In the present work, the set of stationary solutions of the Gross-Neveu model in the ’t Hooft limit is extended. Such an extension is obtained by striving for a hidden supersymmetry associated with disconnected sets of stationary solutions. How the supersymmetry arises from the Darboux-Miura transformations between Lax pairs of the stationary modified Korteweg–de Vries and the stationary Korteweg–de Vries hierarchies is shown, associating the correspondent superpotentials with self-consistent condensates for the Gross-Neveu model.

We provide an analysis of the structure of renormalization scheme invariants for the case of ${\varphi }^4$ theory, relevant in four dimensions. We give a complete discussion of the invariants, up to four loops, and include some partial results at five loops, showing that there are considerably more invariants than one might naively have expected. We also show that one-vertex reducible contributions may consistently be omitted in a well-defined class of schemes, which of course includes $\overline{\mathrm{MS}}$.

We explore nonlinear perturbations in different static fluid systems. We find that the equations, corresponding to the perturbation of the integrals of motion, i.e., Bernoulli’s constant and the mass flow rate, satisfy the massless scalar field equation in a time dependent acoustic metric. When one is interested up to the second order behavior of the perturbations, the emergent time dependent acoustic metric of the system, derived from the massless scalar field equations of the perturbations of the integrals of motion, has some astounding similarities with the metric describing gravitational wave in Minkowski spacetime.

A form of infinite derivative gravity is free from ghostlike instabilities with improved small scale behavior. In this theory, we calculate the tree-level scattering amplitude and the corresponding weak field potential energy between two localized covariantly conserved spinning pointlike sources that also have velocities and orbital motion. We show that the spin-spin and spin-orbit interactions take the same form as in Einstein’s gravity at large separations, whereas at small separations, the results are different. We find that not only the usual Newtonian potential energy but also the spin-spin and spin-orbit interaction terms in the potential energy are nonsingular as one approaches $r\to 0$.

We consider static spherically symmetric self-gravitating configurations of the perfect fluid within the framework of the torsion-based extended theory of gravity. In particular, we use the covariant formulation of $f(T)$ gravity with $f(T)=T+\frac{\alpha }{2}{T}^2$, and for the fluid, we assume the polytropic equation of state with the adiabatic exponent $\mathrm{\Gamma }=2$. The constructed solutions have a sharply defined radius [as in General Relativity (GR)] and can be considered as models of nonrotating compact stars. The particle number–to–stellar radius curves reveal that with positive (negative) values of $\alpha$ a smaller (greater) number of particles can be supported against gravity then in GR. For the interpretation of the energy density and the pressure within the star, we adopt the GR picture where the effects due to nonlinearity of $f(T)$ are seen as a $f(T)$ fluid, which together with the polytropic fluid contributes to the effective energy momentum. We find that sufficiently large positive $\alpha$ gives rise to an abrupt sign change (phase transition) in the energy density and in the principal pressures of the $f(T)$ fluid, taking place within the interior of the star. The corresponding radial profile of the effective energy density is approximately constant over the central region of the star, mimicking an incompressible core. This interesting phenomenon is not found in configurations with negative $\alpha$.

We formulate the Einstein-Cartan-Dirac equations in the Newman-Penrose (NP) formalism, thereby presenting a more accurate and explicit analysis of previous such studies. The equations show in a transparent way how the Einstein-Dirac equations are modified by the inclusion of torsion. In particular, the Hehl-Datta equation is presented in NP notation. We then describe a few solutions of the Hehl-Datta equation on Minkowski space-time, and in particular report a solitonic solution which removes the unphysical behavior of the corresponding Dirac solution. The present work serves as a prelude to similar studies for nondegenerate Poincaré gauge gravity.

In this paper, we show that the baryon-to-photon ratio $\eta$ is in general not conserved before decoupling in nonminimally coupled theories of gravity. We use big-bang nucleosynthesis and cosmic microwave background (CMB) limits on the baryon-to-photon ratio $\eta$ to derive new constraints on modified gravity theories with a universal nonminimal coupling between matter and curvature, showing that they rule out a specific class of models previously considered in the literature as a substitute for the dark matter. We also compare these new constraints with the ones obtained from the COBE-FIRAS limits on CMB spectral distortions, highlighting the complementarity between them.

