bound states are found in both the doubly charmed and doubly bottomed tetraquark systems. The predicted mass of the $cc\overline{u}\overline{d}$ state is consistent with the recent measurement from the LHCb Collaboration.

We establish a holographic QCD model for four flavors, where a light scalar field X and a heavy scalar field H are introduced separately. The H field is responsible for the breaking of $SU(N_f=4)$ to $SU(N_f=3)$. The ground state and its radial Regge excitation of meson spectra in the light flavor sector and heavy flavor sector as well as the light-heavy mesons are well in agreement with the Particle Data Group. Due to the additional introduction of the H field in the model, different Regge slopes for light and heavy mesons can be achieved.

We explore a weakly coupled $SU(N_c)$ gauge theory, examining its fixed-point structure and the transition from infrared conformality to spontaneous symmetry breaking. Following a previous study, we couple the gauge field to $N_s$ scalars and $N_f$ fermions, take the large-$N_c$ limit with $N_s/N_c$ and $N_f/N_c$ fixed, and adjust these ratios to produce weakly coupled infrared fixed points while maintaining asymptotic freedom. We map out renormalization-group trajectories and describe the transition to symmetry breaking as the ratio $N_s/N_c$ is increased. We examine the breaking by employing the one-loop effective potential. At tree level, a scalar-field vacuum expectation value (VEV) of a certain form is allowed, leading to masses for a subset of the scalar fields. Among the remaining massless scalars, one corresponds to a massless dilaton and the others are Nambu-Goldstone bosons absorbed by the gauge fields. The one-loop potential breaks the scale symmetry explicitly, determining the VEV and generating a dilaton mass suppressed relative to the other masses by a factor of the weak scalar coupling.

We remark that the recent exact six-loop and seven-loop computations of renormalization group functions for the $O(N)$-symmetric four dimensional ${\varphi }^4$ quantum field theory show hints that the associated large-order behavior is dominated by instantons rather than renormalons. This is consistent with a long-standing conjecture that renormalization group functions in the minimal subtraction (MS) renormalization scheme are not sensitive to renormalons.

The detection of gravitational waves from compact binary coalescence by Advanced LIGO and Advanced Virgo provides an opportunity to study the strong-field, highly relativistic regime of gravity. Gravitational-wave tests of general relativity (GR) typically assume Gaussian and stationary detector noise and, thus, do not account for non-Gaussian, transient noise features (glitches). We present the results obtained by performing parametrized gravitational-wave tests on simulated signals from binary-black-hole coalescence overlapped with three classes of frequently occurring instrumental glitches with distinctly different morphologies. We then review and apply three glitch mitigation methods and evaluate their effects on reducing false deviations from GR. By considering nine cases of glitches overlapping with simulated signals, we show that the short-duration, broadband blip and tomte glitches under consideration introduce false violations of GR, and using an inpainting filter and glitch model subtraction can consistently eliminate such false violations without introducing additional effects.

We perform the Batalin-Fradkin-Vilkovisky (BFV) quantization of the $2+1$ projectable and the $3+1$ nonprojectable versions of the Hořava theory. This is a Hamiltonian formalism, and noncanonical gauges can be used with it. In the projectable case, we show that the integration on canonical momenta reproduces the quantum Lagrangian known from the proof of renormalization of Barvinsky et al. This quantum Lagrangian is nonlocal, its nonlocality originally arose as a consequence of getting regular propagators. The matching of the BFV quantization with the quantum Lagrangian reinforces the program of quantization of the Hořava theory. We introduce a local gauge-fixing condition, hence a local Hamiltonian, that leads to the nonlocality of the Lagrangian after the integration. For the case of the nonprojectable theory, this procedure allows us to obtain the complete (nonlocal) quantum Lagrangian that takes into account the second-class constraints. We compare with the integration in general relativity, making clear the relationship between the underlying anisotropic symmetry of the Hořava theory and the nonlocality of its quantum Lagrangian.

