It has been shown that the disk-level S-matrix elements of one Ramond-Ramond (RR) and two Neveu-Schwarz-Neveu-Schwarz (NSNS) states could be found by applying the Ward identity associated with the string duality and the gauge symmetry on a given component of the S matrix. These amplitudes have appeared as the components of six different T-dual multiplets. It is predicted in the literature that there are some nonzero disk-level scattering amplitudes, such as one RR ($p-1$) form with zero transverse index and two $NSNS$ states, could not be captured by the T-dual Ward identity. We explicitly find this amplitude in terms of a minimal context of the integral functions by the insertion of one closed string RR vertex operator and two NSNS vertex operators. From the amplitude invariance under the Ward identity associated with the NSNS gauge transformations and T-duality, we also find some integral identities.

We analyze the moduli space dynamics of domain walls in $SU(N)$ QCD at $\overline{\theta }=\pi$, by softly breaking $\mathcal{N}=1$ SQCD with sfermion mixing. In the supersymmetric limit, BPS domain walls between neighboring vacua are known to possess nontranslational flavor moduli that form a $\mathbb{C}{\mathrm{P}}^{N-1}$ sigma model. For the simplest case with gauge group $SU(2)$ and $N_f=2$, we show that this sigma model also exhibits a Hopf term descending from the bulk Wess-Zumino term with a quantized coefficient. On soft-breaking of supersymmetry via sfermion mixing that preserves the flavor symmetry, these walls and their moduli-space dynamics survives when $\overline{\theta }=\pi$ so that there are two degenerate vacua.

Gravitational wave measurements of binary neutron star coalescences offer information about the properties of the extreme matter that comprises the stars. Despite our expectation that all neutron stars in the Universe obey the same equation of state, i.e. the properties of the matter that forms them are universal, current tidal inference analyses treat the two bodies as independent. We present a method to measure the effect of tidal interactions in the gravitational wave signal—and hence constrain the equation of state—that assumes that the two binary components obey the same equation of state. Our method makes use of a relation between the tidal deformabilities of the two stars given the ratio of their masses, a relation that has been shown to only have a weak dependence on the equation of state. We use this to link the tidal deformabilities of the two stars in a realistic parameter inference study while simultaneously marginalizing over the error in the relation. This approach incorporates more physical information into our analysis, thus leading to a better measurement of tidal effects in gravitational wave signals. Through simulated signals we estimate that uncertainties in the measured tidal parameters are reduced by a factor of at least 2—and in some cases up to 10—depending on the equation of state and mass ratio of the system.

We present a new computational framework for the Galerkin-collocation method for double domain in the context of ADM $3+1$ approach in numerical relativity. This work enables us to perform high resolution calculations for initial sets of two arbitrary black holes. We use the Bowen-York method for binary systems and the puncture method to solve the Hamiltonian constraint. The nonlinear numerical code solves the set of equations for the spectral modes using the standard Newton-Raphson method, LU decomposition and Gaussian quadratures. We show convergence of our code for the conformal factor and the ADM mass. Thus, we display features of the conformal factor for different masses, spins and linear momenta.

We obtain from the first principles a general-relativistic Keplerian rotation law for self-gravitating disks around spinning black holes. This is an extension of a former rotation law that was designed mainly for toroids around spinless black holes. We integrate numerically axial stationary Einstein equations with self-gravitating disks around spinless or spinning black holes; that includes the first ever integration of the Keplerian selfgravitating tori. This construction can be used for the description of tight black hole-torus systems produced during coalescences of two neutron stars or modelling of compact active galactic nuclei.

We show that the quantum dynamics of a thin spherical shell in general relativity is equivalent to the Coulomb-Dirac equation on the half line. The Hamiltonian has a one-parameter family of self-adjoint extensions with a discrete energy spectrum $|E|<m$, and a continuum of scattering states for $|E|>m$, where $m$ is the rest mass of the shell and $E$ is the Arnowitt-Deser-Misner mass. For sufficiently large $m$, the ground state energy level is negative. This suggests that classical positivity of energy does not survive quantization. The scattering states provide a realization of singularity avoidance. We speculate on the consequences of these results for black hole radiation.

