In this paper, we deal with the $f(R,Q)$ gravity whose action depends, besides of the scalar curvature $R$, on the higher-derivative invariant $Q=R_{\mu \nu }{R}^{\mu \nu }$. In order to compare this theory with the usual general relativity (GR), we verify the consistency of Gödel-type solutions within the $f(R,Q)$ gravity and discuss the related causality issues are discussed. Explicitly, we show that in the $f(R,Q)$ gravity there are new Gödel-type completely causal solutions having no analogue in the general relativity. In particular, a remarkable Gödel-type solution corresponding to the conformally flat space and maximally symmetric for physically well-motivated matter sources, with no necessity of cosmological constant, has been considered. We demonstrate that, in contrast to GR framework, $f(R,Q)$ gravity supports new vacuum solutions with the requirement for the cosmological constant to be nonzero. Finally, causal solutions are obtained for a particular choice $f(R,Q)=R+\alpha R^2+\beta Q$.

Carter and Lichnerowicz have established that barotropic fluid flows are conformally geodesic and obey Hamilton’s principle. This variational approach can accommodate neutral, or charged and poorly conducting, fluids. We show that, unlike what has been previously thought, this approach can also accommodate perfectly conducting magnetofluids, via the Bekenstein-Oron description of ideal magnetohydrodynamics. When Noether symmetries associated with Killing vectors or tensors are present in geodesic flows, they lead to constants of motion polynomial in the momenta. We generalize these concepts to hydrodynamic flows. Moreover, the Hamiltonian descriptions of ideal magnetohydrodynamics allow one to cast the evolution equations into a hyperbolic form useful for evolving rotating or binary compact objects with magnetic fields in numerical general relativity. In this framework, Ertel’s potential vorticity theorem for baroclinic fluids arises as a special case of a conservation law valid for any Hamiltonian system. Moreover, conserved circulation laws, such as those of Kelvin, Alfvén and Bekenstein-Oron, emerge simply as special cases of the Poincaré-Cartan integral invariant of Hamiltonian systems. We use this approach to obtain an extension of Kelvin’s theorem to baroclinic (nonisentropic) fluids, based on a temperature-dependent time parameter. We further extend this result to perfectly or poorly conducting baroclinic magnetoflows. Finally, in the barotropic case, such magnetoflows are shown to also be geodesic, albeit in a Finsler (rather than Riemann) space.

Gravitational waves emitted by high redshift sources propagate through various epochs of the Universe including the current era of measurable, accelerated expansion. Historically, the calculation of gravitational wave power on cosmological backgrounds is based on various simplifications, including a $1/r$-expansion and the use of an algebraic projection to retrieve the radiative degrees of freedom. On a de Sitter spacetime, recent work has demonstrated that many of these calculational techniques and approximations do not apply. Here we calculate the power emitted by a binary system on a de Sitter background using techniques tailored to de Sitter spacetime. The common expression for the power radiated by this source in an Friedmann-Lemaître-Robertson-Walker spacetime, calculated using far wave-zone techniques, gives the same expression as the late time expansion specialized to the de Sitter background in the high-frequency approximation.

Linear perturbation theory is a powerful toolkit for studying black hole spacetimes. However, the perturbation equations are hard to solve unless we can use separation of variables. In the Kerr spacetime, metric perturbations do not separate, but curvature perturbations do. The cost of curvature perturbations is a very complicated metric-reconstruction procedure. This procedure can be avoided using a symmetry-adapted choice of basis functions in highly symmetric spacetimes, such as near-horizon extremal Kerr. In this paper, we focus on this spacetime and (i) construct the symmetry-adapted basis functions; (ii) show their orthogonality; and (iii) show that they lead to separation of variables of the scalar, Maxwell, and metric perturbation equations. This separation turns the system of partial differential equations into one of ordinary differential equations over a compact domain, the polar angle.

