We study anomalous chiral symmetry breaking in two-flavor QCD induced by gravitational and QCD-instantons within asymptotically safe gravity within the functional renormalization group approach. Similarly to QCD-instantons, gravitational ones, associated to a K3-surface connected by a wormhole-like throat in flat spacetime, generate contributions to the ’t Hooft coupling proportional to $\exp (-1/g_N)$ with the dimensionless Newton coupling $g_N$. Hence, in the asymptotically safe gravity scenario with a nonvanishing fixed point coupling $g_N^{*}$, the induced ’t Hooft coupling is finite at the Planck scale, and its size depends on the chosen UV-completion. Within this scenario the gravitational effects on anomalous $U(1{)}_A$-breaking at the Planck scale may survive at low energy scales. In turn, fermion masses of the order of the Planck scale cannot be present. This constrains the allowed asymptotically safe UV-completion of the gravity-QCD system. We map out the parameter regime that is compatible with the existence of light fermions in the low-energy regime.

Recently, it was shown that there is an anomalous singularity of propagators in spacetimes with horizons for thermal states with noncanonical temperatures. In this paper, I extend these observations to the situation when the background geometry is given by the four-dimensional Schwarzschild and Reissner-Nordström black holes. Namely, I demonstrate that the two-point function in the free scalar field theory acquires an anomalous singularity when the two points are located on the horizon. This singularity is anomalous in the sense that the coefficient before the divergent term in the two-point function differs from the canonical one and depends explicitly on the temperature of the state. As was previously shown, it leads to the explosive behavior of the regularized stress-energy tensor on the horizon when the temperature of the state does not coincide with the canonical temperature of the horizon.

We accurately approximate the contribution that photons make to the effective potential of a charged inflaton for inflationary geometries with an arbitrary first slow roll parameter $\epsilon$. We find a small, nonlocal contribution and a numerically larger, local part. The local part involves first and second derivatives of $\epsilon$, coming exclusively from the constrained part of the electromagnetic field which carries the long range interaction. This causes the effective potential induced by electromagnetism to respond more strongly to geometrical evolution than for either scalars, which have no derivatives, or spin one-half particles, which have only one derivative. For $\epsilon =0$, our final result agrees with that of Allen [Nucl. Phys. B226, 228 (1983)] on de Sitter background, while the flat space limit agrees with the classic result of Coleman and Weinberg [Phys. Rev. D 7, 1888 (1973)].

BMS (Bondi-Metzner-Sachs) group (and its various generalizations) at null infinity has been studied extensively in the literature as the symmetry group of asymptotically flat spacetimes. The intricate relationship between soft theorems and the BMS symmetries has also motivated the definition of such asymptotic symmetries to timelike infinity [M. Campiglia, Null to time-like infinity Green’s functions for asymptotic symmetries in Minkowski spacetime, J. High Energy Phys. 11 (2015) 160.]. Although the vector fields that generate the (generalized) BMS algebra at timelike infinity were defined in the literature, the algebra has not been investigated. In this paper. we fill this gap. We show that the supertranslations and vector fields that generate sphere diffeomorphisms close under the modified Lie bracket proposed by Barnich and Troessaert [Aspects of the BMS/CFT correspondence, J. High Energy Phys. 05 (2010) 062.].

We construct and analyze Kerr black holes (BHs) with synchronized axionic hair. These are the BH generalizations of the recently constructed rotating axion boson stars [J. F. Delgado, C. A. Herdeiro, and E. Radu, Rotating axion boson stars, J. Cosmol. Astropart. Phys. 06 (2020) 037]. Such BHs are stationary, axially symmetric, asymptotically flat solutions of the complex Einstein-Klein-Gordon theory with a QCD axionlike potential. They are regular everywhere on and outside the event horizon. The potential is characterized by two parameters: the mass of the axionlike particle, $m_a$, and the decay constant, $\widetilde{f_a}$. The limit $\widetilde{f_a}\to \infty$ recovers the original example of Kerr BHs with synchronized scalar hair [C. A. R. Herdeiro and E. Radu, Kerr Black Holes with Scalar Hair, Phys. Rev. Lett. 112, 221101 (2014)]. The effects of the nonlinearities in the potential become important for $\widetilde{f_a}\lesssim 1$. We present an overview of the parameter space of the solutions together with a study of their basic geometric and phenomenological properties, for an illustrative value of the coupling that yields a non-negligible impact of the self-interactions.

