We present several classes of exact solutions in the Einstein-Klein-Gordon system with a cosmological constant. The spacetime has spherical, plane, or hyperbolic symmetry and the higher-dimensional solutions are obtained in a closed form only in the plane symmetric case. Among them, the class-I solution represents an asymptotically locally anti-de Sitter (AdS) dynamical black hole or wormhole. In four and higher dimensions, the generalized Misner-Sharp quasilocal mass blows up at AdS infinity, inferring that the spacetime is only locally AdS. In three dimensions, the scalar field becomes trivial and the solution reduces to the Bañados-Teitelboim-Zanelli black hole.

We consider modified gravity models driven by a scalar field whose effects are screened in high density regions due to the presence of nonlinearities in its interaction potential and/or its coupling to matter. Our approach covers chameleon, $f(R)$ gravity, dilaton and symmetron models and allows a unified description of all these theories. We find that the dynamics of modified gravity are entirely captured by the time variation of the scalar field mass and its coupling to matter evaluated at the cosmological minimum of its effective potential, where the scalar field has sat since an epoch prior to big bang nucleosynthesis. This new parametrization of modified gravity allows one to reconstruct the potential and coupling to matter and therefore to analyze the full dynamics of the models, from the scale dependent growth of structures at the linear level to nonlinear effects requiring $N$-body simulations. This procedure is illustrated with explicit examples of reconstruction for chameleon, dilaton, $f(R)$ and symmetron models.

We analyze one-loop vacuum stability, perturbativity, and phenomenological constraints on a complex singlet extension of the standard model scalar sector containing a scalar dark matter candidate. We study vacuum stability considerations using a gauge-invariant approach and compare with the conventional gauge-dependent procedure. We show that, if new physics exists at the TeV scale, the vacuum stability analysis and experimental constraints from the dark matter sector, electroweak precision data, and LEP allow both a Higgs-like scalar in the mass range allowed by the latest results from CMS and ATLAS and a lighter singlet-like scalar with weak couplings to standard model particles. If instead no new physics appears until higher energy scales, there may be significant tension between the vacuum stability analysis and phenomenological constraints (in particular electroweak precision data) to the extent that the complex singlet extension with light Higgs and singlet masses would be ruled out. We comment on the possible implications of a scalar with $\sim 125\mathrm{GeV}$ mass and future ATLAS invisible decay searches.

We consider general relativistic magnetohydrodynamics from a charged multifluids point of view, taking a variational approach as our starting point. We develop the case of two charged components in detail, accounting for a phenomenological resistivity, providing specific examples for pair plasmas and proton-electron systems. We discuss both cold, low-velocity, plasmas and hot systems where we account for a dynamical entropy component. The results for the cold case (which accord with recent work in the literature) provide a complete model for resistive relativistic magnetohydrodynamics, clarifying the assumptions that lead to various models that have been used in astrophysical applications. The analysis of the hot case is (as far as we are aware) novel, accounting for the relaxation times that are required to ensure causality and demonstrating the explicit coupling between fluxes of heat and charge.

We find in theories with spontaneous $P$ and $CP$ violation that symmetries needed to set the tree-level strong $CP$ phase to zero can also set all nonzero tree-level $CP$ violating phases to the maximal value $\pi /2$ in the symmetry basis, simultaneously explaining the smallness of $\overline{\theta }$ and the largeness of the Cabibbo-Kobayashi-Maskawa (CKM) $CP$ violating phase. In these models we find the one-loop lower bound $\overline{\theta }\ge {10}^{-11}$ relevant for early discovery of neutron electric dipole moment (EDM) $d_n\ge {10}^{-27}\mathrm{e}\mathrm{cm}$. The lower bound relaxes to $\overline{\theta }\ge {10}^{-13}$ or $d_n\ge {10}^{-29}\mathrm{e}\mathrm{cm}$ for the case where the $CP$ phases are nonmaximal. Interestingly the spontaneous $CP$ phase appears in the quark sector, not the Higgs sector, and is enabled by a heavy left-right symmetric vectorlike quark family with mass $M$. These results do not vanish in the decoupling limit of $M_{H_2^{+}}>M\to \infty$ (where $M_{H_2^{+}}$ is the mass of heavy Higgses at the parity breaking scale) and the age-old expectation that laws of nature (or its Lagrangian) are parity and matter-antimatter symmetric may be testable by the above predictions and EDM experiments, even if new physics occurs only at seesaw, grand unified theory (GUT), or Planck scales. There is also a region in parameter space with $M_{H_2^{+}}<M$ where the above bounds are dampened by the factor $(M_{H_2^{+}}/M{)}^2$. By using flavor symmetries and texture arguments we also make predictions for the CKM phase that arises from the maximal phase on diagonalization to the physical basis. There are no axions predicted in this model.

