We propose a class of higher-derivative gravities that can be viewed as the Gauss-Bonnet extension of the Starobinsky model. The theory admits the Minkowski spacetime vacuum whose linear spectrum consists of the graviton and a massive scalar mode. In addition to the usual Schwarzschild black hole, we use numerical analysis to establish that in some suitable mass range, new black holes carrying the massive scalar hair can emerge. The new black hole serves as a “wall” separating the naked spacetime singularity and wormholes in the parameter space of the scalar hair. Our numerical results also indicate that although the new hairy black hole and the Schwarzschild black hole have different spacetime geometry, their entropy and temperature are the same for the same mass.

Dark energy is the constituent with an enormous abundance in the present Universe, responsible for the Universe’s accelerated expansion. Therefore, it is plausible that dark energy may interact within any compact astrophysical object. The author in [S. S. Yazadjiev, Phys. Rev. D 83, 127501 (2011)] constructs an exact star solution consisting of ordinary matter and a phantom field from a constant density star (CDS) known as the Schwarzschild interior solution. The star denotes a dark energy star (DES). The author claims that the phantom field represents dark energy within the star. So far, the role of the phantom field as dark energy in a DES is not systematically studied yet. Related to this issue, we analyze the energy condition of a DES. We expect that DESs shall violate the strong energy condition (SEC) for a particular condition. We discover that a SEC is fully violated only when the compactness reaches the Buchdahl limit. Furthermore, we also investigate the causal conditions and stabilities due to the convective motion and gravitational cracking. We also find that those conditions are violated. These results indicate that DES is not physically stable. However, we may consider DES as an ultracompact object of which we can calculate the gravitational wave echo time and echo frequency and compare them to those of CDS. We find that the contribution of the phantom field delays the gravitational wave echoes. The effective potential of the perturbed DES is also studied. The potential also enjoys a potential well like CDS but with a deeper well. We also investigate the possibility that DES could form a gravastar when $C=1$. It is found that a gravastar produced from DES possesses no singularity with a dS-like phase as the interior. These results could open more opportunities for the observational study of dark energy in the near future, mostly from the compact astrophysical objects.

In recent years, weak lensing of the cosmic microwave background (CMB) has emerged as a powerful tool to probe fundamental physics, such as neutrino masses, primordial non-Gaussianity, dark energy, and modified gravity. The prime target of CMB lensing surveys is the lensing potential, which is reconstructed from the observed CMB temperature $T$ and polarization $E$ and $B$ fields. Until very recently, this reconstruction has been performed with quadratic estimators (QEs), which, although known to be suboptimal for high-sensitivity experiments, are numerically efficient and useful to make forecasts and cross-check the results of more sophisticated likelihood-based methods. It is expected that ongoing and near-future CMB experiments, such as AdvACT, SPT-3G, and the Simons Observatory (SO), will also rely on QEs. In this work, we review different QEs and clarify and quantify their differences. In particular, we show that the Hu-Okamoto (HO02) estimator is not the absolute optimal lensing estimator that can be constructed out of quadratic combinations of $T$, $E$, and $B$ fields. Instead, we derive the global-minimum-variance (GMV) lensing quadratic estimator. Although this estimator can be found elsewhere in the literature, it was erroneously described as equivalent to the HO02 estimator and has never been used in real data analyses. Here, we show explicitly that the HO02 estimator is suboptimal to the GMV estimator, with a reconstruction noise larger by up to $\sim 9\%$ for a SO-like experiment. We further show that the QE used in the Planck and recent SPT lensing analysis are suboptimal to both the HO02 and GMV estimator and would have a reconstruction noise up to $\sim 11\%$ larger than that of the GMV estimator for a SO-like experiment. In addition to clarifying differences between different QEs, this work should thus provide motivation to implement the GMV estimator in future lensing analyses relying on QEs.

In this work we investigate whether a certain phenomenological extension to the general relativity, in the form of a gravitational phase transition in the Universe, can reduce the external Planck tensions with the local Hubble measurements and the distribution of matter, characterized by ${\sigma }_8$, as well as its internal inconsistencies in the lensing amplitude and the low-high $\ell$ parameter estimates. We introduce new degrees of freedom into the background and the two scalar perturbation equations in the Newtonian gauge, with simultaneous transitions from an early gravitational phase equivalent to general relativity toward a late phase. We model the transition as a “tanh” parametrized by the transition redshift $z_{\mathrm{t}}$ and width $\alpha$, with amplitudes $\mathrm{\Lambda }(z)$ and $(\mu (z),\gamma (z))$ for the background and perturbations, respectively. We verify the consistency of the datasets used in this work in the gravitational phase transition framework and confirm that the individual tensions do not require conflicting transitions. We find that the joint datasets prefer a recent transition at $z_{\mathrm{t}}\approx 0.9$ in the background and perturbed Einstein equations, driven mainly by the local Hubble measurement. This transition relaxes all the tensions considered in this work.