We perform fully nonlinear numerical simulations within the spherically symmetric Einstein-(complex)-Proca system. Starting with Proca field distributions that obey the Hamiltonian, momentum and Gaussian constraints, we show that the self-gravity of the system induces the formation of compact objects, which, for appropriate initial conditions, asymptotically approach stationary solitonlike solutions known as Proca stars. The excess energy of the system is dissipated by the mechanism of gravitational cooling in analogy to what occurs in the dynamical formation of scalar boson stars. We investigate the dependence of this process on the phase difference between the real and imaginary parts of the Proca field, as well as on their relative amplitudes. Within the timescales probed by our numerical simulations the process is qualitatively insensitive to either choice: the phase difference and the amplitude ratio are conserved during the evolution. Thus, whereas a truly stationary object is expected to be approached only in the particular case of equal amplitudes and opposite phases, quasistationary compact solitonic objects are, nevertheless, formed in the general case.

We investigate the existence of invariantly defined quasilocal hypersurfaces in the Kastor-Traschen solution containing $N$ charge-equal-to-mass black holes. These hypersurfaces are characterized by the vanishing of particular curvature invariants, known as Cartan invariants, which are generated using the frame approach. The Cartan invariants of interest describe the expansion of the outgoing and ingoing null vectors belonging to the invariant null frame arising from the Cartan-Karlhede algorithm. We show that the evolution of the hypersurfaces surrounding the black holes depends on an upper-bound on the total mass for the case of two and three equal mass black holes. We discuss the results in the context of the geometric horizon conjectures.

We consider how a nearly massless scalar field conformally and disformally coupled to matter can affect the dynamics of gravitationally interacting bodies. We focus on the case of two interacting objects, and we obtain the effective metric driving the dynamics of the two-body system when reduced to one body in the center-of-mass frame. We then concentrate on the case of a light particle in the scalar and gravitational fields generated by a heavy object and find the effects of the conformal and disformal couplings on the body’s trajectory such as the advance of the perihelion and the Shapiro time delay. The disformal coupling leads to a negligible contribution to the Shapiro effect and therefore no constraint from the Cassini experiment. On the other hand, it contributes to the perihelion advance leading to a weak bound on the strength of the disformal coupling itself. Finally, we remark that the disformal coupling gives rise to a contribution to the perihelion advance which varies quadratically with the mass of the heavy body, leading to possible strong effects for stars in the vicinity of astrophysical black holes. For neutron stars in a binary system, the disformal effects vary as the quartic power of the size of the orbit which might lead to interesting consequences in the inspiralling phase prior to a merger.

We present a new parameterization of quintessence potentials for dark energy based directly upon the dynamical properties of the equations of motion. Such parameterization arises naturally once the equations of motion are written as a dynamical system in terms of properly defined polar variables. We have identified two different classes of parameters, and we dubbed them dynamical and passive parameters. The dynamical parameters appear explicitly in the equations of motion, but the passive parameters play just a secondary role in their solutions. The new approach is applied to the so-called thawing potentials, and it is argued that only three dynamical parameters are sufficient to capture the evolution of the quintessence fields at late times. This work reconfirms the arbitrariness of the quintessence potentials as the recent observational data fail to constrain the dynamical parameters.

We investigate the impact of the recent observation of the 21-cm global signal by EDGES on the primordial power spectrum, particularly focusing on the running parameters ${\alpha }_s$ and ${\beta }_s$ which characterize the detailed scale dependence of the primordial spectrum. When the primordial power spectrum is enhanced or suppressed on small scales, the structure formation proceeds faster or slower and changes the abundance of small size halos, which affects the sources of Lyman $\alpha$ radiation at high redshifts to alter the position of the absorption line. A recent observation of EDGES detected the 21-cm absorption line at $z=17.2$, and this result also indicates that the brightness temperature is consistent with zero for $z\lesssim 14$ and $z\gtrsim 22$, which can exclude a scenario giving the absorption line at such redshifts. We argue that the bound on the running parameters can be obtained by requiring that the absorption line should not exceed observational bounds at such redshift ranges and find that the parameter space of ${\alpha }_s$ and ${\beta }_s$ allowed by Planck may be disfavored for some values of astrophysical parameters.

