Based on a recently derived secular spin evolution of black holes, neutron stars, gravastars, or boson stars in precessing compact binaries on eccentric orbit, we carry out a linear stability analysis of fixed point configurations. We identify the aligned and more generic coplanar configurations of the spins and orbital angular momentum as fixed points. Through a dynamical system analysis, we investigate their linear stability as function of the mass quadrupole parameter. Our most important results are as follows. Marginal stability holds for the binary configurations with both spins antialigned to the orbital angular momentum, for both spins aligned to the orbital angular momentum (with the exception of certain quadrupolar parameter ranges of neutron stars and boson stars), and for the extremal mass ratio. For equal masses, the configurations of one of the spins aligned and the other antialigned is stable for gravastar binaries, for neutron star binaries in the high quadrupolar parameter range, and for boson star binaries. For some unequal mass gravastar binaries, black hole binaries or neutron star binaries, a transition from stability to instability can occur during the inspiral, when one of the spins is aligned, while the other is antialigned to the orbital angular momentum. We also discover a transitional instability regime during the inspiral of certain gravastar, neutron star, or boson star binaries with opposing spins. For coplanar configurations we recover the marginally stable configurations leading to the libration phenomenon identified in previous numerical investigations lacking mass quadrupole contributions, and we analyze how it is affected by the quadrupolar structure of the sources. We also investigate the linear stability of black hole, neutron star, and boson star binaries, also of mixed black hole - gravastar, black hole - neutron star and black hole - boson star binaries. We find instabilities only for the gravastar - gravastar, boson star - boson star and black hole - boson star binaries. For a given spin configuration, marginal stability strongly depends on the value of the quadrupolar parameters. The stability region is larger for neutron star binaries than for black hole binaries, while the mixed systems have a restricted stability parameter region.

We discuss precessing compact binaries on eccentric orbit with gravastar, black hole, neutron star, or boson star components. We derive the secular evolution equations to second post-Newtonian–order accuracy, with leading-order spin-orbit, spin-spin, and mass quadrupole-monopole contributions included. The emerging closed system of first-order differential equations evolves the pairs of polar and azimuthal angles of the spin and orbital angular momentum vectors together with the periastron angle. In contrast with the instantaneous dynamics, the secular dynamics is autonomous. The validity of the latter is confirmed numerically, showing that secular evolutions look like smoothed-out instantaneous evolutions over timescales where radiation reaction is negligible. The secular evolution of the spin polar angles and the difference of their azimuthal angles generates a closed subsystem, which, despite the apparent singularity of spherical polar coordinates, remains well defined through aligned configurations. We study analytically this system for the particular cases of one spin dominating over the other and for black hole - boson star binaries of equal masses. In the first case, known large flip-flops of the smaller spin are reproduced, when the larger spin is almost coplanar with the orbit. We also find new, quadrupole-induced flip-flops occurring when the neutron star with dominant spin has a quadrupolar parameter $w_1\approx 3$. Finally, we analyze the evolutions of the spin angles numerically by comparing the cases when the black hole companion is either a gravastar, another black hole, or a boson star with identical mass. We find that both the amplitude and period of the flip-flop are the largest, when the companion is a black hole. In the case of a boson star companion, the frequency of the flip-flop increases significantly. Further, while in the case of gravastars and black holes a swinging-type azimuthal evolution occurs, with the spins of the components periodically overpassing each other, their sequence is conserved when the companion is a boson star.

We present a novel and remarkably simple formulation of degenerate higher-order scalar-tensor (DHOST) theories whose Lagrangian is quadratic in the second derivatives of some scalar field. Using disformal transformations of the metric, we identify a special “frame” (or metric) for which the Lagrangian of quadratic DHOST theories reduces to the usual Einstein-Hilbert term plus a few terms that depend on simple geometric quantities characterizing the uniform scalar-field hypersurfaces. In particular, for quadratic DHOST theories in the physically interesting class Ia, the Lagrangian simply consists of the Einstein-Hilbert term plus a term proportional to the three-dimensional scalar curvature of the uniform scalar-field hypersurfaces. The classification of all quadratic DHOST theories becomes particularly transparent in this geometric reformulation, which also applies to scalar-tensor theories that are degenerate only in the unitary gauge.

