We consider gauge theories from the free evolution point of view, in which initial data satisfying constraints of a theory are given, and because the constraints satisfy a closed evolution system, they remain so. We study a model constrained Hamiltonian theory and identify a particular structure in the equations of motion which we call the standard gauge freedom. The pure gauge subsystem of this model theory is identified, and the manner in which the gauge variables couple to the field equations is presented. We demonstrate that the set of gauge choices that can be coupled to the field equations to obtain a strongly hyperbolic formulation is exactly the set of strongly hyperbolic pure gauges. Consequently we analyze a parametrized family of formulations of general relativity. The generalization of the harmonic gauge formulation to a five parameter family of gauge conditions is obtained.

We present a class of modified-gravity theories which we call ultralocal models. We add a scalar field, with negligible kinetic terms, to the Einstein-Hilbert action. We also introduce a conformal coupling to matter. This gives rise to a new screening mechanism which is not entirely due to the nonlinearity of the scalar-field potential or the coupling function but to the absence of the kinetic term. As a result this removes any fifth force between isolated objects in vacuum. It turns out that these models are similar to chameleon-type theories with a large mass when considered outside the Compton wavelength but differ on shorter scales. The predictions of these models only depend on a single free function, as the potential and the coupling function are degenerate, with an amplitude given by a parameter $\alpha \lesssim {10}^{-6}$, whose magnitude springs from requiring a small modification of Newton’s potential astrophysically and cosmologically. This singles out a redshift $z_{\alpha }\sim {\alpha }^{-1/3}\gtrsim 100$ where the fifth force is the greatest. The cosmological background follows the $\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) history within a ${10}^{-6}$ accuracy, while cosmological perturbations are significantly enhanced (or damped) on small scales, $k\gtrsim 2h{\mathrm{Mpc}}^{-1}$ at $z=0$. The spherical collapse and the halo mass function are modified in the same manner. We find that the modifications of gravity are greater for galactic or subgalactic structures. We also present a thermodynamic analysis of the nonlinear and inhomogeneous fifth-force regime where we find that the Universe is not made more inhomogeneous before $z_{\alpha }$ when the fifth force dominates, and does not lead to the existence of clumped matter on extra small scales inside halos for large masses while this possibility exists for masses $M\lesssim 10^{11}{M}_{\odot }$ where the phenomenology of ultralocal models would be most different from $\mathrm{\Lambda }\mathrm{CDM}$.

A model of nonlinear electrodynamics coupled with the gravitational field is studied. We obtain the asymptotic black hole solutions at $r\to 0$ and $r\to \infty$. The asymptotic at $r\to 0$ is shown, and we find corrections to the Reissner-Nordström solution and Coulomb’s law at $r\to \infty$. The mass of the black hole is evaluated having the electromagnetic origin. We investigate the thermodynamics of charged black holes and their thermal stability. The critical point corresponding to the second-order phase transition (where heat capacity diverges) is found. If the mass of the black hole is greater than the critical mass, the black hole becomes unstable.

Adopting the notation of Teukolsky and Press, we derive the connection relation for asymptotic solutions of the massless Dirac equation on a Kerr background. We show that, unlike bosonic fields, the connection relation for massless Dirac fields (neutrino) provides a rigorous proof of mode stability. The same relation also implies that every incoming mode can be absorbed by the black hole or there is no superradiance. Recent works on overspinning black holes have shown that this can lead to the formation of naked singularities. We argue that the fact that both the mode stability of the black hole under neutrino perturbations and the instability of the event horizon (therefore the instability of the black hole) can be derived from the same connection relation leads to a paradox. In other words mode, stability implies event horizon instability as far as neutrino perturbations are concerned.

We consider the motion of test particles and light rays in a static cylindrically symmetric conformal spacetime given by Said et al. [Phys. Rev. D 85, 104054 (2012)]. We derive the equations of motion and present their analytical solutions in terms of the Weierstrass $\wp$ function and the Kleinian $\sigma$ function. Using parametric diagrams and effective potentials, we analyze the possible orbits and characterize them in terms of the energy and the angular momentum of the test particles. Finally, we show some examples of orbits.

