We give an explicit gauge invariant, off-shell, and local double copy construction of gravity from Yang-Mills theory to quartic order. To this end we use the framework of homotopy algebras, and we identify a rich new algebraic structure associated with color-stripped Yang-Mills theory. This algebra, which is a generalization of a Batalin-Vilkovisky algebra, is the underlying structure necessary for double copy. We give a self-contained introduction into these algebras by illustrating them for Chern-Simons theory in three dimensions. We then construct $N=0$ supergravity in the form of double field theory in terms of the algebraic Yang-Mills building blocks to quartic order in interactions. As applications of the same universal formula, we rederive the four-graviton scattering amplitude and compute a chiral form of the Courant algebroid gauge structure of double field theory.

We investigate string amplitudes by using the partial modular transformation which we introduced in our previous works. This enables us to extract stringy threshold corrections from the full string amplitudes and interpret them in terms of the Wilsonian effective field theory in a natural way. We calculate mass shifts and wave function renormalizations for massless scalar fields on brane-antibrane systems. We find that the mass shift can be exponentially small and negative. We also propose a strategy for realizing a hierarchical mass spectrum on D-branes.

The nondiagonal Bianchi models are studied in the loop framework for their classical and quantum formulations. The expressions of the Ashtekar-Barbero-Immirzi variables and their properties are found to provide a loop quantization of these models. In the special case of a Bianchi I universe, it is shown that the geometrical operators result invariant from the diagonal description. Hence, the kinematical Hilbert space of the nondiagonal Bianchi I model has similar features to the diagonal one.

We report the differential representation of three- and four-point amplitudes for Yang-Mills fields and Einstein gravity in anti–de Sitter spacetime at tree level. The amplitudes exhibit the flat-space structures by using the weight-shifting operators with reordering, which makes the differential double copy relation at the three-point level straightforward. For four-point Yang-Mills amplitudes, we establish the differential Bern-Carrasco-Johansson relation, which can be useful for proving the differential doubly copy at the four-point level in the future.

We formulate $U(1{)}_k$ Chern-Simons theory on a Euclidean spacetime lattice using the modified Villain approach. Various familiar aspects of continuum Chern-Simons theory such as level quantization, framing, the discrete 1-form symmetry and its ’t Hooft anomaly, as well as the electric charge of monopole operators are manifest in our construction. The key technical ingredient is the cup product and its higher generalizations on the (hyper-)cubic lattice, which recently appeared in the literature. All unframed Wilson loops are projected out by a peculiar subsystem symmetry, leaving topological, ribbonlike Wilson loops which have the correct correlation functions and topological spins expected from the continuum theory. Our action can be obtained from a new definition of the theta term in four dimensions which improves upon previous constructions within the modified Villain approach. This bulk action coupled to background fields for the 1-form symmetry is given by the Pontryagin square, which provides anomaly inflow directly on the lattice.

We compute Araki’s relative entropy associated with a bounded interval $I=(a,b)$ between a thermal state and a coherent excitation of itself in the bosonic U(1)-current model, namely the (derivative of the) chiral boson. For this purpose we briefly review some recent results on the entropy of standard subspaces and on the relative entropy of nonpure states such as thermal states. In particular, recently Bostelmann, Cadamuro, and Del Vecchio have obtained the relative entropy at finite temperature for the unbounded interval $(-\infty ,t)$, using previous results of Borchers and Yngvason, mainly a unitary dilation that provides the modular evolution in the negative half-line. Here we find a unitary rotation in order to make use of the full $\mathrm{PSL}(2,\mathbb{R})$ symmetries and obtain the modular group, the modular Hamiltonian, and the relative entropy $S$ of a bounded interval at finite temperature. Such relative entropy entails both a Bekenstein-like bound and a QNEC-like bound, but violates $S^{\prime \prime }\ge 0$ (derivative with respect to the length of the interval, with its center fixed). Finally, we extend the results to the free massless boson in $1+1$ dimensions with analogous bounds.

We discuss the motion of a binary system around a supermassive black hole. Using Fermi-Walker transport, we construct a local inertial reference frame and set up a Newtonian binary system. Assuming a circular geodesic observer around a Schwarzschild black hole, we write down the equations of motion of a binary. Introducing a small acceleration of the observer, we remove the interaction terms between the center of mass (CM) of a binary and its relative coordinates. The CM follows the observer’s orbit, but its motion deviates from an exact circular geodesic. We first solve the relative motion of a binary system, and then find the motion of the CM by the perturbation equations with the small acceleration. We show that von Zeipel-Lidov-Kozai (vZLK) oscillations appear when a binary is compact and the initial inclination is larger than a critical angle. In a hard binary system, vZLK oscillations are regular, whereas in a soft binary system, oscillations are irregular both in period and in amplitude, although stable. We find an orbital flip when the initial inclination is large. As for the motion of the CM, the radial deviations from a circular orbit become stable oscillations with very small amplitude.

