We introduce a new loop expansion that provides a resolution of the identity in the Hilbert space of loop quantum gravity on a fixed graph. We work in the bosonic representation obtained by the canonical quantization of the spinorial formalism. The resolution of the identity gives a tool for implementing the projection of states in the full bosonic representation onto the space of solutions to the Gauss and area matching constraints of loop quantum gravity. This procedure is particularly efficient in the semiclassical regime, leading to explicit expressions for the loop expansions of coherent, heat kernel and squeezed states.

We provide a simple derivation of the equivalence between Einstein and conformal gravity (CG) with Neumann boundary conditions given by Maldacena. As Einstein spacetimes are Bach flat, a generic solution to CG would contain both Einstein and non-Einstein parts. Using this decomposition of the spacetime curvature in the Weyl tensor makes manifest the equivalence between the two theories, both at the level of the action and the variation of it. As a consequence, we show that the on-shell action for critical gravity in four dimensions is given uniquely in terms of the Bach tensor.

We address the astrophysical imaging of a family of deformed Kerr black holes (BHs). These are stationary, asymptotically flat BH spacetimes that are solutions of general relativity minimally coupled to a massive, complex scalar field: Kerr BHs with scalar hair (KBHsSH). Such BHs bifurcate from the vacuum Kerr solution and can be regarded as a horizon within a rotating boson star. In a recent letter [P. V. P. Cunha, C. A. R. Herdeiro, E. Radu, and H. F. Rúnarsson, Phys. Rev. Lett. 115, 211102 (2015).], it was shown that KBHsSH can exhibit very distinct shadows from the ones of their vacuum counterparts. The setup therein, however, considers the light source to be a celestial sphere sufficiently far away from the BH. Here, we analyze KBHsSH surrounded by an emitting torus of matter simulating a more realistic astrophysical environment, and study the corresponding lensing of light as seen by a very faraway observer, to appropriately model ground-based observations of Sgr ${\mathrm{A}}^{*}$. We find that the differences in imaging between KBHsSH and comparable vacuum Kerr BHs remain, albeit less dramatic than those observed for the corresponding shadows in the previous setup. In particular, we highlight two observables that might allow differentiating KBHsSH and Kerr BHs. The first is the angular size of the photon ring (in a Kerr spacetime) or lensing ring (in a KBHSH spacetime), the latter being significantly smaller for sufficiently non-Kerr-like spacetimes. The second is the existence of an edge in the intensity distribution (the photon ring in Kerr spacetime). This edge can disappear for very non-Kerr-like KBHsSH. It is plausible, therefore, that sufficiently precise very long baseline interferometric observations of BH candidates can constrain this model.

By applying loop quantum gravity techniques to 3D gravity with a positive cosmological constant $\mathrm{\Lambda }$, we show how the local gauge symmetry of the theory, encoded in the constraint algebra, acquires the quantum group structure of ${\mathfrak{so}}_q(4)$, with $q=\exp (i\hslash \sqrt{\mathrm{\Lambda }}/2\kappa )$. By means of an Inonu-Wigner contraction of the quantum group bi-algebra, keeping $\kappa$ finite, we obtain the kappa-Poincaré algebra of the flat quantum spacetime symmetries.

We calculate the energy and angular-momentum fluxes across the event horizon of a tidally deformed, rapidly rotating black hole to next-to-leading order in the curvature of the external spacetime. These are expressed in terms of tidal quadrupole moments and their time derivatives, which provide a characterization of a generic tidal environment. As an application of our results, we provide an expression for the energy and angular-momentum fluxes across the horizon when the black hole is a member of a binary system on a slowly moving, quasicircular orbit. Our expressions are accurate to 1.5 post-Newtonian order beyond the leading-order fluxes, but they are valid for arbitrary mass ratios. We compare our results to those previously obtained in the case of an extreme mass ratio binary, and find that they do not agree at the 1.5 post-Newtonian order. We investigate a number of possible sources for this discrepancy, but are ultimately unable to resolve it.

A gravitational theory of a scalar field nonminimally coupled with torsion and a boundary term is considered with the aim to construct Lorentzian wormholes. Geometrical parameters including shape and redshift functions are obtained for these solutions. We adopt the formalism of the Noether gauge symmetry approach in order to find symmetries, Lie brackets and invariants (conserved quantities). Furthermore by imposing specific forms of potential function, we are able to calculate metric coefficients and discuss their geometrical behavior.