We consider a situation where a light source orbiting the innermost stable circular orbit (ISCO) of the Kerr black hole is gently falling from the marginally stable orbit due to an infinitesimal perturbation. Assuming that the light source emits photons isotropically, we show that the last radius at which more than 50% of emitted photons can escape to infinity is approximately halfway between the ISCO radius and the event horizon radius. To evaluate them, we determine emitter orbits from the vicinity of the ISCO, which are uniquely specified for each black hole spin, and identify the conditions for a photon to escape from any point on the equatorial plane of the Kerr spacetime to infinity by specifying regions in the two-dimensional photon impact parameter space completely. We further show that the proper motion of the emitter affects the photon escape probability and blueshifts the energy of emitted photons.

The recent observation of GW190412, the first high-mass ratio binary black hole merger, by the LIGO-Virgo Collaboration (LVC) provides a unique opportunity to probe the impact of subdominant harmonics and precession effects encoded in a gravitational wave signal. We present refined estimates of source parameters for GW190412 using nrsur7dq4, a recently developed numerical relativity waveform surrogate model that includes all $\ell \le 4$ spin-weighted spherical harmonic modes as well as the full physical effects of precession. We compare our results with two different variants of phenomenological precessing binary black hole waveform models, imrphenompv3hm and imrphenomxphm, as well as to the LVC results. Our results are broadly in agreement with imrphenomxphm results and the reported LVC analysis compiled with the seobnrv4phm waveform model, but in tension with imrphenompv3hm. Using the nrsur7dq4 model, we provide a tighter constraint on the mass ratio (${0.26}_{-0.06}^{+0.08}$) as compared to the LVC estimate of ${0.28}_{-0.07}^{+0.13}$ (both reported as median values with 90% credible intervals). We also constrain the binary to be more face on, and find a broader posterior for the spin precession parameter. We further find that even though $\ell =4$ harmonic modes have negligible signal-to-noise ratio, omission of these modes will influence the estimated posterior distribution of several source parameters including chirp mass, effective inspiral spin, luminosity distance, and inclination. We also find that commonly used model approximations, such as neglecting the asymmetric modes (which are generically excited during precession), have negligible impact on parameter recovery for moderate signal-to-noise ratio events similar to GW190412.

Gravitational-wave memory effects are identified by their distinctive effects on families of freely falling observers: after a burst of waves pass by their locations, memory effects can cause lasting relative displacements of the observers. These effects are closely related to the infrared properties of gravity, including its asymptotic symmetries and conserved quantities. In this paper, we investigate the connection between memory effects, symmetries, and conserved quantities in Brans-Dicke theory. We compute the field equations in Bondi coordinates, and we define a set of boundary conditions that represent asymptotically flat solutions in this context. Next, we derive the asymptotic symmetry group of these spacetimes, and we find that it is the same as the Bondi-Metzner-Sachs group in general relativity. Because there is an additional polarization of gravitational waves in Brans-Dicke theory, we compute the memory effects associated with this extra polarization (the so-called “breathing” mode). This breathing mode produces a uniform expansion (or contraction) of a ring of freely falling observers. After these breathing gravitational waves pass by the observers’ locations, there are two additional memory effects that depend on their initial displacements and relative velocities. Neither of these additional memory effects seems to be related to asymptotic symmetries or conserved quantities; rather, they are determined by the properties of the nonradiative region before and after the bursts of the scalar field and the gravitational waves. We discuss the properties of these regions necessary to support nontrivial breathing-mode-type memory effects.

