Thanks to the recent discoveries of gravitational wave signals from binary black hole mergers by Advanced Laser Interferometer Gravitational Wave Observatory and Advanced Virgo, the genuinely strong-field dynamics of spacetime can now be probed, allowing for stringent tests of general relativity (GR). One set of tests consists of allowing for parametrized deformations away from GR in the template waveform models and then constraining the size of the deviations, as was done for the detected signals in previous work. In this paper, we construct reduced-order quadratures so as to speed up likelihood calculations for parameter estimation on future events. Next, we explicitly demonstrate the robustness of the parametrized tests by showing that they will correctly indicate consistency with GR if the theory is valid. We also check to what extent deviations from GR can be constrained as information from an increasing number of detections is combined. Finally, we evaluate the sensitivity of the method to possible violations of GR.

Without using conformal transformation, a simple type of five-dimensional $f(R)$-brane model is linearized directly in its higher-order frame. In this paper, the linearization is conducted in the equation of motion approach. We first derive all the linear perturbation equations without specifying a gauge condition. Then, by taking the curvature gauge, we derive the master equations of the linear perturbations. We show that these equations are equivalent to those obtained in the quadratical action approach [Phys. Rev. D 95, 104060 (2017)], except the vector sector, in which a constraint equation can be obtained in the equation of motion approach but is absent in the quadratical action approach. Our work sets an example on how to linearize higher-order theories without using conformal transformation, and might be useful for studying more complicated theories.

In this work, we analyze the spatial and time variation of the fine structure constant ($\alpha$) upon the theoretical framework developed by Bekenstein (Phys. Rev. D 66, 123514 (2002)). We have computed the field $\psi$ related to $\alpha$ at first order of the weak-field approximation and have also improved the estimation of the nuclear magnetic energy and, therefore, their contributions to the source term in the equation of motion of $\psi$. We obtained that the results are similar to the ones published in L. Kraiselburd and H. Vucetich, Int. J. Mod. Phys. E 20, 101 (2011) which were computed using the zero order of the approximation, showing that one can neglect the first order contribution to the variation of the fine structure constant. Through the comparison between our theoretical results and the observational data of the Eötvös-type experiments or the time variation of $\alpha$ over the cosmological time scale, we set constraints on the free parameter of the Bekenstein model, namely the Bekenstein length.

We determine the dynamical attractors associated with anisotropic hydrodynamics (aHydro) and the DNMR equations for a $0+1\mathrm{d}$ conformal system using kinetic theory in the relaxation time approximation. We compare our results to the nonequilibrium attractor obtained from the exact solution of the $0+1\mathrm{d}$ conformal Boltzmann equation, the Navier-Stokes theory, and the second-order Mueller-Israel-Stewart theory. We demonstrate that the aHydro attractor equation resums an infinite number of terms in the inverse Reynolds number. The resulting resummed aHydro attractor possesses a positive longitudinal-to-transverse pressure ratio and is virtually indistinguishable from the exact attractor. This suggests that an optimized hydrodynamic treatment of kinetic theory involves a resummation not only in gradients (Knudsen number) but also in the inverse Reynolds number. We also demonstrate that the DNMR result provides a better approximation of the exact kinetic theory attractor than the Mueller-Israel-Stewart theory. Finally, we introduce a new method for obtaining approximate aHydro equations which relies solely on an expansion in the inverse Reynolds number. We then carry this expansion out to the third order, and compare these third-order results to the exact kinetic theory solution.

We have systematically constructed the general structure of the fermion self-energy and the effective quark propagator in the presence of a nontrivial background such as a hot magnetized medium. This is applicable to both QED and QCD. The hard thermal loop approximation has been used for the heat bath. We have also examined transformation properties of the effective fermion propagator under some of the discrete symmetries of the system. Using the effective fermion propagator we have analyzed the fermion dispersion spectra in a hot magnetized medium along with the spinor for each fermion mode obtained by solving the modified Dirac equation. The fermion spectra is found to reflect the discrete symmetries of the two-point functions. We note that for a chirally symmetric theory the degenerate left- and right-handed chiral modes in vacuum or in a heat bath get separated and become asymmetric in the presence of a magnetic field without disturbing the chiral invariance. The obtained general structure of the two-point functions is verified by computing the three-point function, which agrees with the existing results in one-loop order. Finally, we have computed explicitly the spectral representation of the two-point functions which would be very important to study the spectral properties of the hot magnetized medium corresponding to QED and QCD with background magnetic field.