Inflation due to a nonminimally coupled scalar field, as first proposed by Salopek, Bardeen and Bond (SBB), is in good agreement with the observed value of the spectral index and constraints on the tensor-to-scalar ratio. Here we explore the possibility that SBB inflation represents the late stage of a Universe which emerges from an early contracting era. We present a model in which the Universe smoothly transitions from an anamorphic contracting era to late-time SBB inflation without encountering a singular bounce. This corresponds to a continuous expansion in the Einstein frame throughout. We show that the anamorphic contracting era is able to provide the smooth superhorizon initial conditions necessary for subsequent SBB inflation to occur. The model predicts corrections to the nonminimal coupling, kinetic term and potential of SBB inflation which can observably increase the spectral index relative to its SBB prediction.

Using three-dimensional simulations, we study the dynamics and final structure of merging solitonic cores predicted to form in ultralight axion dark matter halos. The classical, Newtonian equations of motion of a self-gravitating scalar field are described by the Schrödinger-Poisson equations. We investigate mergers of ground state (boson star) configurations with varying mass ratios, relative phases, orbital angular momenta and initial separation with the primary goal to understand the mass loss of the emerging core by gravitational cooling. Previous results showing that the final density profiles have solitonic cores and Navarro-Frenk-White-like tails are confirmed. In binary mergers, the final core mass does not depend on initial phase difference or angular momentum and only depends on mass ratio, total initial mass, and total energy of the system. For nonzero angular momenta, the otherwise spherical cores become rotating ellipsoids. The results for mergers of multiple cores are qualitatively identical.

Cosmic microwave background (CMB) experiments, such as WMAP and Planck, measure intensity anisotropies and build maps using a linearized formula for relating them to the temperature blackbody fluctuations. However, this procedure also generates a signal in the maps in the form of $y$-type distortions which is degenerate with the thermal Sunyaev Zel’dovich (tSZ) effect. These are small effects that arise at second order in the temperature fluctuations not from primordial physics but from such a limitation of the map-making procedure. They constitute a contaminant for measurements of our peculiar velocity, the tSZ and primordial $y$-distortions. They can nevertheless be well modeled and accounted for. We show that the distortions arise from a leakage of the CMB dipole into the $y$-channel which couples to all multipoles, mostly affecting the range $\ell \lesssim 400$. This should be visible in Planck’s $y$-maps with an estimated signal-to-noise ratio of about 12. We note however that such frequency-dependent terms carry no new information on the nature of the CMB dipole. This implies that the real significance of Planck’s Doppler coupling measurements is actually lower than reported by the collaboration. Finally, we quantify the level of contamination in tSZ and primordial $y$-type distortions and show that it is above the sensitivity of proposed next-generation CMB experiments.

Nonobservation of superpartners of the Standard Model particles at the early runs of the LHC provide strong motivation for introducing an $R$-symmetric minimal supersymmetric Standard Model. This model also comes with a pair of extra scalars which couple only to superpartners at the tree level. We demonstrate that in the case when the $U(1{)}_R$ symmetry is mildly broken one of these scalars develops all the properties necessary to explain the 750 GeV diphoton resonance recently observed at the LHC, as well as the nonobservation of associated signals in other channels. Some confirmatory tests in the upcoming LHC runs are proposed.

Jarzynski’s theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a nonequilibrium transformation of a system, to the free-energy difference between two equilibrium ensembles. In this article, we apply Jarzynski’s theorem in lattice gauge theory, for two examples of challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schrödinger functional and for simulations at finite density using reweighting techniques.

We present a comprehensive study of the determination of the strong coupling from $\tau$ decay, using the most recent release of the experimental ALEPH data. We critically review all theoretical strategies used in previous works and put forward various novel approaches which allow one to study complementary aspects of the problem. We investigate the advantages and disadvantages of the different methods, trying to uncover their potential hidden weaknesses and test the stability of the obtained results under slight variations of the assumed inputs. We perform several determinations, using different methodologies, and find a very consistent set of results. All determinations are in excellent agreement, and allow us to extract a very reliable value for ${\alpha }_s(m_{\tau }^2)$. The main uncertainty originates in the pure perturbative error from unknown higher orders. Taking into account the systematic differences between the results obtained with the contour-improved perturbation theory and fixed-order perturbation theory prescriptions, we find ${\alpha }_s^{(n_f=3)}(m_{\tau }^2)=0.328\pm 0.013$ which implies ${\alpha }_s^{(n_f=5)}(M_Z^2)=0.1197\pm 0.0015$.