We study gravitational perturbations of slowly rotating black holes in a general effective-field-theory extension of general relativity that includes up to eight-derivative terms. We show that two Schrödinger-like equations with spin-dependent effective potentials govern the odd- and even-parity master variables. These equations are coupled for parity-violating corrections, and this coupling affects the quasinormal modes even at linear order in the higher-derivative corrections, due to their isospectrality in general relativity. We provide results for the shifts in the fundamental quasinormal mode frequencies at linear order in the spin, which we expect to be valuable for high-precision phenomenology through future gravitational wave observations.

We explore memory effects for novel Kundt wave spacetimes in the recently proposed Eddington-inspired Born-Infeld (EiBI) theory of gravity. First, we construct new, exact Kundt wave geometries in this theory for two different matter sources—(i) generic matter designed to satisfy the field equations as well as energy conditions, and (ii) electromagnetic field. For both sources we find that the EiBI theory parameter $\kappa$ couples only with the nonradiative part of the physical metric solution. Thereafter, we solve the geodesic and the geodesic deviation equations in the above spacetimes with the aim of arriving at memory effects. This analysis is carried out numerically and reveals unique memory features depending on the type of matter source present and the signature of the spacetime scalar curvature. The role of $\kappa$ in influencing the memory effect, for a given background spacetime, is also noted. Thus, apart from providing novel radiative solutions in EiBI gravity, we also show how different matter configurations are responsible for distinct memory characteristics.

Recent years have witnessed a surge of interest of the lensing of the black holes arising from general as well as other modified theories of gravity due to the experimental data available from the Event Horizon Telescope (EHT) results. The EHT may open a new door indicating the possible existence of the rotating black hole solutions in modified theories of gravity in the strong field regime. With this motivation, we investigate in the present paper the equatorial lensing $(\theta =\pi /2)$ by a recently obtained exact rotating black holes solution in Eddington-inspired Born-Infeld (EiBI) theory in both the strong- and weak-field limits. Such black holes are the modification of Kerr-Newman black holes in general relativity, characterized by their mass $M$, the charge $Q$, and the rotation parameter $a$. and an additional term $\epsilon$ accounting for the correction to the Kerr-Newman solutions. We show numerically the variations of the impact parameter $u_m$, the light deflection coefficients $p$ and $q$, and the total azimuthal bending angle ${\alpha }_D$ and find a close dependence of these quantities on the charge parameter $r_q$, the correction term $\epsilon$, and the spin $a$. We also calculate the angular position ${\theta }_{\infty }$, the angular separation $s$, and the magnification of the relativistic images. In addition, we also discuss the weak lensing of the black holes in Eddington-inspired Born-Infeld (EiBI) theory using the Gauss-Bonnet theorem. We calculate the weak lensing parameter and find its variation with different values of the parameters $r_q$ and $\epsilon$.

It is by now well established that charged rotating Kerr-Newman black holes can support bound-state charged-matter configurations which are made of minimally coupled massive-scalar fields. We here prove that the externally supported stationary charged scalar configurations cannot be arbitrarily compact. In particular, for linearized-charged-massive-scalar fields supported by charged rotating near-extremal Kerr-Newman black holes, we derive the remarkably compact lower bound $(r_{\text{field}}-r_{+})/(r_{+}-r_{-})>1/s^2$ on the effective lengths of the external charged scalar “clouds” [here $r_{\text{field}}$ is the radial peak location of the stationary scalar configuration, and $\{s\equiv J/M^2,r_{\pm }\}$ are, respectively, the dimensionless angular momentum and the horizon radii of the central supporting Kerr-Newman black hole]. Remarkably, this lower bound is universal in the sense that it is independent of the physical parameters (proper mass, electric charge, and angular momentum) of the supported charged scalar fields.