The exploration of teleparallel gravity has been done from a dynamical systems point of view in order to be tested against the cosmological evolution currently observed. So far, the proposed autonomous systems have been restrictive over a constant dynamical variable, which contains information related to the dynamics on the $H_0$ value. It is therefore that in this paper we consider a generalization of the dynamical system by imposing a nonconstant degree of freedom over it which allows us to rewrite a generic autonomous dynamical analysis. We describe the treatment of our nonlinear autonomous system by studying the hyperbolic critical points and discuss an interesting phenomenological feature in regards to $H_0$: the possibility to obtain a best-fit value for this parameter in a cosmologically viable $f(T,B)$ model, a mixed power law. This result allows us to present a generic scenario in which it is possible to fix constraints to solve the $H_0$ tension at late times where its linearized solutions are considered.

We interpret the cosmological constant as the energy of the vacuum, and under a minimum amount of assumptions, we show that it is deformed in the vicinity of a black hole. This leads us to reexamine the Kerr–de Sitter solution. We provide a new solution, simpler and geometrically richer, which shows the impact of the rotation in form of a warped curvature. We carry out a detailed and exact study on the new black hole solution, and we conclude with a conjecture regarding the possible impact of our results on alternative theories.

The primordial scalar power spectrum is well constrained by the cosmological data on large scales, primarily from the observations of the anisotropies in the cosmic microwave background. Over the last few years, it has been recognized that a sharp rise in power on small scales will lead to the enhanced formation of primordial black holes (PBHs) and also generate secondary gravitational waves (GWs) of higher and, possibly, detectable amplitudes. It is well understood that scalar power spectra with COBE normalized amplitude on the cosmic microwave background scales and enhanced amplitudes on smaller scales can be generated due to deviations from slow roll in single, canonical scalar field models of inflation. In fact, an epoch of so-called ultraslow roll inflation can lead to the desired amplification. We find that scenarios that lead to ultraslow roll can be broadly classified into two types, one wherein there is a brief departure from inflation (a scenario referred to as punctuated inflation) and another wherein such a departure does not arise. In this work, we consider a set of single field inflationary models involving the canonical scalar field that lead to ultraslow roll and punctuated inflation and examine the formation of PBHs as well as the generation of secondary GWs in these models. Apart from considering specific models, we reconstruct potentials from certain functional choices of the first slow roll parameter leading to ultraslow roll and punctuated inflation and investigate their observational signatures. In addition to the secondary tensor power spectrum, we calculate the secondary tensor bispectrum in the equilateral limit in these scenarios. Moreover, we calculate the inflationary scalar bispectrum that arises in all the cases and discuss the imprints of the scalar non-Gaussianities on the extent of PBHs formed and the amplitude of the secondary GWs generated. We conclude with a discussion on the wider implications of our results.

Using $N$-body simulations of cosmological large-scale structure formation, for the first time, we show that the anisotropic primordial non-Gaussianity causes a scale-dependent modification, given by $1/k^2$ at small $k$ limit, in the three-dimensional power spectra of halo shapes (intrinsic alignments), whilst the conventional power spectrum of halo number density field remains unaffected. We discuss that wide-area imaging and spectrocopic surveys observing the same region of the sky allow us to constrain the quadrupole primordial non-Gaussianity coefficient $f_{\mathrm{NL}}^{s=2}$ at a precision comparable with or better than that of the cosmic microwave background.

We show how the renormalization constant of the Higgs vacuum expectation value fixed by a tadpole condition is responsible for gauge dependences in various definitions of parameters in the $R_{\xi }$-gauge. Then we show the relationship of this renormalization constant to the Fleischer-Jegerlehner (FJ) scheme, which is used to avoid these gauge dependences. In this way, we also present a viewpoint on the FJ scheme complementary to the ones already existing in the literature. Additionally, we compare and discuss different approaches to the renormalization of tadpoles by identifying the similarities and relations between them. The relationship to the Higgs background-field renormalization is also discussed.