A new set of field equations for a space-time dependent Newton’s constant $G(x)$ and cosmological constant $\mathrm{\Lambda }(x)$ in the presence of matter is presented. We prove that it represents the most general mathematically consistent, physically plausible, set of evolution equations assuming at most second derivatives in the dynamical variables. In the new Einstein’s equations, only $\mathrm{\Lambda }$-kinetic terms arise, while in the modified conservation equation, derivative terms of $G$ also appear. As an application, this formalism is applied in the context of the asymptotic safety scenario to the early Universe, assuming a perfect fluid with a radiation equation of state. Cosmological solutions are obtained for all types of spatial curvature, displaying a variety of interesting cosmic evolutions. As an indication of such behaviors, bouncing solutions, recollapsing solutions, or nonsingular expanding solutions with a transient acceleration era are discussed in detail.

Thermodynamics of $z=4$ Hořava-Lifshitz black holes in $3+1$ dimensions is studied in extended phase space. By using the scaling argument we find the Smarr relation and the first law for the black hole solutions of $z=4$ Hořava-Lifshitz gravity. We find that it is necessary to take into account the variation of dimensionful parameters of the theory in the first law. We find that the reverse isoperimetric inequality can be violated for spherical, flat, and hyperbolic horizons and in all such cases we have black holes for which the specific heat at constant pressure and volume are positive. This provides a counterexample to a recent conjecture stating that black holes violating the reverse isoperimetric inequality are thermodynamically unstable. We find for $z=4$ Hořava-Lifshitz black holes with hyperbolic horizons that there are two critical points: one showing Van der Waals behavior, the other reverse Van der Waals behavior.

The renormalization group flow of unimodular quantum gravity is investigated within two different classes of truncations of the flowing effective action. In particular, we search for nontrivial fixed-point solutions for polynomial expansions of the $f(R)$-type as well as of the $F(R_{\mu \nu }{R}^{\mu \nu })+RZ(R_{\mu \nu }{R}^{\mu \nu })$ family on a maximally symmetric background. We close the system of beta functions of the gravitational couplings with anomalous dimensions of the graviton and Faddeev-Popov ghosts treated according to two independent prescriptions: one based on the so-called background approximation and the other based on a hybrid approach which combines the background approximation with simultaneous vertex and derivative expansions. For consistency, in the background approximation, we employ a background-dependent correction to the flow equation which arises from the proper treatment of the functional measure of the unimodular path integral. We also investigate how different canonical choices of the endomorphism parameter in the regulator function affect the fixed-point structure. Although we find evidence for the existence of a nontrivial fixed point for the two classes of polynomial projections, the $f(R)$ truncation exhibits better (apparent) convergence properties. Furthermore, we consider the inclusion of matter fields without self-interactions minimally coupled to the unimodular gravitational action and we find evidence for compatibility of asymptotically safe unimodular quantum gravity with the field content of the Standard Model and some of its common extensions.

In a previous paper [P. D. Mannheim, Phys. Rev. D 102, 123535 (2020)] we studied cosmological perturbation theory in the cosmology associated with the fourth-order derivative conformal gravity theory, and provided an exact solution to the theory in the recombination era. In this paper we present an exact solution that holds all the way from recombination until the current era.

In the present work, we adopt a nonlinear scalar field theory coupled to the gravity sector to model galactic dark matter. We find analytical solutions for the scalar field considering the weak field gravity limit, which is usually done in galaxy rotation curves analysis and in order to do so we assume an isotropic spacetime and a field potential, with a position dependent form of the superpotential, which entails the nonlinear dynamics of the model with self-interactions. The model introduces a position dependent enhancement of the self-interaction of the scalar fields toward the galaxy center, and while going toward the galaxy border the interaction tends to vanish building a non–self-interacting DM scenario. The developed approach is able to provide a reasonable analytical description of the rotation curves in both dwarf and low surface brightness late-type galaxies, with parameters associated with the dynamics of the scalar field.