We discuss the topological phenomena in the QCD-like theories with a variable number of fundamental fermions $N_f$, focusing on the temperatures at or above the critical value $T_c$ of chiral symmetry restoration. The nonzero average of the Polyakov line, or holonomy, splits instantons into (anti)self-dual dyons, and we study both the bosonic and fermionic interactions between them. The high temperature phase is a dilute gas of “molecules” made of $2N_c$ dyons, neutral in topological, electric, and magnetic charges. At intermediate temperatures the diluteness of the “molecular gas” reaches some critical level at which chiral symmetry gets restored: we comment on why it is different for the fundamental and adjoint fermions. At high density the ensemble is a strongly coupled liquid with crystal-like short range order: we speculate about its possible structure at small and large $N_f$. We finally show that certain lattice observations are in agreement with the proposed model, and suggest a number of further lattice tests.

The lepton flavor-violating $Z^{\prime }\to \tau \mu$ decay is studied in the context of several extended models that predict the existence of a new gauge boson named $Z^{\prime }$. A calculation of the strength of the lepton flavor-violating $Z^{\prime }\mu \tau$ coupling is presented by using the most general renormalizable Lagrangian that includes lepton flavor violation. We used the experimental value of the muon magnetic dipole moment to bound this coupling, from which the $\mathrm{Re}({\Omega }_{L\mu \tau }{\Omega }_{R\mu \tau }^{*})$ parameter is constrained, and it was found that $\mathrm{Re}({\Omega }_{L\mu \tau }{\Omega }_{R\mu \tau }^{*})\sim {10}^{-2}$ for a $Z^{\prime }$ boson mass of 2 TeV. We also employed the experimental restrictions over the $\tau \to \mu \gamma$ and $\tau \to \mu {\mu }^{+}{\mu }^{-}$ processes in the context of several models that predict the existence of the $Z^{\prime }$ gauge boson to bound the mentioned coupling. The most restrictive bounds come from the calculation of the three-body decay. For this case, it was found that the most restrictive result is provided by a vectorlike coupling, denoted as $|{\Omega }_{\mu \tau }{|}^2$, for the $Z_{\chi }$ case, finding around ${10}^{-2}$ for a $Z^{\prime }$ boson mass of 2 TeV. We used this information to estimate the branching ratio for the $Z^{\prime }\to \tau \mu$ decay. According to the analyzed models the least optimistic result is provided by the sequential $Z$ model, which is of the order of ${10}^{-2}$ for a $Z^{\prime }$ boson mass around 2 TeV.

Differently from the canonical seesaw mechanism, which is grounded in grand unified theories, the inverse seesaw mechanism lacks a special framework that realizes it naturally. In this work we advocate that the 3-3-1 model with right-handed neutrinos has such an appropriate framework to accommodate the inverse seesaw mechanism. We also discuss the smallness of the lepton number violating mass and estimate the branching ratio for the rare lepton flavor violation process $\mu \to e\gamma$.