We analytically study a scattering of long linear surface waves on stationary currents in a duct (canal) of constant depth and variable width. It is assumed that the background velocity linearly increases or decreases with the longitudinal coordinate due to the gradual variation of duct width. Such a model admits an analytical solution of the problem in hand, and we calculate the scattering coefficients as functions of incident wave frequency for all possible cases of sub-, super-, and transcritical currents. For completeness we study both cocurrent and countercurrent wave propagation in accelerating and decelerating currents. The results obtained are analyzed in application to recent analog gravity experiments and shed light on the problem of hydrodynamic modeling of Hawking radiation.

Quantum gravity computations suggest the existence of an ultraviolet and an infrared fixed point where quantum scale invariance emerges as an exact symmetry. We discuss a particular variable gravity model for the crossover between these fixed points which can naturally account for inflation and dark energy, using a single scalar field. In the Einstein-frame formulation, the potential can be expressed in terms of Lambert functions, interpolating between a power-law inflationary potential and a mixed-quintessence potential. For two natural heating scenarios, the transition between inflation and radiation domination proceeds through a “graceful reheating” stage. The radiation temperature significantly exceeds the temperature of big bang nucleosynthesis. For this type of model, the observable consequences of the heating process can be summarized in a single parameter, the heating efficiency. Our quantitative analysis of compatibility with cosmological observations reveals the existence of realistic models able to describe the whole history of the Universe using only a single metric and scalar field and involving just a small number of order 1 parameters.

Tidal disruption events (TDEs) by supermassive or intermediate mass black holes have been suggested as candidate sources of ultrahigh-energy cosmic rays (UHECRs) and high-energy neutrinos. Motivated by the recent measurements from the Pierre Auger Observatory, which indicates a metal-rich cosmic-ray composition at ultrahigh energies, we investigate the fate of UHECR nuclei loaded in TDE jets. First, we consider the production and survival of UHECR nuclei at internal shocks, external forward and reverse shocks, and nonrelativistic winds. Based on the observations of Swift $\mathrm{J}1644+57$, we show that the UHECRs can survive for external reverse and forward shocks, and disk winds. On the other hand, UHECR nuclei are significantly disintegrated in internal shocks, although they could survive for low-luminosity TDE jets. Assuming that UHECR nuclei can survive, we consider implications of different composition models of TDEs. We find that the tidal disruption of main sequence stars or carbon-oxygen white dwarfs does not successfully reproduce UHECR observations, namely the observed composition or spectrum. The observed mean depth of the shower maximum and its deviation could be explained by oxygen-neon-magnesium white dwarfs, although they may be too rare to be the sources of UHECRs.

We study a possible symmetry restoration due to the radiative effect of particles which are explosively produced in preheating after inflation. As its application, we consider a scenario for leptogenesis based on the lepton number asymmetry generated in the right-handed neutrino sector through the inflaton decay. The scenario is examined in a one-loop radiative neutrino mass model extended with singlet scalars.

We analyze the prospects of observing the light charge parity ($CP$)-even neutral Higgs bosons ($h_1$) in their decays into $b\overline{b}$ quarks, in the neutral and charged current production processes $e{h}_{1}q$ and $\nu h_{1}q$ at the upcoming Large Hadron Electron Collider (LHeC), with $\sqrt{s}\approx 1.296\mathrm{TeV}$. Assuming that the intermediate Higgs boson ($h_2$) is Standard Model (SM)-like, we study the Higgs production within the framework of next-to-minimal supersymmetric Standard Model (NMSSM). We consider the constraints from dark-matter, sparticle masses, and the Higgs boson data. The signal in our analysis can be classified as three jets, with electron (missing energy) coming from the neutral (charged) current interaction. We demand that the number of $b$-tagged jets in the central rapidity region be greater or equal to two. The remaining jet is tagged in the forward regions. With this forward jet and two $b$-tagged jets in the central region, we reconstructed three jets invariant masses. Applying some lower limits on these invariant masses turns out to be an essential criterion to enhance the signal–to–background rates, with slightly different sets of kinematical selections in the two different channels. We consider almost all reducible and irreducible SM background processes. We find that the non-SM like Higgs boson, $h_1$, would be accessible in some of the NMSSM benchmark points, at approximately the $0.4\sigma$ ($2.5\sigma$) level in the $e+3\mathrm{j}$ channel up to Higgs boson masses of 75 GeV, and in the ${\cancel{E}}_T+3\mathrm{j}$ channel could be discovered with the $1.7\sigma$ ($2.4\sigma$) level up to Higgs boson masses of 88 GeV with $100{\mathrm{fb}}^{-1}$ of data in a simple cut-based (with optimization) selection. With ten times more data accumulation at the end of the LHeC run, and using optimization, one can have $5\sigma$ discovery in the electron (missing energy) channel up to 85 (more than 90) GeV.