The large-scale structure (LSS) of the Universe has the potential to provide decisive answers to the remaining open questions in cosmology. Early attempts at modeling it analytically focused on using perturbation theory. However, small-scale effects introduced by gravitational collapse cannot be described perturbatively and this failure of perturbation theory is reflected even on the largest scales. The effective field theory (EFT) of LSS has emerged as a consistent method for describing LSS on large scales by introducing counterterms that account for the effects of small-scale dynamics. So far studies of the EFT have mostly focused on the two and three point functions with little attention devoted to the four point function or trispectrum. The trispectrum probes cubic interactions arising from nonlinear clustering, biasing, and primordial non-Gaussianities, and constitutes a key element of the covariance matrix of the power spectrum. In this paper, we present explicit calibrations of the EFT counterterms for the one-loop trispectrum. Specifically, we find clear evidence for nonzero EFT corrections. We define two one-parameter ansatz for the counterterm of the one-loop propagator and show that they provide a good correction to the residual at scales below $k\sim 0.07h{\mathrm{Mpc}}^{-1}$. We then take the amplitudes of the linear and quadratic counterkernels calculated in our previous paper on the bispectrum and use them in the remaining counterterms, establishing consistency of the counterterms in the two, three, and four point function. We also show that the commonly used Einstein–de Sitter approximation for the growth of the density fields leads to errors that are of the same magnitude as loop corrections to the trispectrum on large scales.

In studying temperature fluctuations in the cosmic microwave background Weinberg has noted that some ease of calculation and insight can be achieved by looking at the structure of the perturbed light cone on which the perturbed photons propagate. In his approach Weinberg worked in a specific gauge and specialized to fluctuations around the standard Robertson-Walker cosmological model with vanishing spatial three-curvature. In this paper we generalize this analysis by providing a gauge invariant treatment in which no choice of gauge is made, and by considering geometries with non-vanishing spatial three-curvature. By using the scalar, vector, tensor fluctuation basis we find that the relevant gauge invariant combinations that appear in the light cone temperature fluctuations have no explicit dependence on the spatial curvature even if the spatial curvature of the background geometry is nonvanishing. We find that a not previously considered, albeit not too consequential, temperature fluctuation at the observer has to be included in order to enforce gauge invariance. As well as working with comoving time we also work with conformal time in which a background metric of any given spatial three-curvature can be written as a time-dependent conformal factor (the comoving time expansion radius as written in conformal time) times a static Robertson-Walker geometry of the same spatial three-curvature. For temperature fluctuations on the light cone this conformal factor drops out identically. Thus the gauge invariant combinations that appear in the photon temperature fluctuations have no explicit dependence on either the conformal factor or the spatial three-curvature at all.

Localizing the sky position of the gravitational wave source is a key scientific goal for gravitational wave observations. Employing the Fisher information matrix approximation, we compute the angular resolutions of LISA and TianQin, two planned space-based gravitational wave detectors, and examine how detectors’ configuration properties, such as the orientation change of the detector plane, heliocentric, or geocentric motion and the arm length etc., affect the accuracy of source localization for monochromatic sources at selected values of frequencies. We find that the amplitude modulation due to the annual changing orientation of the detector plane helps LISA get better accuracy in the sky localization and better sky coverage at frequencies below several mHz, and its effect on TianQin is negligible although the orientation of TianQin’s detector plane is fixed. At frequencies above roughly 30 mHz, TianQin’s ability in the sky localization is better than LISA. Further we explore potential space detector networks for fast and accurate localization of the gravitational wave sources. The LISA-TianQin network has better ability in sky localization for sources with frequencies in the range 1–100 mHz and the network has larger sky coverage for the angular resolution than the individual detector.