We provide a detailed study of reheating in the kination regime in a scenario where the particle content is produced by gravitational production of massive scalars decaying into massless scalars and fermions which eventually reheat the Universe. A detailed calculation is given by using Boltzmann equations and decay rates obtained using formalism of quantum field theory in curved spacetime. By numerical calculations the reheating temperature is found to be in the ${10}^9–{10}^{13}\mathrm{GeV}$ regime. Moreover, the fermionic channel of decay is found to be the dominant channel of decay when the mass $m$ of the decaying particle is small raising the reheating temperature as opposed to a single scalar decay channel.

Primordial null energy condition (NEC) violation would imprint a blue-tilted spectrum on gravitational wave background (GWB). However, its implications on the GWB might be far richer than expected. We present a scenario, in which after a slow-roll (NEC-preserving) inflation with Hubble parameter $H\simeq H_{inf1}$, the Universe goes through an NEC-violating period and then enters subsequent slow-roll inflation with a higher $H$ ($=H_{inf2}\gg H_{inf1}$). The resulting primordial gravitational wave spectrum is nearly flat at the cosmic microwave background band, as well as at the frequency $f\sim 1/\mathrm{yr}$ but with higher amplitude (compatible with the recent NANOGrav result). It is also highlighted that for the multistage inflation if the NEC violations happened intermittently, we might have a Great Wall–like spectrum of the stochastic GWB at the corresponding frequency band.

The recent release of the second Gravitational-Wave Transient Catalog (GWTC-2) has increased significantly the number of known GW events, enabling unprecedented constraints on formation models of compact binaries. One pressing question is to understand the fraction of binaries originating from different formation channels, such as isolated field formation versus dynamical formation in dense stellar clusters. In this paper, we combine the cosmic binary population synthesis suite and the cmc code for globular cluster evolution to create a mixture model for black hole binary formation under both formation scenarios. For the first time, these code bodies are combined self-consistently, with cmc itself employing cosmic to track stellar evolution. We then use a deep-learning enhanced hierarchical Bayesian analysis to continuously sample over and constrain the common envelope efficiency $\alpha$ assumed in cosmic, the initial cluster virial radius $r_v$ adopted in cmc, and the intrinsic mixture fraction $f$ between each channel. Under specific assumptions about other uncertain aspects of isolated binary and globular cluster evolution, we report the median and 90% confidence interval of three physical parameters for the intrinsic population $(f,\alpha ,r_v)=({0.20}_{-0.18}^{+0.32},{2.26}_{-1.84}^{+2.65},{2.71}_{-1.17}^{+0.83})$. This simultaneous constraint agrees with observed properties of globular clusters in the Milky Way and is an important first step in the pathway toward learning the astrophysics of compact binary formation through GW observations.

Methods for extracting the $\psi (3770)\to e^{+}{e}^{-}$ decay width from the data on the reaction cross section $e^{+}{e}^{-}\to D\overline{D}$ are discussed. Attention is drawn to the absence of the generally accepted method for determining ${\mathrm{\Gamma }}_{\psi (3770)e^{+}{e}^{-}}$ in the presence of interference between the contributions of the $\psi (3770)$ resonance and background. It is shown that the model for the experimentally measured $D$ meson form factor, which satisfies the requirement of the Watson theorem and takes into account the contribution of the complex of the mixed $\psi (3770)$ and $\psi (2S)$ resonances, allows us to uniquely determine the value of ${\mathrm{\Gamma }}_{\psi (3770)e^{+}{e}^{-}}$ by fitting. The ${\mathrm{\Gamma }}_{\psi (3770)e^{+}{e}^{-}}$ values found from the data processing are compared with the estimates in the potential models.

We study the scalar sector of the most general multi-Higgs doublet model satisfying explicitly an exact symmetry. We prove that such a model will exhibit decoupling if and only if the vacuum also satisfies the same symmetry. This general property is also shown independently and explicitly for three Higgs doublet models by considering in detail all symmetry-constrained models and their possible vacua. We also discuss some specific characteristics of different decoupling patterns.