Twin Higgs models solve the little hierarchy problem without introducing new colored particles; however, they are often in tension with measurements of the radiation density at late times. Here we explore viable cosmological histories for twin Higgs models. In particular, we show that mixing between the Standard Model (SM) and twin neutrinos can thermalize the two sectors below the twin QCD phase transition, significantly reducing the twin sector’s contribution to the radiation density. The requisite twin neutrino masses of $\mathcal{O}(1–20)\mathrm{GeV}$ and mixing angle with SM neutrinos of ${10}^{-3}-{10}^{-5}$ can be probed in a variety of current and planned experiments. We further find that these parameters can be naturally accessed in a warped UV completion, where the neutrino sector can also generate the $Z_2$-breaking Higgs mass term needed to produce the hierarchy between the symmetry breaking scales $f$ and $v$.

We employ machine learning techniques to investigate the volume minimum of Sasaki-Einstein base manifolds of noncompact toric Calabi-Yau three-folds. We find that the minimum volume can be approximated via a second-order multiple linear regression on standard topological quantities obtained from the corresponding toric diagram. The approximation improves further after invoking a convolutional neural network with the full toric diagram of the Calabi-Yau three-folds as the input. We are thereby able to circumvent any minimization procedure that was previously necessary and find an explicit mapping between the minimum volume and the topological quantities of the toric diagram. Under the AdS/CFT correspondence, the minimum volumes of Sasaki-Einstein manifolds correspond to central charges of a class of $4d$ $\mathcal{N}=1$ superconformal field theories. We therefore find empirical evidence for a function that gives values of central charges without the usual extremization procedure.

We study the confinement-deconfinement phase transition in a holographic soft-wall QCD model. By solving the Einstein-Maxwell-scalar system analytically, we obtain the phase structure of the black hole backgrounds. We then impose probe open strings in such a background to investigate the confinement-deconfinement phase transition from different open string configurations under various temperatures and chemical potentials. Furthermore, we study the Wilson loop by calculating the minimal surface of the probing open string world sheet and obtain the Cornell potential in the confinement phase analytically.

We study corrections to the soft graviton theorem at all loop orders in Yukawa and scalar theories, both in the high-energy and low-energy regions. It is found that the tree-level soft theorem is corrected by matrix elements coupled to the Riemann curvature tensor of linearized gravity. Further corrections appear in the high-energy region and we develop a power counting technique to classify all such loop corrections according to their order of magnitude. This leads to the construction of factorized contributions to the soft theorem, to which we apply an analysis analogous to Low’s theorem based on the gravitational Ward identity. In this analysis, we emphasize the role played by the external kinematics.

