With the launch of the Gaia mission, general relativity (GR) is now at the very core of astrometry. Given the high level of accuracy of the measurements, the development of a suitable relativistic model for carrying out the correct data processing and analysis has become a critical necessity; its primary goal is to have a consistent set of stellar astrometric parameters by which to map a relativistic kinematic of a large portion of the Milky Way and, therefore, taking the first step of the cosmic distance ladder to higher accuracy. To trace light trajectories back to the emitting stars requires an appropriate treatment of local gravity and a relativistic definition of the observable, according to the measurement protocol of GR, so that astrometry cannot be set apart from fundamental physics. Consequently, the final Gaia outputs, following completion of its operational life, will have important new implications and an overwhelming potential for astrophysical phenomena requiring the highest precision. In this regard, the present work establishes the background GR procedure to treat such relativistic measurements from within the weak gravitational field of the Solar System. In particular, we make the method explicit in the framework of the RAMOD relativistic models, consistent with the IAU (standard) resolutions and, therefore, suitable for validating the GREM approach baselined for Gaia.

We study one loop quantum gravitational corrections to the long range force induced by the exchange of a massless scalar between two massive scalars. The various diagrams contributing to the flat space $S$ matrix are evaluated in a general covariant gauge, and we show that dependence on the gauge parameters cancels at a point considerably before forming the full $S$ matrix, which is unobservable in cosmology. It is possible to interpret our computation as a solution to the effective field equations—which could be done even in cosmology—but taking account of quantum gravitational corrections from the source and from the observer.

We study Born-Infeld gravity coupled to an anisotropic fluid in a static, spherically symmetric background. The free function characterizing the fluid is selected on the following grounds: i) recovery of the Reissner-Nordström solution of General Relativity at large distances, ii) fulfillment of classical energy conditions, and iii) inclusion of models of nonlinear electrodynamics as particular examples. Four branches of solutions are obtained, depending on the signs of two parameters on the gravity and matter sectors. On each branch, we discuss in detail the modifications on the innermost region of the corresponding solutions, which provides a plethora of configurations, including nonsingular black holes and naked objects, wormholes, and de Sitter cores. The regular character of these configurations is discussed according to the completeness of geodesics and the behavior of curvature scalars.

Certain alternative theories of gravity predict that gravitational waves will disperse as they travel from the source to the observer. The recent binary black hole observations by Advanced-LIGO have set limits on a modified dispersion relation from the constraints on their effects on gravitational-wave propagation. Using an identical modified dispersion, of the form $E^2=p^2{c}^2+\mathbb{A}{p}^{\alpha }{c}^{\alpha }$, where $\mathbb{A}$ denotes the magnitude of dispersion and $E$ and $p$ are the energy and momentum of the gravitational wave, we estimate the projected constraints on the modified dispersion from observations of compact binary mergers by third-generation ground-based detectors such as the Einstein Telescope and Cosmic Explorer as well as the space-based detector Laser Interferometer Space Antenna. We find that third-generation detectors would bound dispersion of gravitational waves much better than their second-generation counterparts. The Laser Interferometer Space Antenna, with its extremely good low-frequency sensitivity, would place stronger constraints than the ground-based detectors for $\alpha \le 1$, whereas for $\alpha >1$, the bounds are weaker. We also study the effect of the spins of the compact binary constituents on the bounds.

We calculate the parameters $\gamma$ and $\beta$ in the parametrized post-Newtonian (PPN) formalism for scalar-tensor gravity (STG) with an arbitrary potential, under the assumption that the source matter is given by a nonrotating sphere of constant density, pressure, and internal energy. For our calculation we write the STG field equations in a form which is manifestly invariant under conformal transformations of the metric and redefinitions of the scalar field. This easily shows that also the obtained PPN parameters are invariant under such transformations. Our result is consistent with the expectation that STG is a fully conservative theory, i.e., only $\gamma$ and $\beta$ differ from their general relativity values $\gamma =\beta =1$, which indicates the absence of preferred frame and preferred location effects. We find that the values of the PPN parameters depend on both the radius of the gravitating mass source and the distance between the source and the observer. Most interestingly, we find that also at large distances from the source $\beta$ does not approach $\beta =1$, but receives corrections due to a modified gravitational self-energy of the source. Finally, we compare our result to a number of measurements of $\gamma$ and $\beta$ in the Solar System. We find that in particular measurements of $\beta$ improve the previously obtained bounds on the theory parameters, due to the aforementioned long-distance corrections.