We analyze Yukawa unification in the context of $E_8\times E_8$ heterotic Calabi-Yau models which rely on breaking to a grand unified theory (GUT) via a nonflat gauge bundle and subsequent Wilson line breaking to the standard model. Our focus is on underlying GUT theories with gauge group $SU(5)$ or $SO(10)$. We provide a detailed analysis of the fact that, in contrast to traditional field theory GUTs, the underlying GUT symmetry of these models does not enforce Yukawa unification. Using this formalism, we present various scenarios where Yukawa unification can occur as a consequence of additional symmetries. These additional symmetries arise naturally in some heterotic constructions, and we present an explicit heterotic line bundle model which realizes one of these scenarios.

We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to nontrivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling $G_{\mathrm{eff}}$ with matter density perturbations under a quasistatic approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility for reducing $G_{\mathrm{eff}}$. In fact, within the parameter space, $G_{\mathrm{eff}}$ can be even smaller than the Newton gravitational constant $G$ at the late cosmological epoch, with a peculiar phantom dark energy equation of state (without ghosts). The modifications to the slip parameter $\eta$ and the evolution of the growth rate $f{\sigma }_8$ are discussed as well. Thus, dark energy models in the framework of generalized Proca theories can be observationally distinguished from the $\mathrm{\Lambda }\mathrm{CDM}$ model according to both cosmic growth and expansion history. Furthermore, we study the evolution of vector perturbations and show that outside the vector sound horizon the perturbations are nearly frozen and start to decay with oscillations after the horizon entry.

We discuss the physical interpretation of stress-energy tensors that source static spherically symmetric Kerr-Schild metrics. We find that the sources of such metrics with no curvature singularities or horizons do not simultaneously satisfy the weak and strong energy conditions. Sensible stress-energy tensors usually satisfy both of them. Under most circumstances, these sources are not perfect fluids and contain shear stresses. We show that for these systems the classical double copy associates the electric charge density to the Komar energy density. In addition, we demonstrate that the stress-energy tensors are determined by the electric charge density and their conservation equations.

We study higher-dimensional scenarios of massive bigravity, which is a very interesting extension of nonlinear massive gravity since its reference metric is assumed to be fully dynamical. In particular, the Einstein field equations along with the following constraint equations for both physical and reference metrics of a five-dimensional massive bigravity will be addressed. Then, we study some well-known cosmological spacetimes such as the Friedmann-Lemaitre-Robertson-Walker, Bianchi type I, and Schwarzschild-Tangherlini metrics for the five-dimensional massive bigravity. As a result, we find that massive graviton terms will serve as effective cosmological constants in both physical and reference sectors if a special scenario, in which reference metrics are chosen to be proportional to physical ones, is considered for all mentioned metrics. Thanks to the constancy property of massive graviton terms, consistent cosmological solutions will be figured out accordingly.

We develop a mathematical construction of non-Gaussian fields whose bispectra satisfy the single-clock inflation consistency relation. At the same order that our basis for bispectra recovers the two simplest single-clock templates, we also find a third orthogonal template which has the single-clock squeezed limit, peaks in folded configurations, and has very small coupling in the equilateral limit. We explore the map between templates and operators in a very general Lagrangian for single-clock fluctuations and find no significant overlap between the new template and models in the literature. We comment on the physical implications of this conclusion. Our findings add support for the idea that both theory- and data-driven considerations will be best served if next-generation non-Gaussianity constraints are made in a basis that uses the degree of coupling between long- and short-wavelength modes as an organizing principle.