In the $SU(2{)}_L\times SU(2{)}_R$ linear sigma model with partially conserved axial-vector currents, a tower of Ward-Takahashi identities (WTI) have long been known to give relations among 1-scalar-particle-irreducible ($1\text{−}\varphi \text{−}\mathrm{I}$) Green’s functions, and among I-scalar-particle-reducible ($1\text{−}\varphi \text{−}\mathrm{R}$) transition-matrix (T-matrix) elements for external scalars [i.e. the Brout-Englert-Higgs (BEH) scalar $H$, and three pseudoscalars $\overrightarrow{\pi }$]. In this paper, we extend these WTI and the resulting relations to the $SU(3{)}_C\times SU(2{)}_L\times U(1{)}_Y$ linear sigma model including the heaviest generation of Standard Model (SM) fermions—the ungauged (i.e. global) Standard Model ${\mathrm{SM}}_{tb\tau {\nu }_{\tau }}^G$—supplemented with the minimum necessary neutrino content—right-handed neutrinos and Yukawa-coupling-induced Dirac neutrino mass—to obtain the charge-parity ($CP$)-conserving ${\nu }_D{\mathrm{SM}}_{tb\tau {\nu }_{\tau }}^{\mathrm{G}}$, and extract powerful constraints on the effective Lagrangian: e.g. showing that they make separate tadpole renormalization unnecessary, and guarantee infrared finiteness. The crucial observation is that ultraviolet quadratic divergences (UVQD), and all other relevant operators, contribute only to $m_{\pi }^2$, a pseudo-Nambu-Goldstone boson (NGB) mass-squared, which appears in intermediate steps of calculations. A WTI between T-matrix elements (or, in this global theory equivalently the Goldstone theorem) then enforces $m_{\pi }^2=0$ exactly for the true NGB in the spontaneous symmetry breaking (SSB) mode of the theory. The Goldstone theorem thus causes all relevant operator contributions, originating to all-loop-orders from virtual scalars $H,\overrightarrow{\pi }$, quarks $q_L^c;t_R^c;b_R^c$ and leptons $l_L;{{\nu }_{\tau }}_R;{\tau }_R$ with ($c=r$, $w$, $b$), to vanish identically.

We show that our regularization-scheme-independent, WTI-driven results are unchanged by the addition of certain $SU(3{)}_C\times SU(2{)}_L\times U(1{)}_Y$ heavy ($M_{\text{Heavy}}^2\gg |q^2|,m_{\text{Weak}}^2$) $CP$-conserving matter, such as originate in certain beyond the SM (BSM) models. The global axial-vector WTI again cause all UVQD and finite relevant operators to vanish, in the ${\nu }_D{\mathrm{SM}}_{tb\tau {\nu }_{\tau }+\text{Heavy}}^{\mathrm{G}}$ model. We demonstrate this with two examples: a singlet $M_S^2\gg m_{\text{Weak}}^2$ real scalar field $S$ with discrete $Z_2$ symmetry and $⟨S⟩=0$; and a singlet right-handed type I see-saw Majorana neutrino ${\nu }_R$ with $M_{{\nu }_R}^2\gg m_{\text{Weak}}^2$. Specifically, we prove that these heavy degrees of freedom decouple completely from the low-energy ${\nu }_D{\mathrm{SM}}_{tb\tau {\nu }_{\tau }}^{\mathrm{G}}$ effective Lagrangian, contributing only irrelevant operators after quartic-coupling renormalization.

The growth of commutators of initially commuting local operators diagnoses the onset of chaos in quantum many-body systems. We compute such commutators of local field operators with $N$ components in the ($2+1$)-dimensional $O(N)$ nonlinear sigma model to leading order in $1/N$. The system is taken to be in thermal equilibrium at a temperature $T$ above the zero temperature quantum critical point separating the symmetry broken and unbroken phases. The commutator grows exponentially in time with a rate denoted ${\lambda }_L$. At large $N$ the growth of chaos as measured by ${\lambda }_L$ is slow because the model is weakly interacting, and we find ${\lambda }_L\approx 3.2T/N$. The scaling with temperature is dictated by conformal invariance of the underlying quantum critical point. We also show that operators grow ballistically in space with a “butterfly velocity” given by $v_B/c\approx 1$ where $c$ is the Lorentz-invariant speed of particle excitations in the system. We briefly comment on the behavior of ${\lambda }_L$ and $v_B$ in the neighboring symmetry broken and unbroken phases.

We study dynamics of an (anomalous) Galilean superfluid up to first order in derivative expansion, both in parity-even and parity-odd sectors. We construct a relativistic system—null superfluid, which is a null fluid (introduced in N. Banerjee, S. Dutta, and A. Jain Akash, [Phys. Rev. D 93, 105020 (2016).]) with a spontaneously broken global U(1) symmetry. A null superfluid is in one-to-one correspondence with a Galilean superfluid in one lower dimension; i.e., they have the same symmetries, thermodynamics, constitutive relations and are related to each other by a mere choice of basis. The correspondence is based on null reduction, which is known to reduce the Poincaré symmetry of a theory to Galilean symmetry in one lower dimension. To perform this analysis, we use off-shell formalism of (super)fluid dynamics, adopting it appropriately to null (super)fluids. We also verify these results via $c\to \infty$ limit of a parent relativistic system.