We study strong-coupling lattice QCD with staggered-Wilson fermions, with an emphasis on discrete symmetries and the possibility of their spontaneous breaking. We perform hopping parameter expansion and effective potential analyses in the strong-coupling limit. From gap equations we find the nonzero pion condensate in some range of a mass parameter, which indicates the existence of the parity-broken phase in lattice QCD with staggered-Wilson fermions. We also find massless pions and PCAC relations around the second-order phase boundary. These results suggest that we can take a chiral limit by tuning a mass parameter in lattice QCD with staggered-Wilson fermions as we would with the Wilson fermion.

We show, in the imaginary time formalism, that the temperature dependent parts of all the retarded (advanced) amplitudes vanish in the Schwinger model. We trace this behavior to the $CPT$ invariance of the theory and give a physical interpretation of this result in terms of forward scattering amplitudes of on-shell thermal particles.

We construct magnetized stars composed of a fluid stably stratified by entropy gradients in the framework of general relativity, assuming ideal magnetohydrodynamics and employing a barotropic equation of state. We first revisit basic equations for describing stably stratified stationary axisymmetric stars containing both poloidal and toroidal magnetic fields. As sample models, the magnetized stars considered by Ioka and Sasaki [23], inside which the magnetic fields are confined, are modified to the ones stably stratified. The magnetized stars newly constructed in this study are believed to be more stable than the existing relativistic models because they have both poloidal and toroidal magnetic fields with comparable strength, and magnetic buoyancy instabilities near the surface of the star, which can be stabilized by the stratification, are suppressed.

We study black hole solutions in extended gravities with higher-order curvature terms, including conformal and Einstein-Weyl gravities. In addition to the usual anti-de Sitter (AdS) vacuum, the theories admit Lifshitz and Schrödinger vacua. The AdS black hole in conformal gravity contains an additional parameter over and above the mass, which may be interpreted as a massive spin-2 hair. By considering the first law of thermodynamics, we find that it is necessary to introduce an associated additional intensive/extensive pair of thermodynamic quantities. We also obtain new Lifshitz black holes in conformal gravity and study their thermodynamics. We use a numerical approach to demonstrate that AdS black holes beyond the Schwarzschild-AdS solution exist in Einstein-Weyl gravity. We also demonstrate the existence of asymptotically Lifshitz black holes in Einstein-Weyl gravity. The Lifshitz black holes arise at the boundary of the parameter ranges for the AdS black holes. Outside the range, the solutions develop naked singularities. The asymptotically AdS and Lifshitz black holes provide an interesting phase transition, in the corresponding boundary field theory, from a relativistic Lorentzian system to a nonrelativistic Lifshitz system.

The detection of gravitational waves from extreme-mass-ratio inspirals (EMRI) binaries, comprising a stellar-mass compact object orbiting around a massive black hole, is one of the main targets for low-frequency gravitational-wave detectors in space, like the Laser Interferometer Space Antenna (LISA) or evolved LISA/New Gravitational Observatory (eLISA/NGO). The long-duration gravitational-waveforms emitted by such systems encode the structure of the strong field region of the massive black hole, in which the inspiral occurs. The detection and analysis of EMRIs will therefore allow us to study the geometry of massive black holes and determine whether their nature is as predicted by general relativity and even to test whether general relativity is the correct theory to describe the dynamics of these systems. To achieve this, EMRI modeling in alternative theories of gravity is required to describe the generation of gravitational waves. However, up to now, only a restricted class of theories has been investigated. In this paper, we explore to what extent EMRI observations with a space-based gravitational-wave observatory like LISA or eLISA/NGO might be able to distinguish between general relativity and a particular modification of it, known as dynamical Chern-Simons modified gravity. Our analysis is based on a parameter estimation study which uses approximate gravitational waveforms obtained via a radiative-adiabatic method. In this framework, the trajectory of the stellar object is modeled as a sequence of geodesics in the spacetime of the modified-gravity massive black hole. The evolution between geodesics is determined by flux formulae based on general relativistic post-Newtonian and black hole perturbation theory computations. Once the trajectory of the stellar compact object has been obtained, the waveforms are computed using the standard multipole formulae for gravitational radiation applied to this trajectory. Our analysis is restricted to a five-dimensional subspace of the EMRI configuration space, including a Chern-Simons parameter which controls the strength of gravitational deviations from general relativity. We find that, if dynamical Chern-Simons modified gravity is the correct theory, an observatory like LISA or even eLISA/NGO should be able to measure the Chern-Simons parameter with fractional errors below 5%. If general relativity is the true theory, these observatories should put bounds on this parameter at the level ${\xi }^{1/4}<{10}^4\mathrm{km}$, which is four orders of magnitude better than current Solar System bounds.