We calculate the gravitino production rate, computing its one-loop thermal self-energy. Gravitino production processes that do not result through thermal cuts of its self-energy, have been identified and taken into account. Correcting analytical errors and numerical approximations in the previous calculations, we present our result. This deviates from the latest estimation by almost 10%. More importantly, we provide a convenient formula, for calculating the gravitino production rate and its thermal abundance, as a function of the reheating temperature of the Universe.

We derive machine learning algorithms from discretized Euclidean field theories, making inference and learning possible within dynamics described by quantum field theory. Specifically, we demonstrate that the ${\varphi }^4$ scalar field theory satisfies the Hammersley-Clifford theorem, therefore recasting it as a machine learning algorithm within the mathematically rigorous framework of Markov random fields. We illustrate the concepts by minimizing an asymmetric distance between the probability distribution of the ${\varphi }^4$ theory and that of target distributions, by quantifying the overlap of statistical ensembles between probability distributions and through reweighting to complex-valued actions with longer-range interactions. Neural network architectures are additionally derived from the ${\varphi }^4$ theory which can be viewed as generalizations of conventional neural networks and applications are presented. We conclude by discussing how the proposal opens up a new research avenue, that of developing a mathematical and computational framework of machine learning within quantum field theory.

In the present work, it is intended to calculate and study the single and double differential cross sections of the prompt single-photon production as a function of produced single-photon transverse momentum and rapidity, in the high-energy $p-p(\overline{p})$ colliders, such as LHC and TEVATRON. The differential cross sections of prompt single-photon production are calculated in the $k_t$-factorization frameworks using various angular ordering unintegrated parton distribution functions (UPDF), namely the Kimber et al. and Martin et al. procedures. These scheme-dependent UPDF are generated in the leading and next-to-leading order levels to predict and analyze the different partonic contributions to the above cross sections. The above two procedures utilize the phenomenological parton distribution functions (PDF) libraries of Martin et al., i.e., MMHT2014. It is shown that the calculated prompt single-photon production differential cross sections in the above frameworks are relatively successful in generating satisfactory results compared to the experimental data of different collaborations, i.e., CDF (2017), ATLAS (2017), CMS (2011) and D0 (2006), as well as the other theoretical predictions such as collinear factorization Monte Carlo calculations (the JETPHOX, SHERPA, PYTHIA, and MCFM methods). Also, for a closer precision, the differential cross section for the NLO gluon-gluon, quark-gluon, and quark-(anti)quark processes are calculated. An extensive discussion and comparison are made regarding (i) the behavior of the contributing partonic subprocesses, (ii) the possible double-counting between the $2\to 2$ and $2\to 3$ subprocesses, i.e., gluons-fusion, in our calculated prompt single-photon production differential cross-sections and (iii) the sensibility check of our results to the different angular ordering constraints.

We compute the chiral susceptibility in quark-gluon plasma in the presence of a finite chemical potential and a weak magnetic field within hard thermal loop approximation. First we construct the massive effective quark propagator in a thermomagnetic medium. Then we obtain a completely analytic expression for the chiral susceptibility in the weak magnetic field approximation. In the absence of a magnetic field, the thermal chiral susceptibility increases in the presence of a finite chemical potential. The effect of the thermomagnetic correction is found to be very marginal as temperature is the dominant scale in a weak field approximation.

We present complete calculations of the electromagnetic form factors of the ${\mathrm{\Omega }}^{-}$ in the spacelike region and in the timelike region. The four elastic form factors: electric charge ($G_{E0}$), magnetic dipole ($G_{M1}$), electric quadrupole ($G_{E2}$), and magnetic octupole ($G_{M3}$), are estimated within the covariant spectator quark model, in terms of the square momentum transfer $q^2$. The free parameters of the ${\mathrm{\Omega }}^{-}$ wave function, including a $S$-wave state and two independent $D$-wave states radial wave functions and the admixture coefficients, are fixed by the comparison with the lattice QCD data in the spacelike region ($Q^2=-q^2\le 0$) and with the recent $e^{+}{e}^{-}\to {\mathrm{\Omega }}^{-}{\overline{\mathrm{\Omega }}}^{+}$ data from CLEO in the timelike region ($q^2>0$). The estimates in the timelike region for square momentum transfer $q^2\ge 4M_{\mathrm{\Omega }}^2$ are based on large-$q^2$ asymptotic relations ($M_{\mathrm{\Omega }}$ is the ${\mathrm{\Omega }}^{-}$ mass). We examine also the impact of the large-$Q^2$ correlations between different form factors and analyze the possible solutions. The electric quadrupole and the magnetic octupole moments of the ${\mathrm{\Omega }}^{-}$ and the $e^{+}{e}^{-}\to {\mathrm{\Omega }}^{-}{\overline{\mathrm{\Omega }}}^{+}$ integrated cross sections for very large $q^2$ are estimated based on the model results.