This work proposes a stellar model under Gauss-Bonnet $f(\mathcal{G},T)$ gravity with the conjecture theorized by Mazur and Mottola, well known as the gravitational vacuum stars (gravastars). By taking into account the $f(\mathcal{G},T)$ stellar model, the structure of the gravastar with its exclusive division of three different regions, namely, (i) the core interior region, (ii) the junction region (shell), and (iii) the exterior region, has been investigated with reference to the existence of energy density, pressure, ultrarelativistic plasma, and repulsive forces. The different physical features, like the equation of state parameter, length of the shell, entropy, and energy-thickness relation of the gravastar shell model, have been discussed. Also, some other physically valid aspects have been presented with the connection to nonsingular and event-horizon-free gravastar solutions, which in contrast to a black hole solution, might be stable without containing any information paradox.

We calculate the self-force on an electric charge and electric dipole held at rest in a closed universe that results from joining two copies of Minkowski spacetime at a common boundary. Spacetime is strictly flat on each side of the boundary, but there is curvature at the surface layer required to join the two Minkowski spacetimes. We find that the self-force on the charge is always directed away from the surface layer. This is analogous to the case of an electric charge held at rest inside a spherical shell of matter, for which the self-force is also directed away from the shell. For the dipole, the direction of the self-force is a function of the dipole’s position and orientation. Both self-forces become infinite when the charge or dipole is made to approach the surface layer. This study reveals that a self-force can arise even when the Riemann tensor vanishes at the position of the charge or dipole; in such cases the self-force is a manifestation of the global curvature of spacetime.

In an ever-expanding spatially closed universe, the fractional change of the volume is the preeminent intrinsic time interval to describe evolution in general relativity. The expansion of the universe serves as a subsidiary condition which transforms Einstein’s theory from a first class to a second class constrained system when the physical degrees of freedom (d.o.f.) are identified with transverse traceless excitations. The super-Hamiltonian constraint is solved by eliminating the trace of the momentum in terms of the other variables, and spatial diffeomorphism symmetry is tackled explicitly by imposing transversality. The theorems of Maskawa-Nishijima appositely relate the reduced phase space to the physical variables in canonical functional integral and Dirac’s criterion for second class constraints to nonvanishing Faddeev-Popov determinants in the phase space measures. A reduced physical Hamiltonian for intrinsic time evolution of the two physical d.o.f. emerges. Freed from the first class Dirac algebra, deformation of the Hamiltonian constraint is permitted, and natural extension of the Hamiltonian while maintaining spatial diffeomorphism invariance leads to a theory with Cotton-York term as the ultraviolet completion of Einstein’s theory.

In the first paper of this series, we showed that the CMB quadrupole at high redshifts results in a small circular polarization of the emitted 21 cm radiation. In this paper we forecast the sensitivity of future radio experiments to measure the CMB quadrupole during the era of first cosmic light ($z\sim 20$). The tomographic measurement of 21 cm circular polarization allows us to construct a 3D remote quadrupole field. Measuring the $B$-mode component of this remote quadrupole field can be used to put bounds on the tensor-to-scalar ratio $r$. We make Fisher forecasts for a future Fast Fourier Transform Telescope (FFTT), consisting of an array of dipole antennas in a compact grid configuration, as a function of array size and observation time. We find that a FFTT with a side length of 100 km can achieve $\sigma (r)\sim 4\times {10}^{-3}$ after ten years of observation and with a sky coverage $f_{\mathrm{sky}}\sim 0.7$. The forecasts are dependent on the evolution of the Lyman-$\alpha$ flux in the pre-reionization era, that remains observationally unconstrained. Finally, we calculate the typical order of magnitudes for circular polarization foregrounds and comment on their mitigation strategies. We conclude that detection of primordial gravitational waves with 21 cm observations is in principle possible, so long as the primordial magnetic field amplitude is small, but would require a very futuristic experiment with corresponding advances in calibration and foreground suppression techniques.

We propose a new method to measure the tensor-to-scalar ratio $r$ using the circular polarization of the 21 cm radiation from the pre-reionization epoch. Our method relies on the splitting of the $F=1$ hyperfine level of neutral hydrogen due to the quadrupole moment of the cosmic microwave background (CMB). We show that unlike the Zeeman effect, where $M_F=\pm 1$ have opposite energy shifts, the CMB quadrupole shifts $M_F=\pm 1$ together relative to $M_F=0$. This splitting leads to a small circular polarization of the emitted 21 cm radiation. In this paper (Paper I in a series on this effect), we present calculations on the microphysics behind this effect, accounting for all processes that affect the hyperfine transition. We conclude with an analytic formula for the circular polarization from the Dark Ages as a function of pre-reionization parameters and the value of the remote quadrupole of the CMB. We also calculate the splitting of the $F=1$ hyperfine level due to other anisotropic radiation sources and show that they are not dominant. In a companion paper (Paper II) we make forecasts for measuring the tensor-to-scalar ratio $r$ using future radio arrays.