We consider the effect of stochastic fluctuations of the gravitational coupling $G$ on the evolution of binary systems. We work at an elementary level, in the Newtonian limit, and focus mainly on laser ranging. We show that, due to cumulative effects, observational data may be used to put bounds on the stochastic fluctuations. We also reanalyze previous results on the implications of stochastic fluctuations of $G$ on cosmological models.

Recently, asymptotically flat black holes with multiple photon spheres have been discovered and found to produce distinctive observational signatures. In this paper, we focus on whether these black hole solutions are physically viable, e.g., satisfying energy conditions of interest. Intriguingly, black hole and naked singularity solutions with two photon spheres and one antiphoton sphere are shown to exist in physically reasonable models, which satisfy the null, weak, dominant and strong energy conditions. Our findings reveal that black holes with multiple photon spheres may not be frequent, but they are not exotic.

We examine the quantum gravitational entanglement of two test masses in the context of linearized general relativity with specific nonlocal interaction with matter. To accomplish this, we consider an energy-momentum tensor describing two test particles of equal mass with each possessing some nonzero momentum. After discussing the quantization of the linearized theory, we compute the gravitational energy shift, which is operator valued in this case. As compared to the local gravitational interaction, we find that the change in the gravitational energy due to the self-interaction terms is finite. We then move on to study the quantum-gravity-induced entanglement of masses for two different scenarios. The first scenario involves treating the two test masses as harmonic oscillators with an interaction Hamiltonian given by the aforesaid gravitational energy shift. In the second scenario, each of the test masses is placed in a quantum spatial superposition of two locations, based on their respective spin states, and their entanglement being induced by the gravitational interaction and the shift in the vacuum energy. For these two scenarios, we compute both the concurrence and the von Neumann entropy, showing that an increase in the nonlocality of the gravitational interaction results in a decrease in both of these quantities.

In the framework of a simple gravitational theory that contains a scalar field minimally coupled to gravity, we investigate the emergence of analytic black-hole solutions with nontrivial scalar hair of secondary type. Although it is possible for one to obtain asymptotically (anti)de Sitter solutions using our setup, in the context of the present work, we are solely interested in asymptotically flat solutions. At first, we study the properties of static and spherically symmetric black-hole solutions emanating from both regular and phantom scalar fields. We find that the regular-scalar-field-induced solutions are solutions describing ultracompact black holes, while the phantom scalar fields generate ultrasparse black-hole solutions. The latter are black holes that can be potentially of very low density since, contrary to ultracompact ones, their horizon radius is always greater than the horizon radius of the corresponding Schwarzschild black hole of the same mass. Then, we generalize the above static solutions to slowly rotating ones and compute their angular velocities explicitly. Finally, the study of the axial perturbations of the derived solutions takes place, in which we show that there is always a region in the parameter space of the free parameters of our theory that allows the existence of both ultracompact and ultrasparse black holes.

The late-time nonlinear Lagrangian displacement field is highly correlated with the initial field, so reconstructing it could enable us to extract primordial cosmological information. Our previous work [A. Ota et al., Phys. Rev. D 104, 123508 (2021)] carefully studied the displacement field reconstructed from the late-time density field using the iterative method proposed by Schmittfull et al. [Phys. Rev. D 96, 023505 (2017)] and found that it does not fully converge to the true, underlying displacement field (e.g., $\sim 8\%$ offset at $k\sim 0.2h{\mathrm{Mpc}}^{-1}$ at $z=0.6$). We also constructed the Lagrangian perturbation theory model for the reconstructed field, but the model could not explain the discrepancy between the true and the reconstructed fields in the previous work. The main sources of the discrepancy were speculated to be a numerical artifact in the displacement estimator due to the discreteness of the sample. In this paper, we develop two new estimators of the displacement fields to reduce such a numerical discreteness effect, the normalized momentum estimator and the rescaled resumed estimator. We show that the discrepancy Ota et al. [Phys. Rev. D 104, 123508 (2021)] reported is not due to the numerical artifacts. We conclude that the method from Schmittfull et al. [Phys. Rev. D 96, 023505 (2017)] cannot fully reconstruct the shape of the nonlinear displacement field at the redshift we studied, while it is still an efficient baryon acoustic oscillation reconstruction method. In parallel, by properly accounting for the UV-sensitive term in a reconstruction procedure with an effective field theory approach, we improve the theoretical model for the reconstructed displacement field, by almost 5 times, from $\sim 15\%$ to the level of a few percent at $k\sim 0.2h{\mathrm{Mpc}}^{-1}$ at the redshift $z=0.6$.