In the framework of the theory of general relativity, models of stars with an unusual equation of state $\rho c^2<0$, $P>0$, where $\rho$ is the mass density and $P$ is the pressure, are constructed. These objects create outside themselves the forces of gravitational repulsion. The equilibrium of such stars is ensured by a nonstandard balance of forces. Negative mass density, acting gravitationally on itself, creates an acceleration of the negative mass, directed from the center. Therefore, in the absence of pressure, such an object tends to expand. At the same time, the positive pressure, which falls just like in ordinary stars from the center to the surface, creates a force directed from the center. This force acts on the negative mass density, which causes acceleration directed opposite of the acting force, that is, to the center of the star. This acceleration balances the gravitational repulsion produced by the negative mass. Thus, in our models, gravity and pressure change roles: the negative mass tends to create a gravitational repulsion, while the gradient of the pressure acting on the negative mass tends to compress the star. In this paper, we construct several models of such a star with various equations of state.

Enhanced density fluctuations on small scales would lead to the formation of numerous dark matter minihalos, so limits on the minihalo abundance can place upper bounds on the small-scale primordial power spectrum. In particular, the ultracompact minihalo (UCMH), a dark matter structure hypothesized to possess a $\rho \propto r^{-9/4}$ density profile due to its formation at $z\ge 1000$, has been used to establish an upper bound on the primordial power spectrum at scales smaller than 2 Mpc. The extreme slope of this density profile amplifies the observational signals of UCMHs. However, we recently showed via N-body simulations that the $\rho \propto r^{-9/4}$ density profile does not develop in realistic formation scenarios, throwing UCMH-derived power spectrum constraints into question. Instead, minihalos develop shallower inner profiles with power-law indices between $-3/2$ and $-1$. In this paper, we expand on that result and discuss its implications. Using a model that is calibrated to simulation results and predicts halo structures in spiked power spectra based on their formation times, we calculate new upper bounds on the primordial power spectrum based on limits on the dark matter annihilation rate within the Galaxy. We find that despite assuming shallower profiles, this minihalo model actually yields stronger constraints than the previous UCMH picture owing to its inclusion of all minihalos instead of only the earliest-forming ones.

The detection of the gravitational capture of a stellar-mass compact object by a massive black hole (MBH) will allow us to test gravity in the strong regime. The repeated, accumulated bursts of gravitational radiation from these sources can be envisaged as a geodesic mapping of space-time around the MBH. These sources form via two-body relaxation, by exchanging energy and angular momentum, and inspiral in a slow, progressive way down to the final merger. The frequencies fall in the millihertz range for MBHs with masses $\sim {10}^6{M}_{\odot }$, i.e., that of space-borne gravitational-wave observatories such as LISA. In this article we show that, depending on their orbital parameters, intermediate-mass ratio inspirals (IMRIs) of MBHs with masses between a hundred and a few thousand $M_{\odot }$ have frequencies that make them detectable (i) with ground-based observatories, or (ii) with both LISA and ground-based observatories (such as advanced LIGO/Virgo) and third-generation observatories [such as the Einstein Telescope (ET)]. The binaries have a signal-to-noise ratio large enough to ensure detection. More extreme values of the orbital parameters correspond to systems that are only detectable with ground-based detectors and in particular enter the LIGO/Virgo band in many different harmonics for masses up to $2000M_{\odot }$. We show that environmental effects are negligible, so the source should not have this kind of complication. The accumulated phase shift is measurable with LISA and ET, and for some cases also with LIGO, so that it is possible to recover information about the eccentricity and formation scenario. For IMRIs with a total mass $⪅2000M_{\odot }$ and initial eccentricities up to 0.999, LISA can give a advanced warning to ground-based detectors with seconds of precision. The possibility of detecting IMRIs from the ground alone or combined with space-borne observatories opens new possibilities for gravitational-wave astronomy.