We point out the existence of a second feature in the matter two-point function, besides the acoustic peak, due to the baryon-baryon correlation in the early Universe and positioned at twice the distance of the peak. We discuss how the existence of this feature is implied by the well-known heuristic argument that explains the baryon bump in the correlation function. A standard ${\chi }^2$ analysis to estimate the detection significance of the second feature is mimicked. We conclude that, for realistic values of the baryon density, a SKA-like galaxy survey will not be able to detect this feature with standard correlation function analysis.

We derive the probability for a newly formed binary black hole (BBH) to undergo an eccentric gravitational wave (GW) merger during binary-single interactions inside a stellar cluster. By integrating over the hardening interactions such a BBH must undergo before ejection, we find that the observable rate of BBH mergers with eccentricity $>0.1$ at 10 Hz relative to the rate of circular mergers can be as high as $\sim 5\%$ for a typical globular cluster (GC). This further suggests that BBH mergers forming through GW captures in binary-single interactions, eccentric or not, are likely to constitute $\sim 10\%$ of the total BBH merger rate from GCs. Such GW capture mergers can only be probed with an $N$-body code that includes general relativistic corrections, which explains why recent Newtonian cluster studies have not been able to resolve this population. Finally, we show that the relative rate of eccentric BBH mergers depends on the compactness of their host cluster, suggesting that an observed eccentricity distribution can be used to probe the origin of BBH mergers.

In this paper, we use the equation of state based on a modification of the $2+1$ flavors Nambu-Jona-Lasinio (NJL) model to study the quark matter of hybrid stars. For comparison, we utilize five EOSs of the relativistic mean-field (RMF) model to describe the hadronic phase. With the three-window crossover interpolation approach, we try to construct relatively soft hybrid EOSs but find the maximum masses of hybrid stars do not differ much. The results are quite close to the 2 solar mass, which is consistent with the mass constraint of PSR $\mathrm{J}0348+0432$. Furthermore, it is noteworthy that the heaviest stable stars have central densities higher than that of the deconfinement transition, suggesting a pure quark core in the hybrid star.

The central engines of some superluminous supernovae (SLSNe) are generally suggested to be newly born fast rotating magnetars, which spin down mainly through magnetic dipole radiation and gravitational wave emission. We calculate the magnetar-powered SLSNe light curves (LCs) with the tilt angle evolution of newly born magnetars involved. We show that, depending on the internal toroidal magnetic fields ${\overline{B}}_{\mathrm{t}}$, the initial spin periods $P_{\mathrm{i}}$, and the radii $R_{\mathrm{DU}}$ of direct Urca (DU) cores of newly born magnetars, as well as the critical temperature $T_{\mathrm{c}}$ for ${}^3{P}_2$ neutron superfluidity, bumps could appear in the SLSNe LCs after the maximum lights when the tilt angles grow to $\pi /2$. The value of $T_{\mathrm{c}}$ determines the arising time and the relative amplitude of a bump. The quantity $R_{\mathrm{DU}}$ can affect the arising time and the luminosity of a bump, as well as the peak luminosity of a LC. For newly born magnetars with dipole magnetic fields $B_{\mathrm{d}}=5\times {10}^{14}\mathrm{G}$, ${\overline{B}}_{\mathrm{t}}=4.6\times {10}^{16}\mathrm{G}$, and $P_{\mathrm{i}}=1\mathrm{ms}$, there are no bumps in the LCs if $T_{\mathrm{c}}=2\times {10}^9\mathrm{K}$, or $R_{\mathrm{DU}}=1.5\times {10}^5\mathrm{cm}$. Moreover, it is interesting that a stronger ${\overline{B}}_{\mathrm{t}}$ will lead to both a brighter peak and a brighter bump in a LC. While keeping other quantities unchanged, the bump in the LC disappears for the magnetar with smaller $P_{\mathrm{i}}$. We suggest that, once the SLSNe LCs with such kinds of bumps are observed, by fitting these LCs with our model, not only $B_{\mathrm{d}}$ and $P_{\mathrm{i}}$ of newly born magnetars but also the crucial physical quantities ${\overline{B}}_{\mathrm{t}}$, $R_{\mathrm{DU}}$, and $T_{\mathrm{c}}$ could be determined. Nonobservation of SLSNe LCs with such kinds of bumps hitherto may already put some (though very rough) constraints on ${\overline{B}}_{\mathrm{t}}$, $P_{\mathrm{i}}$, $R_{\mathrm{DU}}$, and $T_{\mathrm{c}}$. Therefore, observation of SLSNe LCs may provide a new approach to probe the physics of newly born magnetars.