The weak-scale $U(1{)}_Y$ Abelian Higgs model (AHM) is the simplest spontaneous symmetry breaking (SSB) gauge theory: a scalar $\varphi =\frac{1}{\sqrt{2}}(H+i\pi )\equiv \frac{1}{\sqrt{2}}\tilde{H}{e}^{i\tilde{\pi }/⟨H⟩}$ and a vector $A^{\mu }$. The extended AHM (E-AHM) adds certain heavy ($M_{\mathrm{\Phi }}^2,M_{\psi }^2\sim M_{\text{Heavy}}^2\gg ⟨H{⟩}^2\sim m_{\text{Weak}}^2$) spin $S=0$ scalars $\mathrm{\Phi }$ and $S=\frac{1}{2}$ fermions $\psi$. In Lorenz gauge, ${\partial }_{\mu }{A}^{\mu }=0$, the SSB AHM (and E-AHM) has a global $U(1{)}_Y$ conserved physical current, but no conserved charge. As shown by T. W. B. Kibble, the Goldstone theorem applies, so $\tilde{\pi }$ is a massless derivatively coupled Nambu-Goldstone boson (NGB).

Proof of all-loop-orders renormalizability and unitarity for the SSB case is tricky because the Becchi-Rouet-Stora-Tyutin (BRST)-invariant Lagrangian is not $U(1{)}_Y$ symmetric. Nevertheless, Slavnov-Taylor identities guarantee that on-shell T-matrix elements of physical states $A^{\mu }$,$\varphi$, $\mathrm{\Phi }$, $\psi$ (but not ghosts $\omega$, $\overline{\eta }$) are independent of anomaly-free local $U(1{)}_Y$ gauge transformations. We observe here that they are therefore also independent of the usual anomaly-free $U(1{)}_Y$ global/rigid transformations. It follows that the associated global current, which is classically conserved only up to gauge-fixing terms, is exactly conserved for amplitudes of physical states in the AHM and E-AHM. We identify corresponding “undeformed” [i.e. with full global $U(1{)}_Y$ symmetry] Ward-Takahashi identities (WTI). The proof of renormalizability and unitarity, which relies on BRST invariance, is undisturbed.

In Lorenz gauge, two towers of “1-soft-pion” SSB global WTI govern the $\varphi$-sector, and represent a new global $U(1{)}_Y\otimes \mathrm{BRST}$ symmetry not of the Lagrangian but of the physics. The first gives relations among off-shell Green’s functions, yielding powerful constraints on the all-loop-orders $\varphi$-sector SSB E-AHM low-energy effective Lagrangian and an additional global shift symmetry for the NGB: $\tilde{\pi }\to \tilde{\pi }+⟨H⟩\theta$. A second tower, governing on-shell T-matrix elements, replaces the old Adler self-consistency conditions with those for gauge theories, further severely constrains the effective potential, and guarantees infrared finiteness for zero NGB ($\tilde{\pi }$) mass. The on-shell WTI include a Lee-Stora-Symanzik theorem, also for gauge theories. This enforces the strong condition $m_{\pi }^2=0$ on the pseudoscalar $\pi$ (not just the much weaker condition $m_{\tilde{\pi }}^2=0$ on the NGB $\tilde{\pi }$), and causes all relevant-operator contributions to the effective Lagrangian to vanish exactly.

In consequence, certain heavy $CP$-conserving $\mathrm{\Phi }$, $\psi$ matter decouple completely in the $m_{Heavy}^2/m_{weak}^2\to \infty$ limit. We prove four new low-energy heavy-particle decoupling theorems that are more powerful than the usual Appelquist-Carazzone decoupling theorem: including all virtual $\varphi$ and $\psi$ loop contributions, relevant operators operators vanish exactly due to the exact $U(1{)}_Y$ symmetry of 1-soft-$\pi$ Adler-self-consistency relations governing on-shell T-matrix elements.