Quantum vacuum fluctuations give rise to effective nonlinear interactions between electromagnetic fields. A prominent signature of quantum vacuum nonlinearities driven by macroscopic fields are signal photons differing in characteristic properties such as frequency, propagation direction and polarization from the driving fields. We devise a strategy for the efficient tracing of the various vacuum-fluctuation-mediated interaction processes in order to identify the most prospective signal photon channels. As an example, we study the collision of up to four optical laser pulses and pay attention to sum and difference frequency generation. We demonstrate how this information can be used to enhance the signal photon yield in laser pulse collisions for a given total laser energy.

From a diabatic bound state approach to $J^{PC}=1^{--}$ and $(0,1,2{)}^{++}$ charmoniumlike resonances below 4.1 GeV, formulated in terms of $c\overline{c}$ and closed meson-meson channels, we calculate mass shifts and widths due to open meson-meson channels. This calculation does not involve any new free parameter, so comparison of our predictions with existing data provides a direct test of our approach. Further mass corrections are also estimated and good agreement with the measured masses comes out. As for the calculated widths, overall reasonable, they point out to the need of some refinement of our current bound state approximation for an accurate description of data. These results give additional support to the diabatic approach in QCD as an adequate framework for a complete unified description of conventional and unconventional charmoniumlike resonances. In this respect, the experimental discovery of a predicted $2^{++}$ resonance with a mass around 4 GeV would be of special relevance.

We investigate photo-production of vector mesons $J/\mathrm{\Psi }$ and $\mathrm{\Psi }(2s)$, based on both HERA and LHC data, using 2 fits of unintegrated gluon distributions. The latter are subject to nonlinear Balitsky-Kovchegov evolution (Kutak-Sapeta gluon; KS) and linear next-to-leading order Balitsky-Kuraev-Fadin-Lipatov evolution (Hentschinski-Sabio Vera-Salas; HSS gluon) respectively. Apart from extending previous studies to the case of radially excited charmonium $\mathrm{\Psi }(2s)$, we further use an improved set of charmonium wave functions, provided in the literature, and give an estimate of the uncertainties associated with the energy dependence of the HSS gluon. While we observe that the difference between linear and non-linear evolution somehow diminishes and a clear distinction between both HSS and KS gluon is not possible using the currently available data set, we find that the differences between both gluon distributions are enhanced for the ratio of the photo-production cross sections of $\mathrm{\Psi }(2s)$ and $J/\mathrm{\Psi }$ vector mesons.

We explore the possibility of $CP$ violation in baryonic ${\mathrm{\Lambda }}_b\to ({\mathrm{\Lambda }}_c^{+},p^{+}){\pi }^{+}{\mu }^{-}{\mu }^{-}$ decays which are mediated by two Majorana sterile neutrinos and are $|\mathrm{\Delta }L|=2$ lepton-number-violating processes. Appreciable $CP$ asymmetry can be obtained if there are two on-shell Majorana neutrinos that are quasidegenerate in mass with the mass difference of the order of average decay widths. We find that, given the present constraints on the heavy to light mixing element $|V_{\mu N}|$, the ${\mathrm{\Lambda }}_b\to p^{+}{\pi }^{+}{\mu }^{-}{\mu }^{-}$ and ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c^{+}{\pi }^{+}{\mu }^{-}{\mu }^{-}$ decay rates are suppressed but could be within the experimental reach at the LHC. If searches of the modes are performed, then experimental limits on the rates can be translated to constraints on the Majorana neutrino mass $m_N$ and heavy to light mixing element squared $|V_{\mu N}{|}^2$. We show that the constraints on the $(m_N,|V_{\mu N}{|}^2)$ parameter space coming from the $|\mathrm{\Delta }L|=2$ baryonic decays are complementary to the bounds coming from other processes.