Recently, the experimental results of the LHCb Collaboration suggested the existence of five new excited states of ${\mathrm{\Omega }}_c^0$: ${\mathrm{\Omega }}_c(3000{)}^0$, ${\mathrm{\Omega }}_c(3050{)}^0$, ${\mathrm{\Omega }}_c(3066{)}^0$, ${\mathrm{\Omega }}_c(3090{)}^0$, and ${\mathrm{\Omega }}_c(3119{)}^0$; however, the quantum numbers of these new particles are not determined now. To understand the nature of these states, a dynamical calculation of ${\mathrm{\Omega }}_c^0$ both in five-quark configuration with quantum numbers $I{J}^P=0(\frac{1}{2}{)}^{-}$, $0(\frac{3}{2}{)}^{-}$, $0(\frac{5}{2}{)}^{-}$ and in three-quark configuration with positive parity and negative parity was performed in the framework of the chiral quark model with the help of the Gaussian expansion method. The results show the masses both of the $1P$ and the $2S$ states in $ssc$ systems are comparable to experimental data; Besides, $\mathrm{\Xi }\overline{D}$, ${\mathrm{\Xi }}_c\overline{K}$, and ${\mathrm{\Xi }}_c^{*}\overline{K}$ are also possible candidates of these new particles if the parity is negative. The distances between quark pairs suggest a compact structure nature.

We report measurements of charm-mixing parameters based on the decay-time-dependent ratio of $D^0\to K^{+}{\pi }^{-}$ to $D^0\to K^{-}{\pi }^{+}$ rates. The analysis uses a data sample of proton-proton collisions corresponding to an integrated luminosity of $5.0{\mathrm{fb}}^{-1}$ recorded by the LHCb experiment from 2011 through 2016. Assuming charge-parity ($CP$) symmetry, the mixing parameters are determined to be $x^{\prime 2}=(3.9\pm 2.7)\times {10}^{-5}$, $y^{\prime }=(5.28\pm 0.52)\times {10}^{-3}$, and $R_D=(3.454\pm 0.031)\times {10}^{-3}$. Without this assumption, the measurement is performed separately for $D^0$ and ${\overline{D}}^0$ mesons, yielding a direct $CP$-violating asymmetry $A_D=(-0.1\pm 9.1)\times {10}^{-3}$, and magnitude of the ratio of mixing parameters $1.00<|q/p|<1.35$ at the 68.3% confidence level. All results include statistical and systematic uncertainties and improve significantly upon previous single-measurement determinations. No evidence for $CP$ violation in charm mixing is observed.

We give a detailed analysis of an Abelianized gauge field model in which a Rarita-Schwinger spin-$\frac{3}{2}$ field is directly coupled to a spin-$\frac{1}{2}$ field. The model permits a perturbative expansion in powers of the gauge field coupling, and from the Feynman rules for the model we calculate the chiral anomaly.

Gravitational waves can teach us not only about sources and the environment where they were generated, but also about the gravitational interaction itself. Here we study the features of gravitational radiation produced during the scattering of a pointlike mass by a black hole. Our results are exact (to numerical error) at any order in a velocity expansion, and are compared against various approximations. At large impact parameter and relatively small velocities our results agree to within percent level with various post-Newtonian and weak-field results. Further, we find good agreement with scaling predictions in the weak-field/high-energy regime. Lastly, we achieve striking agreement with zero-frequency estimates.

Making use of the suitable transformation relations, the action of three-dimensional Einstein-Maxwell-dilaton gravity theory has been obtained from that of scalar-tensor modified gravity theory coupled to the Maxwell’s electrodynamics as the matter field. Two new classes of the static three-dimensional charged dilatonic black holes, as the exact solutions to the coupled scalar, electromagnetic and gravitational field equations, have been obtained in the Einstein frame. Also, it has been found that the scalar potential can be written in the form of a generalized Liouville-type potential. The conserved black hole charge and masses as well as the black entropy, temperature, and electric potential have been calculated from the geometrical and thermodynamical approaches, separately. Through comparison of the results arisen from these two alternative approaches, the validity of the thermodynamical first law has been proved for both of the new black hole solutions in the Einstein frame. Making use of the canonical ensemble method, a black hole stability or phase transition analysis has been performed. Regarding the black hole heat capacity, with the black hole charge as a constant, the points of type-1 and type-2 phase transitions have been determined. Also, the ranges of the black hole horizon radius at which the Einstein black holes are thermally stable have been obtained for both of the new black hole solutions. Then making use of the inverse transformation relations, two new classes of the string black hole solutions have been obtained from their Einstein counterpart. The thermodynamics and thermal stability of the new string black hole solutions have been investigated. It has been found that thermodynamic properties of the new charged black holes are identical in the Einstein and Jordan frames.