An annual modulation signal due to the Earth orbiting around the Sun would be one of the strongest indications of the direct detection of dark matter. In 2016, we reported a search for dark matter by looking for this annual modulation with our single-phase liquid xenon XMASS-I detector. That analysis resulted in a slightly negative modulation amplitude at low energy. In this work, we included more than one year of additional data, which more than doubles the exposure to 800 live days with the same 832 kg target mass. When we assume weakly interacting massive particle (WIMP) dark matter elastically scattering on the xenon target, the exclusion upper limit for the WIMP-nucleon cross section was improved by a factor of 2 to $1.9\times {10}^{-41}{\mathrm{cm}}^2$ at $8\mathrm{GeV}/{\mathrm{c}}^2$ at 90% confidence level with our newly implemented data selection through a likelihood method. For the model-independent case, without assuming any specific dark matter model, we obtained more consistency with the null hypothesis than before with a $p$-value of 0.11 in the 1–20 keV energy region. This search probed this region with an exposure that was larger than that of DAMA/LIBRA. We also did not find any significant amplitude in the data for periodicity with periods between 50 and 600 days in the energy region between 1 to 6 keV.

A new method for separating variables in the Maxwell equations in four- and higher-dimensional Kerr–(A)dS spacetimes proposed recently by Lunin is generalized to any off-shell metric that admits a principal Killing–Yano tensor. The key observation is that Lunin’s ansatz for the vector potential can be formulated in a covariant form—in terms of the principal tensor. In particular, focusing on the four-dimensional case we demonstrate separability of Maxwell’s equations in the Kerr–NUT–(A)dS and the Plebański–Demiański family of spacetimes. The new method of separation of variables is quite different from the standard approach based on the Newman–Penrose formalism.

Gravitational wave detection requires a detailed understanding of the response of the LIGO and Virgo detectors to true signals in the presence of environmental and instrumental noise. Of particular interest is the study of anomalous non-Gaussian transients, such as glitches, since their occurrence rate in LIGO and Virgo data can obscure or even mimic true gravitational wave signals. Therefore, successfully identifying and excising these anomalies from gravitational wave data is of utmost importance for the detection and characterization of true signals and for the accurate computation of their significance. To facilitate this work, we present the first application of deep learning combined with transfer learning to show that knowledge from pretrained models for real-world object recognition can be transferred for classifying spectrograms of glitches. To showcase this new method, we use a data set of twenty-two classes of glitches, curated and labeled by the Gravity Spy project using data collected during LIGO’s first discovery campaign. We demonstrate that our Deep Transfer Learning method enables an optimal use of very deep convolutional neural networks for glitch classification given small and unbalanced training data sets, significantly reduces the training time, and achieves state-of-the-art accuracy above 98.8%, lowering the previous error rate by over 60%. More importantly, once trained via transfer learning on the known classes, we show that our neural networks can be truncated and used as feature extractors for unsupervised clustering to automatically group together new unknown classes of glitches and anomalous signals. This novel capability is of paramount importance to identify and remove new types of glitches which will occur as the LIGO/Virgo detectors gradually attain design sensitivity.

Braneworld models have been proposed as a possible solution to the problem of the accelerated expansion of the Universe. The idea is to dispense the dark energy (DE) and drive the late-time cosmic acceleration with a five-dimensional geometry. We investigate a brane model with variable brane tension as a function of redshift called chrono-brane. We propose the polynomial $\lambda =(1+z{)}^n$ function inspired in tracker-scalar-field potentials. To constrain the $n$ exponent we use the latest observational Hubble data from cosmic chronometers, Type Ia Supernovae from the full joint-light-analysis sample, baryon acoustic oscillations and the posterior distance from the cosmic microwave background of Planck 2015 measurements. A joint analysis of these data estimates $n\simeq 6.19\pm 0.12$ which generates a DE-like (cosmological-constantlike at late times) term, in the Friedmann equation arising from the extra dimensions. This model is consistent with these data and can drive the Universe to an accelerated phase at late times.