Proposed in 1954 by Gell-Mann, Goldberger, and Thirring, crossing symmetry postulates that particles are indistinguishable from antiparticles traveling back in time. Its elusive proof amounts to demonstrating that scattering matrices in different crossing channels are boundary values of the same analytic function, as a consequence of physical axioms such as causality, locality, or unitarity. In this work we report on the progress in proving crossing symmetry on shell within the framework of perturbative quantum field theory. We derive bounds on internal masses above which scattering amplitudes are crossing symmetric to all loop orders. They are valid for four- and five-point processes, or to all multiplicity if one allows deformations of momenta into higher dimensions at intermediate steps.

The NANOGrav Collaboration recently reported a strong evidence for a stochastic common-spectrum process in the pulsar-timing data. We evaluate the evidence of interpreting this process as mergers of super massive black hole binaries and/or various stochastic gravitational-wave background sources in the early Universe, including first-order phase transitions, cosmic strings, domain walls, and large amplitude curvature perturbations. We discuss the implications of the constraints on these possible sources. It is found that the data shows a positive evidence in favor of the cosmic strings against other gravitational-wave sources based on the Bayes factor analysis.

Recently a novel perturbative continuum limit for quantum gravity has been proposed and demonstrated to work at first order. Every interaction monomial $\sigma$ is dressed with a coefficient function $f_{\mathrm{\Lambda }}^{\sigma }(\phi )$ of the conformal factor field, $\phi$. Each coefficient function is parametrized by an infinite number of underlying couplings, and decays at large $\phi$ with a characteristic amplitude suppression scale which can be chosen to be at a common value, ${\mathrm{\Lambda }}_{\mathrm{p}}$. Although the theory is perturbative in couplings it is nonperturbative in $\hslash$. At second order in perturbation theory, one must sum over all melonic Feynman diagrams to obtain the particular integral. We show that it leads to a well-defined renormalized trajectory and thus continuum limit, provided it is solved by starting at an arbitrary cutoff scale $\mathrm{\Lambda }=\mu$ which lies in the range $0<\mu <a{\mathrm{\Lambda }}_{\mathrm{p}}$ ($a$ some nonuniversal number). If $\mu$ lies above this range the resulting coefficient functions become singular, and the flow ceases to exist, before the physical limit is reached. To this one must add a well-behaved complementary solution, containing irrelevant couplings determined uniquely by the first-order interactions, and renormalized relevant couplings. Even though some irrelevant couplings diverge in the limit ${\mathrm{\Lambda }}_{\mathrm{p}}\to \infty$, domains for the underlying relevant couplings can be chosen such that diffeomorphism invariance will be recovered in this limit, and where the underlying couplings disappear to be replaced by effective diffeomorphism invariant couplings.

The properties of exotic stars are investigated. In particular, we study objects made entirely of dark matter, and we take into account intrinsic anisotropies which have been ignored so far. We obtain semianalytical solutions to the structure equations, where all quantities of interest are expressed in terms of the energy density, while the latter is computed numerically. We show that those solutions (i) are well behaved within general relativity and (ii) are capable of describing realistic astrophysical configurations. A direct comparison with their isotropic counterparts with the same radius reveals that the latter are slightly more massive.

Killing vectors play a crucial role in characterizing the symmetries of a given spacetime. However, realistic astrophysical systems are in most cases only approximately symmetric. Even in the case of an astrophysical black hole, one might expect Killing symmetries to exist only in an approximate sense due to perturbations from external matter fields. In this work, we consider the generalized notion of Killing vectors provided by the almost Killing equation, and study the perturbations induced by a perturbation of a background spacetime satisfying exact Killing symmetry. To first order, we demonstrate that for nonradiative metric perturbations (that is, metric perturbations with nonvanishing trace) of symmetric vacuum spacetimes, the perturbed almost Killing equation avoids the problem of an unbounded Hamiltonian for hyperbolic parameter choices. For traceless metric perturbations, we obtain similar results for the second-order perturbation of the almost Killing equation, with some additional caveats. Thermodynamical implications are also explored.