We investigate the generalized uncertainty principle (GUP) corrections to the entropy content and the information flux of black holes, as well as the corrections to the sparsity of the Hawking radiation at the late stages of evaporation. We find that due to these quantum gravity motivated corrections, the entropy flow per particle reduces its value on the approach to the Planck scale due to a better accuracy in counting the number of microstates. We also show that the radiation flow is no longer sparse when the mass of a black hole approaches Planck mass which is not the case for non-GUP calculations.

The identification of a suitable gravitational energy in theories of gravity has a long history, and it is well known that a unique answer cannot be given. In the first part of this paper we present a streamlined version of the derivation of Freud’s superpotential in general relativity. It is found if we once integrate the gravitational field equation by parts. This allows us to extend these results directly to the Einstein-Cartan theory. Interestingly, Freud’s original expression, first stated in 1939, remains valid even when considering gravitational theories in Riemann-Cartan or, more generally, in metric-affine spacetimes.

We write the known invariant definition of the Szekeres-Szafron family of solutions in an intrinsic, deductive, explicit and algorithmic form. We also intrinsically characterize the two commonly considered subfamilies, and analyze other subclasses, also defined by first-order differential conditions. Furthermore, we present a Rainich-like approach to these metrics.

Induced gravity, metrical gravity in which gravitational constant arises from vacuum expectation value of a heavy scalar, is known to suffer from Jordan frame vs Einstein frame ambiguity, especially in inflationary dynamics. Induced gravity in affine geometry, as we show here, leads to an emergent metric and gravity scale, with no Einstein-Jordan ambiguity. While gravity is induced by the vacuum expectation value of the scalar field, nonzero vacuum energy facilitates generation of the metric. Our analysis shows that induced gravity results in a relatively large tensor-to-scalar ratio in both metrical and affine gravity setups. However, the fact remains that the induced affine gravity provides an ambiguity-free framework.

If primordial black holes (PBHs) form directly from inhomogeneities in the early Universe, then the number in the mass range $10^5-{10}^{12}{M}_{\odot }$ is severely constrained by upper limits to the $\mu$ distortion in the cosmic microwave background (CMB). This is because inhomogeneities on these scales will be dissipated by Silk damping in the redshift interval $5\times {10}^4\lesssim z\lesssim 2\times {10}^6$. If the primordial fluctuations on a given mass scale have a Gaussian distribution and PBHs form on the high-$\sigma$ tail, as in the simplest scenarios, then the $\mu$ constraints exclude PBHs in this mass range from playing any interesting cosmological role. Only if the fluctuations are highly non-Gaussian, or form through some mechanism unrelated to the primordial fluctuations, can this conclusion be obviated.

We do a comprehensive study of the Bayesian evidences for a large number of dark energy models using a combination of latest cosmological data from SNIa, CMB, BAO, strong lensing time delay, growth measurements, measurements of Hubble parameter at different redshifts and measurements of angular diameter distance by Megamaser Cosmology Project. We consider a variety of scalar field models with different potentials as well as different parametrizations for the dark energy equation of state. Among 21 models that we consider in our study, we do not find strong evidences in favor of any evolving dark energy model compared to $\mathrm{\Lambda }\mathrm{CDM}$. For the evolving dark energy models, we show that purely nonphantom models have much better evidences compared to those models that allow both phantom and nonphantom behaviors. Canonical scalar field with exponential and tachyon field with square potential have highest evidences among all the models considered in this work. We also show that a combination of low redshift measurements decisively favors an accelerating $\mathrm{\Lambda }\mathrm{CDM}$ model compared to a nonaccelerating power law model.