Following previous works on generalized Abelian Proca theory, also called vector Galileon, we investigate the massive extension of an SU(2) gauge theory, i.e., the generalized SU(2) Proca model, which could be dubbed non-Abelian vector Galileon. This particular symmetry group permits fruitful applications in cosmology such as inflation driven by gauge fields. Our approach consists in building, in an exhaustive way, all the Lagrangians containing up to six contracted Lorentz indices. For this purpose, and after identifying by group theoretical considerations all the independent Lagrangians which can be written at these orders, we consider the only linear combinations propagating 3 degrees of freedom and having healthy dynamics for their longitudinal mode, i.e., whose pure Stückelberg contribution turns into the SU(2) multi-Galileon dynamics. Finally, and after having considered the curved space-time expansion of these Lagrangians, we discuss the form of the theory at all subsequent orders.

Charged massive scalar field perturbations are studied in the gravitational, electromagnetic, dilaton, and axion fields of rotating linear dilaton black holes. In this geometry, we separate the covariant Klein-Gordon equation into radial and angular parts and obtain the exact solutions of both the equations in terms of the confluent Heun functions. Using the radial solution, we study the problems of resonant frequencies, entropy/area quantization, and greybody factor. We also analyze the behavior of the wave solutions near the event horizon of the rotating linear dilaton black hole and derive its Hawking temperature via the Damour-Ruffini-Sannan method.

We present a natural generalization of holographic entanglement entropy proposals beyond the scope of $\mathrm{AdS}/\mathrm{CFT}$ by anchoring extremal surfaces to holographic screens. Holographic screens are a natural extension of the AdS boundary to arbitrary spacetimes and are preferred codimension-1 surfaces from the viewpoint of the covariant entropy bound. A broad class of screens have a unique preferred foliation into codimension-2 surfaces called leaves. Our proposal is to find the areas of extremal surfaces anchored to the boundaries of regions in leaves. We show that the properties of holographic screens are sufficient to prove, under generic conditions, that extremal surfaces anchored in this way always lie within a causal region associated with a given leaf. Within this causal region, a maximin construction similar to that of Wall proves that our proposed quantity satisfies standard properties of entanglement entropy like strong subadditivity. We conjecture that our prescription computes entanglement entropies in quantum states that holographically define arbitrary spacetimes, including those in a cosmological setting with no obvious boundary on which to anchor extremal surfaces.

The dark sector is described by an additional barotropic fluid which evolves adiabatically during the Universe’s history and whose adiabatic exponent $\gamma$ is derived from the standard definitions of specific heats. Although in general $\gamma$ is a function of the redshift, the Hubble parameter and its derivatives, we find that our assumptions lead necessarily to solutions with $\gamma =\text{constant}$ in a Friedmann-Lemaître-Robertson-Walker universe. The adiabatic fluid acts effectively as the sum of two distinct components, one evolving like nonrelativistic matter and the other depending on the value of the adiabatic index. This makes the model particularly interesting as a way of simultaneously explaining the nature of both dark energy and dark matter, at least at the level of the background cosmology. The $\mathrm{\Lambda }\mathrm{CDM}$ model is included in this family of theories when $\gamma =0$. We fit our model to supernovae Ia, $H(z)$ and baryonic acoustic oscillation data, discussing the model selection criteria. The implications for the early Universe and the growth of small perturbations in this model are also discussed.

We consider the process of magnetogenesis in the context of nonsingular bounce cosmology. We show that large primordial magnetic fields can be generated during contraction without encountering strong coupling and backreaction issues. The fields may seed large-scale magnetic fields with observationally interesting strengths. This result leads to a theoretical constraint on the relation of the energy scale of the bounce cosmology to the number of effective $e$-foldings of the contracting phase in the case of scale invariance for the power spectrum of primordial magnetic fields. We show that this constraint can be satisfied in a sizable region of the parameter space for the nonsingular bounce cosmology.

We propose a novel scenario to produce abundant primordial black holes (PBHs) in new inflation which is a second phase of a double inflation in the supergravity framework. In our model, some preinflation phase before the new inflation is assumed and it would be responsible for the primordial curvature perturbations on the cosmic microwave background scale, while the new inflation produces only the small scale perturbations. Our new inflation model has linear, quadratic, and cubic terms in its potential and PBH production corresponds with its flat inflection point. The linear term can be interpreted to come from a supersymmetry-breaking sector, and with this assumption, the vanishing cosmological constant condition after inflation and the flatness condition for the inflection point can be consistently satisfied.