We argue that the description of Feynman loop integrals as integrable systems is intimately connected with their motivic properties and the action of the Cosmic Galois Group. We show how in the case of a family of fishnet graphs, coaction relations between them follow directly from iterative constructions of Q-functions in the quantum spectral curve formalism. Using this observation we conjecture a “differential equation for numbers” that enter these periods.

We study gravitational wave (GW) emission in the strong-field regime by a hierarchical triple system composed of a binary system placed in the vicinity of a supermassive black hole (SMBH). The LIGO-Virgo Collaboration recently reported evidence for coalescences with this dynamical origin. These systems are common in galactic centers and thus, are a target for the space-based LISA mission as well as other advanced detectors. Doppler shifts, aberration, lensing, and strong amplitude modulations are features present in the GW signal from these systems, built into our framework and with no need for phenomenological patches. We find that the binary can resonantly excite the quasinormal modes of the SMBH, as in the resonant excitation of two tuning forks with matching frequencies. The flux of energy crossing the SMBH horizon can be significant, when compared with that from standard extreme-mass-ratio inspirals. Therefore, these triple systems are excellent probes of strong-field physics and of the BH nature of compact objects.

We explore in general relativity the survival time of neutron stars that host an endoparasitic, possibly primordial, black hole at their center. Corresponding to the minimum steady-state Bondi accretion rate for adiabatic flow that we found earlier for stiff nuclear equations of state (EOSs), we derive analytically the maximum survival time after which the entire star will be consumed by the black hole. We also show that this maximum survival time depends only weakly on the stiffness for polytropic EOSs with $\mathrm{\Gamma }\ge 5/3$, so that this survival time assumes a nearly universal value that depends on the initial black-hole mass alone. Establishing such a value is important for constraining the contribution of primordial black holes in the mass range ${10}^{-16}{M}_{\odot }\lesssim M\lesssim {10}^{-10}{M}_{\odot }$ to the dark-matter content of the Universe.

To clarify the geometric information encoded in the $SO(D+1)$ spin-network states for the higher dimensional loop quantum gravity, we generalize the twisted-geometry parametrization of the $SU(2)$ phase space for ($1+3$)-dimensional loop quantum gravity to that of the $SO(D+1)$ phase space for the all-dimensional case. The Poisson structure in terms of the twisted geometric variables suggests a new gauge reduction procedure, with respect to the discretized gauss and simplicity constraints governing the kinematics of the theory. Endowed with the geometric meaning via the parametrization, our reduction procedure serves to identify proper gauge freedom associated with the anomalous discretized simplicity constraints and subsequently leads to the desired classical state space of the (twisted) discrete Arnowitt-Deser-Misner data.

Based on bulk reconstruction from the finite boundary of the Bruhat-Tits tree, the boundary effective theory is obtained after integrating out fields outside this boundary. According to the $p$-adic version of anti–de Sitter/conformal field theory duality, two-point functions of dual theory living on the finite boundary are read out from the effective action. They can be regarded as two-point functions of a deformed conformal field theory over $p$-adic numbers.

We examine the influence of the dispersion relation on the Unruh effect by Lorentz boosting the phase of Minkowski vacuum fluctuations endowed with an arbitrary dispersion relation. We find that, unlike what happens with a linear dispersion relation exhibited by massless fields, thermality is lost for general dispersion relations. We show that thermality emerges with a varying “apparent” Davies-Unruh temperature depending on the acceleration of the observer and on the degree of departure from linearity of the dispersion relation. The approach has the advantage of being intuitive and able to pinpoint why such a loss of thermality occurs and when such a deviation from thermality becomes significant. We discuss the link of our results with the well-known fundamental difference between the thermalization theorem and the concept of Rindler noise. We examine the possible experimental validation of our results based on a successful setup for testing the classical analog of the Unruh effect recently described in the literature.