The effect of gravitational wave of cosmological wavelength on the gravitational lensing is investigated. When the source, deflector, and observer are aligned in a highly symmetric configuration, an Einstein ring will be observed by the observer. There will be no time delays between different locations on the Einstein ring in the absence of gravitational wave. Otherwise, time delays between different locations on the Einstein ring will emerge if cosmological gravitational wave propagates through the system. Previous studies demonstrated that the time delay resulting from the aligned source-deflector-observer configuration in the presence of gravitational wave of cosmological wavelength could be equivalent to that of a similar lens with a nonaligned source-deflector-observer configuration in the absence of gravitational wave. Results in this work show that gravitational lens with the aligned source-deflector-observer configuration could serve as a potential gravitational wave detector when the whole Einstein ring observed by the observer is taken into account.

The well-known Landau-Yang (LY) theorem on the decay of a neutral particle into two photons is generalized for analyzing the decay of a neutral or charged particle into two identical massless particles of any spin. Selection rules categorized by discrete parity invariance and Bose/Fermi symmetry are worked out in the helicity formulation. The general form of the Lorentz-covariant triple vertices are derived and the corresponding decay helicity amplitudes are explicitly calculated in the Jacob-Wick convention. After checking the consistency of all the analytic results obtained by two complementary approaches, we extract out the key aspects of the generalized LY theorem.

In this article we use an electromagnetic Lagrangian constructed so as to include dispersive effects in the description of an electromagnetic wave propagating in the quantum electrodynamic vacuum. This Lagrangian is Lorentz invariant, includes contributions up to six powers in the electromagnetic fields, and involves both fields and their first derivatives. Conceptual limitations inherent to the use of this higher derivative Lagrangian approach are discussed. We consider the one-dimensional spatial limit and obtain an exact solution of the nonlinear wave equation recovering the Korteveg-de Vries type periodic waves and solitons given in S. V. Bulanov et al. [Phys. Rev. D 101, 016016 (2020)].

We reconsider the issue of the search for a nonzero electric dipole form factor (EDM) $d_{\tau }(s)$ using optimal observables in ${\tau }^{+}{\tau }^{-}$ production by $e^{+}{e}^{-}$ collisions in the center-of-mass energy range from the $\tau$-pair threshold to about $\sqrt{s}\sim 15\mathrm{GeV}$. We discuss the general formalism of optimal observables and apply it to two $CP$-odd observables that are sensitive to the real and imaginary part of $d_{\tau }(s)$, respectively. We compute the expectation values and covariances of these optimal $CP$ observables for $\tau$-pair production at $\sqrt{s}=10.58\mathrm{GeV}$ with subsequent decays of ${\tau }^{\pm }$ into major leptonic or semihadronic modes. For the $\tau$ decays to two pions and three charged pions we take the full kinematic information of the hadronic system into account. Assuming that the Belle II experiment at the KEKB accelerator will eventually analyze data corresponding to an integrated luminosity of $50{\mathrm{ab}}^{-1}$ and applying acceptance cuts on the final-state pions, we find that 1 s.d. sensitivities $\delta \mathrm{Re}{d}_{\tau }=6.8\times {10}^{-20}e\mathrm{cm}$ and $\delta \mathrm{Im}{d}_{\tau }=4.0\times {10}^{-20}e\mathrm{cm}$ can be obtained with events where both $\tau$’s decay semihadronically. We consider also the ideal case that no cuts on the final-state particles are applied. With $50{\mathrm{ab}}^{-1}$ at $\sqrt{s}=10.58\mathrm{GeV}$ corresponding to $4.5\times {10}^{10}$ ${\tau }^{+}{\tau }^{-}$ events we find the 1 s.d. sensitivities $\delta \mathrm{Re}{d}_{\tau }=5.8\times {10}^{-20}e\mathrm{cm}$ and $\delta \mathrm{Im}{d}_{\tau }=3.2\times {10}^{-20}e\mathrm{cm}$, again for events where both $\tau$ leptons decay semihadronically. Furthermore, we analyze the potential magnitude of the $\tau$ EDM form factor in the type-II two-Higgs doublet extension and in two scalar leptoquark extensions of the Standard Model, taking into account phenomenological constraints.