In the context of the higher dimensional braneworld scenario, we have argued that the occurrence of horizonless exotic compact objects, as an alternative to classical black holes, is more natural. These exotic compact objects carry a distinctive signature of the higher dimension, namely a tidal charge parameter, related to the size of the extra dimension. Due to the absence of any horizon, rotating exotic compact objects are often unstable because of superradiance. Interestingly, these higher dimensional exotic compact objects are more stable than their four-dimensional counterpart, as the presence of the tidal charge reduces the size of the extra dimension and hence results in a stronger gravitational field on the brane. A similar inference is drawn by analyzing the static modes associated with these exotic compact objects, irrespective of the nature of the perturbation, i.e., it holds true for scalar, electromagnetic and also gravitational perturbation. The postmerger ringdown phase of the exotic compact object in the braneworld scenario, which can be described in terms of the quasinormal modes, holds a plethora of information regarding the nature of the higher dimension. In this connection we have discussed the analytical computation of the quasinormal modes as well as their numerical estimation for perturbations of arbitrary spin, depicting existence of echoes in the ringdown waveform. As we have demonstrated, the echoes in the ringdown waveform depend explicitly on the tidal charge parameter and hence its future detection can provide constraints on the tidal charge parameter, which in turn will enable us to provide a possible bound on the size of the extra dimension.

We introduce an improved version of the eccentric, nonspinning, inspiral-Gaussian-process merger approximant (ENIGMA) waveform model that utilizes a more stable and robust numerical method to smoothly connect the analytical relativity-based inspiral evolution with the numerical relativity-based merger phase. We find that this ready-to-use model can: (i) produce physically consistent signals, without reporting any failures, when sampling over 1M samples that were randomly chosen over the $m_{\{1,2\}}\in [5{\mathrm{M}}_{\odot },50{\mathrm{M}}_{\odot }]$ parameter space, and the entire range of binary inclination angles; (ii) produce waveforms within 0.04 seconds, averaged over 1000 iterations, from an initial gravitational wave frequency $f_{\mathrm{GW}}=15\mathrm{Hz}$ and at a sample rate of 8192 Hz; and (iii) reproduce the physics of quasicircular mergers, since its overlap with SEOBNRv4 waveforms is $\mathcal{O}\ge 0.99$ assuming advanced LIGO zero detuned high power noise configuration, and signals generated from $f_{\mathrm{GW}}=15\mathrm{Hz}$. We utilize ENIGMA to compute the expected signal-to-noise ratio (SNR) distributions of eccentric binary black hole mergers assuming the existence of second and third generation gravitational wave detector networks. For second generation detectors, we assume the geographical location and detection sensitivities of the twin LIGO detectors, Virgo, KAGRA, LIGO-India, and a LIGO-type detector in Australia. For third generation detectors, we assume the geographical location of second generation detectors, and use the proposed sensitivities of the Cosmic Explorer and the Einstein Telescope. In the context of advanced LIGO-type detectors, we find that the SNR of eccentric mergers is always larger than quasicircular mergers for systems with $e_0\le 0.4$ at $f_{\mathrm{GW}}=10\mathrm{Hz}$, even if the timespan of eccentric signals is just a third of quasicircular systems with identical total mass and mass-ratio. For Cosmic Explorer-type detector networks, we find that eccentric mergers have similar SNRs than quasicircular systems for $e_0\le 0.3$ at $f_{\mathrm{GW}}=10\mathrm{Hz}$. Systems with $e_0\sim 0.5$ at $f_{\mathrm{GW}}=10\mathrm{Hz}$ have SNRs that range between 50%-90% of the SNR produced by quasicircular mergers, even if these eccentric signals are just between a third to a tenth the length of quasicircular systems. For Einstein Telescope-type detectors, we find that eccentric mergers have similar SNRs than quasicircular systems for $e_0\le 0.4$ at $f_{\mathrm{GW}}=5\mathrm{Hz}$. The most eccentric events in our sample, $e_0\sim 0.6$ at $f_{\mathrm{GW}}=5\mathrm{Hz}$, merge at least five times faster than quasicircular systems, and may be detectable with SNRs between 50%–85% the SNR of quasicircular mergers with identical binary components.