The most recent measurements of the temperature and low-multipole polarization anisotropies of the cosmic microwave background from the Planck satellite, when combined with galaxy clustering data from the Baryon Oscillation Spectroscopic Survey in the form of the full shape of the power spectrum, and with baryon acoustic oscillation measurements, provide a 95% confidence level (C.L.) upper bound on the sum of the three active neutrinos $\sum m_{\nu }<0.183\mathrm{eV}$, among the tightest neutrino mass bounds in the literature, to date, when the same data sets are taken into account. This very same data combination is able to set, at $\sim 70\%$ C.L., an upper limit on $\sum m_{\nu }$ of 0.0968 eV, a value that approximately corresponds to the minimal mass expected in the inverted neutrino mass hierarchy scenario. If high-multipole polarization data from Planck is also considered, the 95% C.L. upper bound is tightened to $\sum m_{\nu }<0.176\mathrm{eV}$. Further improvements are obtained by considering recent measurements of the Hubble parameter. These limits are obtained assuming a specific nondegenerate neutrino mass spectrum; they slightly worsen when considering other degenerate neutrino mass schemes. Low-redshift quantities, such as the Hubble constant or the reionization optical depth, play a very important role when setting the neutrino mass constraints. We also comment on the eventual shifts in the cosmological bounds on $\sum m_{\nu }$ when possible variations in the former two quantities are addressed.

We propose an improved methodology to constrain spatial variations of the fine structure constant using clusters of galaxies. We use the Planck 2013 data to measure the thermal Sunyaev-Zeldovich effect at the location of 618 x-ray selected clusters. We then use a Monte Carlo Markov Chain algorithm to obtain the temperature of the cosmic microwave background at the location of each galaxy cluster. When fitting three different phenomenological parametrizations allowing for monopole and dipole amplitudes in the value of the fine structure constant we improve the results of earlier analysis involving clusters and the cosmic microwave background power spectrum, and we also find that the best-fit direction of a hypothetical dipole is compatible with the direction of other known anomalies. Although the constraining power of our current data sets do not allow us to test the indications of a fine structure constant dipole obtained though high-resolution optical/UV spectroscopy, our results do highlight that clusters of galaxies will be a very powerful tool to probe fundamental physics at low redshift.

The geosynchronous Laser Interferometer Space Antenna (gLISA) is a space-based gravitational wave (GW) mission that, for the past 5 years, has been under joint study at the Jet Propulsion Laboratory; Stanford University; the National Institute for Space Research (I.N.P.E., Brazil); and Space Systems Loral. If flown at the same time as the LISA mission, the two arrays will deliver a joint sensitivity that accounts for the best performance of both missions in their respective parts of the millihertz band. This simultaneous operation will result in an optimally combined sensitivity curve that is “white” from about $3\times {10}^{-3}\mathrm{Hz}$ to 1 Hz, making the two antennas capable of detecting, with high signal-to-noise ratios (SNRs), coalescing black-hole binaries (BHBs) with masses in the range $(10-10^8)M_{\odot }$. Their ability of jointly tracking, with enhanced SNR, signals similar to that observed by the Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO) on September 14, 2015 (the GW150914 event) will result in a larger number of observable small-mass binary black holes and an improved precision of the parameters characterizing these sources. Together, LISA, gLISA and aLIGO will cover, with good sensitivity, the $({10}^{-4}-10^3)\mathrm{Hz}$ frequency band.

Models of strongly interacting theories with a large mass anomalous dimension (${\gamma }_m$) provide an interesting possibility for the dynamical origin of the electroweak symmetry breaking. A laboratory for these models is QCD with many flavors, which may present a nontrivial fixed point associated to a conformal region. Studies based on conformal field theories and on Schwinger-Dyson equations have suggested the existence of bounds on the mass anomalous dimension at the fixed points of these models. In this note we discuss ${\gamma }_m$ values of multiflavor QCD exhibiting a nontrivial fixed point and affected by relevant four-fermion interactions.

In the minimal supersymmetric standard model (MSSM), the tension between the observed Higgs boson mass and the experimental result of the muon $g-2$ measurement requires a large mass splitting between stops and smuons/charginos/neutralinos. We consider a five-dimensional (5D) framework of the MSSM with the Randall-Sundrum warped background metric, and show that such a mass hierarchy is naturally achieved in terms of geometry. In our setup, the supersymmetry is broken at the ultraviolet (UV) brane, while all the MSSM multiplets reside in the 5D bulk. An appropriate choice of the bulk mass parameters for the MSSM matter multiplets can naturally realize the sparticle mass hierarchy desired to resolve the tension. The gravitino is localized at the UV brane and hence becomes very heavy, while the gauginos spreading over the bulk acquire their masses suppressed by the fifth dimensional volume. As a result, the lightest sparticle neutralino is a candidate for the dark matter as usual in the MSSM. In addition to reproducing the SM-like Higgs boson mass of around 125 GeV and the measured value of the muon $g-2$, we consider a variety of phenomenological constraints, and present the benchmark particle mass spectra that can be explored at the LHC Run-2 in the near future.

We systematically elucidate differences and similarities of the vacuum alignment issue in composite and renormalizable elementary extensions of the Standard Model featuring a pseudo-Goldstone Higgs. We also provide general conditions for the stability of the vacuum in the elementary framework, thereby extending previous studies of the vacuum alignment.