$f(Q)$ gravity is the extension of symmetric teleparallel general relativity (STGR), in which both curvature and torsion vanish and gravity is attributed to nonmetricity. This work performs theoretical analyses of static and spherically symmetric solutions with an anisotropic fluid for general $f(Q)$ gravity. We find that the off-diagonal component of the field equation due to a coincident gauge leads to stringent restrictions on the functional form of $f(Q)$ gravity. In addition, although the exact Schwarzschild solution only exists in STGR, we obtain Schwarzschild-like solutions in nontrivial $f(Q)$ gravity and study its asymptotic behavior and deviation from the exact one.

In the first paper in this series, a class of observables that generalized the gravitational wave memory effect were introduced and given the name “persistent gravitational wave observables.” These observables are all nonlocal in time, nonzero in spacetimes with gravitational radiation, and have an observable effect that persists after the gravitational waves have passed. In this paper, we focus on the persistent observable known as “curve deviation,” and we compute the observable using the Bondi-Sachs approach to asymptotically flat spacetimes at the leading, nontrivial order in inverse Bondi radius. The curve deviation is related to the final separation of two observers who have an initial separation, initial relative velocity, and relative acceleration. The displacement gravitational wave memory effect is the part of the curve deviation that depends on the initial separation and is the entire contribution for initially comoving, inertial observers at large Bondi radius. The spin and center-of-mass memory effects are contained within the dependence of the curve deviation on the initial relative velocity, and the dependence of the curve deviation on relative acceleration contains observables distinct from these known memory effects. We find that the full curve deviation observable can be written in terms of differences in nonradiative data before and after the radiation (which we call the “charge” contribution), along with a nonlinear “flux” contribution that vanishes in the absence of gravitational radiation. This splitting generalizes the notion of “ordinary” and “null” memory that exists for the displacement, spin, and center-of-mass gravitational wave memory effects to the full curve deviation observable.

We derive the equations for the odd and even parity perturbations of coupled electromagnetic and gravitational fields of a black hole with an electric charge within the context of general nonlinear electrodynamics. The Lagrangian density is a generic function of the Lorentz invariant scalar quantities of the electromagnetic fields. We include the Hodge dual of the electromagnetic field tensor and the cosmological constant in our calculations. For each type of parity, we reduce the system of Einstein field equations coupled to nonlinear electrodynamics to two coupled Schrödinger-type wave equations, one for the gravitational field and one for the electromagnetic field. The stability conditions in the presence of the Hodge dual of the electromagnetic field are derived.

A Yang-Mills theory linear in the scalar curvature for two-dimensional gravity with symmetry generated by the semidirect product formed with the Lie derivative of the algebra of diffeomorphisms with the two-dimensional Abelian algebra is formulated. As compared with dilaton models, the role of the dilaton is played by the dual field strength of a $U(1)$ gauge field. All vacuum solutions are found. They are either black holes or have constant scalar curvature. Those with constant scalar curvature have constant dual field strength. In particular, solutions with vanishing cosmological constant but nonzero scalar curvature exist. In the conformal-Lorenz gauge, the model has a conformal field theory interpretation whose residual symmetry combines holomorphic diffeomorphisms with a subclass of $U(1)$ gauge transformations while preserving two-dimensional de Sitter and anti-de Sitter boundary conditions. This is the same symmetry as in Jackiw-Teitelboim-Maxwell gravity considered by Hartman and Strominger. It is argued that this is the only nontrivial Yang-Mills model linear in the scalar curvature that exists for real Lie algebras of dimension four.

The second-order formula of Minkowski functionals in weakly non-Gaussian fields is compared with the numerical $N$-body simulations. Recently, the weakly non-Gaussian formula of Minkowski functionals is extended to include the second-order effects of non-Gaussianity in general dimensions. We apply this formula to the three-dimensional density field in the large-scale structure of the Universe. The parameters of the second-order formula include several kinds of skewness and kurtosis parameters. We apply tree level of nonlinear perturbation theory to estimate these parameters, including novel calculations of quartic cumulants. First we compare the theoretical values with those of numerical simulations on the basis of parameter values, and next we test the performance of the analytic formula combined with the perturbation theory. The second-order formula outperforms the first-order formula in general. The performance of the perturbation theory depends on the smoothing radius applied in defining the Minkowski functionals. The quantitative comparisons are presented in detail.