With low-redshift probes reaching unprecedented precision, uncertainty of the cosmic microwave background (CMB) optical depth is expected to be the limiting factor for future cosmological neutrino mass constraints. In this paper, we discuss to what extent combinations of CMB lensing and galaxy survey measurements at low redshifts $z\sim 0.5–5$ will be able to make competitive neutrino mass measurements without relying on any optical depth constraints. We find that the combination of LSST galaxies and CMB-S4 lensing should be able to achieve constraints on the neutrino mass sum of 25 meV without optical depth information, an independent measurement that is competitive with or slightly better than the constraint of 30 meV possible with CMB-S4 and present-day optical depth measurements. These constraints originate in both structure growth probed by cross-correlation tomography over a wide redshift range as well as, most importantly, the shape of the galaxy power spectrum measured over a large volume. We caution that possible complications such as higher-order biasing and systematic errors in the analysis of high-redshift galaxy clustering are only briefly discussed and may be non-negligible. Nevertheless, our results show that new kinds of high-precision neutrino mass measurements at and beyond the present-day optical depth limit may be possible.

The observation and distinction of two compact stars with an identical mass but a different radius would be a clear sign of hadron-quark phase transition in nuclear matter. Motivated by studies searching for significant deviations in the observables of twin stars, we investigate the differences that manifest in their $r$-mode instability windows and spin-down evolution. Firstly, we obtain a set of hybrid equations of state (which predict the existence of a third stable branch of compact objects) by employing the well-known Maxwell construction within the phenomenological framework of constant speed of sound parametrization. Then, we systematically study the influence of certain parameters, such as the energy density jump (in the resulting hybrid equation of state) and the crust elasticity, on the deviations appearing in the $r$-mode instability windows and spin-down evolution of twin stars. We conclude that two stars with an identical mass and fairly similar spin frequency and temperature, may behave differently with respect to $r$-modes. Thus, the future possible detection of gravitational waves (due to unstable $r$-modes) from a star laying in the stable region of the frequency-temperature plane would be a strong indication for the existence of twin stars. Furthermore, we consider current data for the spin frequencies and temperatures of observed pulsars and compare them to the predictions made from equations of state employed in this study. We find that, depending on the transition density and the rigidness of the crust, hybrid equations of state may be a viable solution for the explanation of existing data.

We investigate the effect of $\mathrm{\Delta }$ baryons on the radial oscillations of neutron and hyperon stars, employing a density-dependent relativistic mean-field model. The spin-$3/2$ baryons are described by the Rarita-Schwinger Lagrangian density. The baryon-meson coupling constants for the spin-$3/2$ decuplet and the spin-$1/2$ baryonic octet are calculated using a unified approach relying on the fact that the Yukawa couplings present in the Lagrangian density of the mean-field models must be invariant under the SU(3) and SU(6) group transformations. We calculate the 20 lowest eigenfrequencies and corresponding oscillation functions of $\mathrm{\Delta }$-inclusive nuclear ($\mathrm{N}+\mathrm{\Delta }$) and hyperonic matter ($\mathrm{N}+\mathrm{H}+\mathrm{\Delta }$) by solving the Sturm-Liouville boundary value problem and also verifying its validity. We see that the lowest mode frequencies for $\mathrm{N}+\mathrm{\Delta }$ and $\mathrm{N}+\mathrm{H}$ EoSs are higher as compared to the pure nucleonic matter because of the deltas and hyperons present. Furthermore, the separation between consecutive modes increases with the addition of hyperons and $\mathrm{\Delta }$s.

The question of what ingredients characterize the quasisteady state of fast neutrino-flavor conversion (FFC) is one of the longstanding riddles in neutrino oscillation. Addressing this issue is necessary for accurate modeling of neutrino transport in core-collapse supernova and binary neutron star merger. Recent numerical simulations of FFC have shown, however, that the quasisteady state is sensitively dependent on boundary conditions in space, and the physical reason for the dependence is not clear at present. In this study, we provide a physical interpretation of this issue based on arguments with stability and conservation laws. The stability can be determined by the disappearance of electron neutrino-lepton number–heavy-leptonic one (ELN-XLN) angular crossings, and we also highlight two conserved quantities characterizing the quasisteady state of FFC: (1) lepton number conservation along each neutrino trajectory and (2) conservation law associated with angular moments, depending on boundary conditions, for each flavor of neutrinos. We present an analytic prescription that matches the results of the nonlinear simulations presented in this work. This study represents a major step forward to a unified picture determining asymptotic states of FFCs.