The axion is a hypothetical particle considered to be the most economical solution to the strong $CP$ problem. It can also be formulated as a compelling component of dark matter. The haloscope, a leading axion detection scheme, relies on the conversion of galactic halo axions into real photons inside a resonant cavity structure in the presence of a static magnetic field, where the generated photon frequency corresponds to the mass of the axion. For maximum sensitivity it is key that the central frequency of the cavity mode structure coincides with the frequency of the generated photon. As the mass of the axion is unknown, it is necessary to perform searches over a wide range of frequencies. Currently there are substantial regions of the promising preinflationary low-mass axion range without any viable proposals for experimental searches. We show that three-dimensional resonant LC circuits with separated magnetic and electric fields, commonly known as reentrant cavities, can be sensitive dark matter haloscopes in this region, with frequencies inherently lower than those achievable in the equivalent size of empty resonant cavity. We calculate the sensitivity and accessible axion mass range of these experiments, designing geometries to exploit and maximize the separated magnetic and electric coupling of the axion to the cavity mode.

Using $\mathrm{AdS}/\mathrm{CFT}$ correspondence, we find that a massless quark moving at the speed of light $v=1$, in arbitrary direction, through a strongly coupled $\mathcal{N}=4$ super Yang-Mills (SYM) vacuum at $T=0$, in the presence of strong magnetic field $\mathcal{B}$, loses its energy at a rate linearly dependent on $\mathcal{B}$, i.e., $\frac{dE}{dt}=-\frac{\sqrt{\lambda }}{6\pi }\mathcal{B}$. We also show that a heavy quark of mass $M\ne 0$ moving at near the speed of light $v^2=v_{*}^2=1-\frac{4{\pi }^2{T}^2}{\mathcal{B}}\simeq 1$, in arbitrary direction, through a strongly coupled $\mathcal{N}=4$ SYM plasma at finite temperature $T\ne 0$, in the presence of strong magnetic field $\mathcal{B}\gg T^2$, loses its energy at a rate linearly dependent on $\mathcal{B}$, i.e., $\frac{dE}{dt}=-\frac{\sqrt{\lambda }}{6\pi }\mathcal{B}{v}_{*}^2\simeq -\frac{\sqrt{\lambda }}{6\pi }\mathcal{B}$. Moreover, we argue that, in the strong magnetic field $\mathcal{B}\gg T^2$ (IR) regime, $\mathcal{N}=4$ SYM and adjoint QCD theories (when the adjoint QCD theory has four flavors of Weyl fermions and is at its conformal IR fixed point $\lambda ={\lambda }^{*}$) have the same microscopic degrees of freedom (i.e., gluons and lowest Landau levels of Weyl fermions) even though they have quite different microscopic degrees of freedom in the UV when we consider higher Landau levels. Therefore, in the strong magnetic field $\mathcal{B}\gg T^2$ (IR) regime, the thermodynamic and hydrodynamic properties of $\mathcal{N}=4$ SYM and adjoint QCD plasmas, as well as the rates of energy loss of a quark moving through the plasmas, should be the same.

An interesting possibility for dark matter is a scalar particle of mass of order 10 MeV–1 GeV, interacting with a $U(1)$ gauge boson (dark photon) which mixes with the photon. We present a simple and natural model realizing this possibility. The dark matter arises as a composite pseudo-Nambu-Goldstone boson (dark pion) in a non-Abelian gauge sector, which also gives a mass to the dark photon. For a fixed non-Abelian gauge group, $SU(N)$, and a $U(1)$ charge of the constituent dark quarks, the model has only three free parameters: the dynamical scale of the non-Abelian gauge theory, the gauge coupling of the dark photon, and the mixing parameter between the dark and standard model photons. In particular, the gauge symmetry of the model does not allow any mass term for the dark quarks, and the stability of the dark pion is understood as a result of an accidental global symmetry. The model has a significant parameter space in which thermal relic dark pions comprise all of the dark matter, consistently with all experimental and cosmological constraints. In a corner of the parameter space, the discrepancy of the muon $g-2$ between experiments and the standard model prediction can also be ameliorated due to a loop contribution of the dark photon. Smoking-gun signatures of the model include a monophoton signal from the $e^{+}{e}^{-}$ collision into a photon and a “dark rho meson.” Observation of two processes in $e^{+}{e}^{-}$ collision—the mode into the dark photon and that into the dark rho meson—would provide strong evidence for the model.