Searches for persistent gravitational radiation from nonpulsating neutron stars in young supernova remnants are computationally challenging because of rapid stellar braking. We describe a practical, efficient, semicoherent search based on a hidden Markov model tracking scheme, solved by the Viterbi algorithm, combined with a maximum likelihood matched filter, the $\mathcal{F}$ statistic. The scheme is well suited to analyzing data from advanced detectors like the Advanced Laser Interferometer Gravitational Wave Observatory (Advanced LIGO). It can track rapid phase evolution from secular stellar braking and stochastic timing noise torques simultaneously without searching second- and higher-order derivatives of the signal frequency, providing an economical alternative to stack-slide-based semicoherent algorithms. One implementation tracks the signal frequency alone. A second implementation tracks the signal frequency and its first time derivative. It improves the sensitivity by a factor of a few upon the first implementation, but the cost increases by 2 to 3 orders of magnitude.

Blockspin transformation of topological defects is applied to the violation of the non-Abelian Bianchi identity (VNABI) on lattice defined as Abelian monopoles. To get rid of lattice artifacts, we introduce (1) smooth gauge fixings such as the maximal center gauge (MCG), (2) blockspin transformations and (3) the tadpole-improved gauge action. The effective action can be determined by adopting the inverse Monte Carlo method. The coupling constants $F(i)$ of the effective action depend on the coupling of the lattice action $\beta$ and the number of the blocking step $n$. But it is found that $F(i)$ satisfies a beautiful scaling; that is, they are a function of the product $b=na(\beta )$ alone for lattice coupling constants $3.0\le \beta \le 3.9$ and the steps of blocking $1\le n\le 12$. The effective action showing the scaling behavior can be regarded as an almost perfect action corresponding to the continuum limit, since $a\to 0$ as $n\to \infty$ for fixed $b$. The infrared effective monopole action keeps the global color invariance when smooth gauges such as MCG keeping the invariance are adopted. The almost perfect action showing the scaling is found to be independent of the smooth gauges adopted here as naturally expected from the gauge invariance of the continuum theory. Then we compare the results with those obtained by the analytic blocking method of topological defects from the continuum, assuming local two-point interactions are dominant as the infrared effective action. The action is formulated in the continuum limit while the couplings of these actions can be derived from simple observables calculated numerically on lattices with a finite lattice spacing. When use is made of Berezinskii-Kosterlitz-Thouless (BKT) transformation, the infrared monopole action can be transformed into that of the string model. Since large $b=na(\beta )$ corresponds to the strong-coupling region in the string model, the physical string tension and the lowest glueball mass can be evaluated analytically with the use of the strong-coupling expansion of the string model. The almost perfect action gives us $\sqrt{\sigma }\simeq 1.3\sqrt{{\sigma }_{\mathrm{phys}}}$ for $b\ge 1.0({\sigma }_{\mathrm{phys}}^{-1/2})$, whereas the scalar glueball mass is kept to be near $M(0^{++})\sim 3.7\sqrt{{\sigma }_{\mathrm{phys}}}$. In addition, using the effective action composed of 10 simple quadratic interactions alone, we can almost explain analytically the scaling function of the squared monopole density determined numerically for a large $b$ region when $b>1.2({\sigma }_{\mathrm{phys}}^{-1/2})$.

We revisit the phase diagram of strong-interaction matter for the two-flavor quark-meson model using the functional renormalization group. In contrast to standard mean-field calculations, an unusual phase structure is encountered at low temperatures and large quark chemical potentials. In particular, we identify a regime where the pressure decreases with increasing temperature and discuss possible reasons for this unphysical behavior.

In this work we calculate the mass spectra of charmonium for $1P,\dots ,4P$ states of $0^{++}$ and $1^{++}$, for $1S,\dots ,5S$ states of $0^{-+}$, and for $1S,\dots ,4D$ states of $1^{--}$ along with the two-photon decay widths of the ground and first excited states of $0^{++}$ quarkonia for the process $O^{++}\to \gamma \gamma$ in the framework of a QCD-motivated Bethe-Salpeter equation (BSE). In this $4\times 4$ BSE framework, the coupled Salpeter equations are first shown to decouple for the confining part of the interaction (under the heavy-quark approximation) and are analytically solved, and later the one-gluon-exchange interaction is perturbatively incorporated, leading to mass spectral equations for various quarkonia. The analytic forms of wave functions obtained are used for the calculation of the two-photon decay widths of ${\chi }_{c0}$. Our results are in reasonable agreement with data (where available) and other models.