We quantitatively study the stationary, axisymmetric, force-free magnetospheres of spinning (Kerr) black holes (BHs) and the conditions needed for relativistic jets to be powered by the Blandford-Znajek mechanism. These jets could be from active galactic nuclei, blazars, quasars, microquasars, radioactive galaxies, and other systems that host Kerr BHs. The structure of the magnetosphere determines how the BH energy is extracted, e.g., via the Blandford-Znajek mechanism, which converts the BH rotational energy into Poynting flux. The key assumption is the force-free condition, which requires the presence of plasma with the density being above the Goldreich-Julian density. Unlike neutron stars, which in principle can supply electrons from the surface, BHs cannot supply plasma at all. The plasma must be generated in situ via an electron-positron cascade, presumably in the gap region. Here we study varying conditions that provide a sufficient amount of plasma for the Blandford-Znajek mechanism to work effectively.

Gauge theory/string theory holographic correspondence for $\mathcal{N}=4$ supersymmetric Yang-Mills (SYM) theory is well under control in the planar limit, and for large (infinitely large) ’t Hooft coupling, $\lambda \to \infty$. Certain aspects of the correspondence can be extended including $\mathcal{O}({\lambda }^{-3/2})$ corrections. There are no reliable first principle computations of the $\mathcal{N}=4$ plasma nonequilibrium properties beyond the stated order. We show extreme sensitivity of the nonhydrodynamic spectra of holographic $\mathcal{N}=4$ SYM plasma to $\mathcal{O}({\lambda }^{-3})$ corrections, challenging any conclusions reached from “resummation” of $\mathcal{O}({\lambda }^{-3/2})$ corrections.

We propose an approach to describe the $D^{+}\to K^{-}{K}^{+}{K}^{+}$ decay amplitude, based on chiral effective Lagrangians, which can be used to extract information about $K\overline{K}$ scattering. It relies on factorization and its main novel feature is the role played by multimeson interactions characteristic of chiral symmetry. Our trial function is an alternative to the widely used isobar model and includes both nonresonant three-body interactions and two-body rescattering amplitudes, based on coupled channels and resonances, for S- and P-waves with isospin 0 and 1. The latter are unitarized in the $K$-matrix approximation and represent the only source of complex phases in the problem. The nonresonant component, given by chiral symmetry as a real polynomium, is an important prediction of the model, which goes beyond the ($2+1$) approximation. Our approach allows one to disentangle the two-body scalar contributions with different isospins, associated with the $f_0(980)$ and $a_0(980)$ channels. We show how the $K\overline{K}$ amplitude can be obtained from the decay $D^{+}\to K^{-}{K}^{+}{K}^{+}$ and discuss extensions to other three-body final states.

We perform a new extraction of polarized parton distribution functions (PPDFs) from the spin structure function experimental data in the fixed-flavor number scheme. In this analysis, we include recent proton and deuteron spin structure functions obtained by the COMPASS Collaboration. We examine the impact of the new COMPASS proton and deuteron data on the polarized parton densities and compare with results from our previous study (KATAO PPDFs), which used the Jacobi polynomial approach. We find the extracted PPDFs of the proton, neutron, and deuteron structure functions are in very good agreement with the experimental data. The results for extracted PPDFs are also compared with available theoretical models from the literature.

In this work, we calculate the $CP$-averaged branching ratios and direct $CP$-violating asymmetries of the quasi-two-body decays $B_{(s)}\to P{f}_2(1270)\to P\pi \pi$ with the two-pion distribution amplitude ${\mathrm{\Phi }}_{\pi \pi }^{\mathrm{D}}$ by using the perturbative QCD factorization approach, where $P$ represents a light pseudoscalar meson $K$, $\pi$, $\eta$ and ${\eta }^{\prime }$. The relativistic Breit-Wigner formula for the $D$-wave resonance $f_2(1270)$ is adopted to parameterize the timelike form factor $F_{\pi }$, which contains the final state interactions between the pions in the resonant regions. The consistency of theoretical results with data can be achieved by determining the Gegenbauer moments of the $D$-wave two-pion distribution amplitudes. The decay rates for the considered decay modes are generally in the order of ${10}^{-9}$ to ${10}^{-6}$. The integrated direct $CP$ asymmetries for the charged modes agree with the BABAR and Belle measurements. As a by-product, we extract the branching ratios of $B_{(s)}\to P{f}_2(1270)$ from the corresponding quasi-two-body decay modes, which still need experimental tests at the ongoing and forthcoming experiments.