We investigate the importance of choosing good tetrads for the study of the field equations of $f(T)$ gravity. It is well known that this theory is not invariant under local Lorentz transformations, and therefore the choice of tetrad plays a crucial role in such models. Different tetrads will lead to different field equations which in turn have different solutions. We suggest to speak of a good tetrad if it imposes no restrictions on the form of $f(T)$. Employing local rotations, we construct good tetrads in the context of homogeneity and isotropy, and spherical symmetry, where we show how to find Schwarzschild–de Sitter solutions in vacuum. Our principal approach should be applicable to other symmetries as well.

Primordial magnetic fields could provide an explanation for the galactic magnetic fields observed today; in which case, they may leave interesting signals in the CMB and the small-scale matter power spectrum. We discuss how to approximately calculate the important nonlinear magnetic effects within the guise of linear perturbation theory and calculate the matter and CMB power spectra including the Sunyaev-Zel’dovich contribution. We then use various cosmological data sets to constrain the form of the magnetic field power spectrum. Using solely large-scale CMB data (WMAP7, QUaD, and ACBAR) we find a 95% C.L. on the variance of the magnetic field at 1 Mpc of $B_{\lambda }<6.4\mathrm{nG}$. When we include South Pole Telescope data to constrain the Sunyaev-Zel’dovich effect, we find a revised limit of $B_{\lambda }<4.1\mathrm{nG}$. The addition of Sloan Digital Sky Survey Lyman-$\alpha$ data lowers this limit even further, roughly constraining the magnetic field to $B_{\lambda }<1.3\mathrm{nG}$.

Recent cosmological data have provided evidence for a “dark” relativistic background at high statistical significance. Parameterized in terms of the number of relativistic degrees of freedom $N_{\mathrm{eff}}$, however, the current data seem to indicate a higher value than the one expected in the standard scenario based on three active neutrinos. This dark radiation component can be characterized not only by its abundance but also by its clustering properties, as its effective sound speed and its viscosity parameter. It is therefore crucial to study the correlations among the dark radiation properties and key cosmological parameters, as the dark energy equation of state or the running of the scalar spectral index, with current and future cosmic microwave background data. We find that dark radiation with viscosity parameters different from their standard values may be misinterpreted as an evolving dark energy component or as a running spectral index in the power spectrum of primordial fluctuations.

The relationship between observed tracers such as galaxies and the underlying dark matter distribution is crucial in extracting cosmological information. As the linear bias model breaks down at quasilinear scales, the standard perturbative approach of the nonlinear Eulerian bias model is not accurate enough in describing galaxy clustering. In this paper, we discuss such a model in the context of resummed perturbation theory and further generalize it to incorporate the subsequent gravitational evolution by combining with a Lagrangian description of galaxies’ motion. The multipoint propagators we constructed for such a model also exhibit exponential damping similar to their dark matter counterparts; therefore the convergence property of statistics built upon these quantities is improved. This is achieved by applying both Eulerian and Lagrangian resummation techniques of dark matter field developed in recent years. As inherited from the Lagrangian description of galaxy density evolution, our approach automatically incorporates the nonlocality induced by gravitational evolution after the formation of the tracer, and also allows us to include a continuous galaxy formation history by temporally weighted-averaging relevant quantities with the galaxy formation rate.