Underlying our results is that global $U(1{)}_Y$ transformations ${\delta }_{U(1{)}_Y}$, and nilpotent $s^2=0$ BRST transformations, commute: we prove $[{\delta }_{U(1{)}_Y},s]$ in G. ’t Hooft’s $R_{\xi }$ gauges. With its on-shell T-matrix constraints, SSB E-AHM physics therefore has more symmetry than does its BRST-invariant Lagrangian $L_{\mathrm{E}\text{−}\mathrm{AHM}}^{R_{\xi }}$: i.e. global $U(1{)}_Y\otimes \mathrm{BRST}$ symmetry.

The NGB $\tilde{\pi }$ decouples from the observable particle spectrum $B^{\mu }$,$\tilde{h}$, $\tilde{\mathrm{\Phi }}$, $\tilde{\psi }$ in the usual way, when the observable vector $B_{\mu }\equiv A_{\mu }+\frac{1}{e⟨H⟩}{\partial }_{\mu }\tilde{\pi }$ absorbs it, as if it were a gauge transformation, hiding both towers of $U(1{)}_Y$ WTI from observable particle physics.

We study the nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) in an attempt to make contact with Weinberg’s asymptotic safety scenario. We find that a fine-tuning is necessary in order to recover semiclassical behavior. Such a fine-tuning is generally associated with the breaking of a target symmetry by the lattice regulator; in this case we argue that the target symmetry is the general coordinate invariance of the theory. After introducing and fine-tuning a nontrivial local measure term, we find no barrier to taking a continuum limit, and we find evidence that four-dimensional, semiclassical geometries are recovered at long distance scales in the continuum limit. We also find that the spectral dimension at short distance scales is consistent with $3/2$, a value that could resolve the tension between asymptotic safety and the holographic entropy scaling of black holes. We argue that the number of relevant couplings in the continuum theory is one, once symmetry breaking by the lattice regulator is accounted for. Such a theory is maximally predictive, with no adjustable parameters. The cosmological constant in Planck units is the only relevant parameter, which serves to set the lattice scale. The cosmological constant in Planck units is of order 1 in the ultraviolet and undergoes renormalization group running to small values in the infrared. If these findings hold up under further scrutiny, the lattice may provide a nonperturbative definition of a renormalizable quantum field theory of general relativity with no adjustable parameters and a cosmological constant that is naturally small in the infrared.

Primordial gravitational waves leave a characteristic imprint on the cosmic microwave background (CMB) in the form of $B$-mode polarization. Photons are also deflected by large scale gravitational waves which intervene between the source screen and our telescopes, resulting in curl-type gravitational lensing. Gravitational waves present at the epoch of reionization contribute to both effects, thereby leading to a nonvanishing cross-correlation between $B$-mode polarization and curl lensing of the CMB. Observing such a cross-correlation would be very strong evidence that an observation of $B$-mode polarization was due to the presence of large scale gravitational waves, as opposed to astrophysical foregrounds or experimental systematic effects. We study the cross-correlation across a wide range of source redshifts and show that a post-SKA experiment aimed to map out the 21-cm sky between $15\le z\le 30$ could rule out non-zero cross-correlation at high significance for $r\ge 0.01$.

We study production of primordial black holes (PBHs) during an early matter-dominated phase. As a source of perturbations, we consider either an inflaton field with a running spectral index or a spectator field that has a blue spectrum and thus provides a significant contribution to PBH production at small scales. First, we identify the region of the parameter space where a significant fraction of the observed dark matter can be produced, taking into account all current PBH constraints. Then, we present constraints on the amplitude and spectral index of the spectator field as a function of the reheating temperature. We also derive constraints on the running of the inflaton spectral index, $\mathrm{d}n/\mathrm{d}\ln k\lesssim 0.001$, which are comparable to those from the Planck satellite for a scenario where the spectator field is absent.