The recent detection of the Geminga pulsar wind nebula (PWN) by HAWC in the multi-TeV band allows us to infer precious information about the transport of pairs in the immediate surroundings of the pulsar and on the spectrum of pairs contributed by a Geminga-like pulsar to the spectrum of pairs in the cosmic radiation. Moreover, this detection allows us to address the issue of how typical are the so-called TeV halos associated to pulsar wind nebulae. Our calculations confirm the need to have suppressed diffusion in a region of at least 20–50 pc around the pulsar, and are used here to infer precious constraints on the spectrum of pairs accelerated at the termination shock: more specifically, we discuss the conditions under which such a spectrum is consistent with that typically expected in a PWN and how it gets modified once it escapes the halo. Finally, we discuss the implications of the existence of a TeV halo around Geminga in terms of acceleration of protons in the pulsar environment, a topic of profound relevance for the whole field of particle acceleration and physics of pulsars.

Axionlike particles (ALPs) arise naturally in many extensions of the Standard Model. We explore the discovery potential for ALPs of the Large Hadron electron Collider (LHeC) via the $W^{+}{W}^{-}$ fusion process. For concreteness, both cases of the ALP decaying to muon pairs and $b\overline{b}$ pairs are investigated. Our numerical results show that the LHeC with the center of mass energy of 1.3 TeV and the integrated luminosity of $1{\mathrm{ab}}^{-1}$ might be more sensitive than the LHC in probing ALPs over a range of masses from a few tens of GeV to 900 GeV, where the promising sensitivities to the coupling of ALPs with $W^{\pm }$ bosons reach nearly 0.15 and $0.32{\mathrm{TeV}}^{-1}$ for the signal processes $e^{-}p\to {\nu }_{e}ja(a\to {\mu }^{+}{\mu }^{-})$ and $e^{-}p\to {\nu }_{e}ja(a\to b\overline{b})$, respectively.

In this work, we have considered an extension of the standard model (SM) with a $SU(2{)}_L$ singlet vectorlike quark (VLQ) with electric charge $Q=+2/3$. The model also contains an additional local $U(1{)}_d$ symmetry group and the corresponding gauge boson is the dark photon. The VLQ is charged while all the SM particles are neutral under the new $U(1{)}_d$ gauge group. Even though in this model the VLQ possesses many properties qualitatively similar to that of the traditional top partner ($T_p$), there are some compelling differences as well. In particular, its branching ratio to the traditional modes ($T_p\to bW,tZ,th$) are suppressed which in turn helps to evade many of the existing bounds, mainly coming from the LHC experiments. In an earlier work, such a VLQ is referred to as “maverick top partner”. It has been shown that the top partner in this model predominantly decays to a top quark and a dark photon/dark Higgs pair ($T_p\to t{\gamma }_d,t{h}_d$) over a large region of the parameter space. The dark photon can be made invisible and consequently, it gives rise to the missing transverse energy (${\cancel{E}}_T$) signature at the LHC detector. We have mainly focused on the LHC signatures and future prospects of such top partners. In particular, we have studied the $t\overline{t}+{\cancel{E}}_T$ and $t+{\cancel{E}}_T$ signatures in the context of the LHC via pair and single productions of the top partner, respectively at 13 and 14 TeV LHC center of mass energies assuming that the dark photon either decays into an invisible mode or it is invisible at the length scale of the detector. We have shown that one can exclude $\sin {\theta }_L\sim 0.025$ (0.05) for $m_{T_p}\le 2.0(2.6)\mathrm{TeV}$ at $\sqrt{s}=14\mathrm{TeV}$ with an integrated luminosity of $3{\mathrm{ab}}^{-1}$ using the single top partner production channel.

We study hybrid inflation with a pseudo-Nambu-Goldstone boson inflaton and two waterfall scalar fields. The $Z_2$ symmetry for the waterfall fields keeps the inflaton potential flat against quantum corrections coming from the waterfall couplings, and it is broken spontaneously in the vacuum without a domain-wall problem within the Hubble horizon of our Universe. We show that the $Z_2$-invariant Higgs portal couplings to the waterfall fields are responsible for the reheating process, leading to a sufficiently large reheating temperature after inflation. In the presence of an extra $Z_2^{\prime }$ symmetry, one of the waterfall fields or another singlet scalar field becomes a dark matter candidate. In particular, we find that preheating is sufficient to account for the correct relic density of the waterfall dark matter.