The tension between the current expansion rate $H_0$ using Planck data and direct model-independent measurements in the local Universe has grown in the context of the $\mathrm{\Lambda }\mathrm{CDM}$ model. The growing tension among early-time and local measurements of $H_0$ has not ameliorated and remains a crucial and open question in cosmology. Solutions to understanding this tension are possible hidden sources of systematic error in the observable measurements or modifications to the concordance $\mathrm{\Lambda }\mathrm{CDM}$ model. In this work, we investigate a solution to the $H_0$ tension by modifying $\mathrm{\Lambda }\mathrm{CDM}$ and we add at early times an extra-relativistic energy density ${\rho }_{\mathrm{ex}}$ beyond the standard model. For a scale factor larger than $a_c$, this extra energy density ${\rho }_{\mathrm{ex}}$ dilutes faster than radiation and becomes subdominant. In some contexts, this ${\rho }_{\mathrm{ex}}$ corresponds to early dark energy or bound dark energy, and we refer to this cosmological model as $\mathrm{\Lambda }\mathrm{CDM}$-Nx. We implement $\mathrm{\Lambda }\mathrm{CDM}$-Nx in CAMB and perform a full COSMOMC analysis, allowing to simultaneously fit the latest data from cosmic microwave background (CMB) anisotropies and the value of $H_0=74.03\pm 1.42\mathrm{km}{\mathrm{s}}^{-1}\text{Mp}{\mathrm{c}}^{-1}$ obtained from distance ladder measurements using Cepheid variables to calibrate the absolute luminosity of type Ia supernovae by Riess et al. [Astrophys. J. 876, 85 (2019)]. The inclusion of ${\rho }_{\mathrm{ex}}$ ameliorates the tension between early- and late-time measurements only slightly, and we obtain a value $H_0=(68.70\pm 0.45\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1})$ which is still in conflict with local measurements. We follow up our analysis by proposing two forecasting standard deviations ${\sigma }_H=1$ and ${\sigma }_H=0.5$ (in units of $\mathrm{km}{\mathrm{s}}^{-1}\text{Mp}{\mathrm{c}}^{-1}$) for local distance measurements, i.e., $H_0=(74.03\pm 1)$ and $H_0=(74.03\pm 0.5)\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$. We implement these new values of $H_0$ in COSMOMC including CMB and Riess data, and we obtain a value of $H_0=(72.83\pm 0.47)\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ at the 68% confidence level for ${\sigma }_H=0.5$, which is fully consistent with Reiss’ results, while the price to pay is a percentage increase of the reduced CMB $({\chi }_{\mathrm{CMB}}^{\mathrm{red}}{)}^2$ of 0.127% vs the $\mathrm{\Lambda }\mathrm{CDM}$ model, corresponding to a very small increase. Finally, the energy density ${\rho }_{\mathrm{ex}}$ leaves distinctive imprints in the matter power spectrum at scales $k\sim k_c$ [with $k_c=a_{c}H(a_c)$] and in the CMB power spectrum, allowing for independent verification of our analysis.

We consider a quantum universe composed of a small system $S$ and a large environment. It has been demonstrated that, for the vast majority of randomly chosen wave functions of the universe satisfying a total energy constraint, the reduced density matrix of the system $S$ is given by the canonical statistical distribution. Here, through the Page-Wootters mechanism, we show that time and nonequilibrium dynamics can emerge as a consequence of the entanglement between the system and the environment present in the (randomly chosen) global wave function of the universe. The clock is provided by the environment, which ticks the temporal evolution of $S$. The paradox of the peaceful coexistence of statistical equilibrium and nonequilibrium dynamics is solved by identifying the trace over the environment degrees of freedom with the temporal trace over the entire history of the system $S$.