We derive the decay rate of a gauged Q-ball into fermions, applying the leading semiclassical approximation. We find that more particles come out from the surface of a gauged Q-ball, compared to the case of a global Q-ball, due to the electric repulsion. We show, however, that the decay rate of a gauged Q-ball is bounded from above due to the Pauli blocking at the surface of the Q-ball, just as in the case of a global Q-ball. We also find that there is a further suppression due to the Coulomb potential outside the Q-ball, which we find to play the role of a potential barrier for the fermions coming from the inside the Q-ball.

Future high-resolution measurements of the cosmic microwave background (CMB) will produce catalogs of tens of thousands of galaxy clusters through the thermal Sunyaev-Zel’dovich (tSZ) effect. We forecast how well different configurations of a CMB Stage-4 experiment can constrain cosmological parameters, in particular, the amplitude of structure as a function of redshift ${\sigma }_8(z)$, the sum of neutrino masses $\mathrm{\Sigma }{m}_{\nu }$, and the dark energy equation of state $w(z)$. A key element of this effort is calibrating the tSZ scaling relation by measuring the lensing signal around clusters. We examine how the mass calibration from future optical surveys like the Large Synoptic Survey Telescope (LSST) compares with a purely internal calibration using lensing of the CMB itself. We find that, due to its high-redshift leverage, internal calibration gives constraints on cosmological parameters comparable to the optical calibration, and can be used as a cross-check of systematics in the optical measurement. We also show that in contrast to the constraints using the CMB lensing power spectrum, lensing-calibrated tSZ cluster counts can detect a minimal $\mathrm{\Sigma }{m}_{\nu }$ at the $3–5\sigma$ level even when the dark energy equation of state is freed up.

We study the polymer quantization of a homogeneous massive scalar field in the early Universe using a prescription inequivalent to those previously appearing in the literature. Specifically, we assume a Hilbert space for which the scalar field momentum is well defined but its amplitude is not. This is closer in spirit to the quantization scheme of loop quantum gravity, in which no unique configuration operator exists. We show that in the semiclassical approximation, the main effect of this polymer quantization scheme is to compactify the phase space of chaotic inflation in the field amplitude direction. This gives rise to an effective scalar potential closely resembling that of hybrid natural inflation. Unlike polymer schemes in which the scalar field amplitude is well defined, the semiclassical dynamics involves a past cosmological singularity; i.e., this approach does not mitigate the big bang.

We study the second-order perturbations in the Einstein-de Sitter Universe in synchronous coordinates. We solve the second-order perturbed Einstein equation with scalar-tensor and tensor-tensor couplings between 1st-order perturbations, and obtain, for each coupling, the solutions of scalar, vector, and tensor metric perturbations, including both the growing and decaying modes for general initial conditions. We perform general synchronous-to-synchronous gauge transformations up to 2nd order, which are generated by a 1st-order vector field and a 2nd-order vector field, and obtain all the residual gauge modes of the 2nd-order metric perturbations in synchronous coordinates. We show that only the 2nd-order vector field is effective for the 2nd-order transformations that we consider because the 1st-order vector field was already fixed in obtaining the 1st-order perturbations. In particular, the 2nd-order tensor is invariant under 2nd-order gauge transformations using ${\xi }^{(2)\mu }$ only, just like the 1st-order tensor is invariant under 1st-order transformations.

We present a systematic study of the 2nd-order scalar, vector, and tensor metric perturbations in the Einstein-de Sitter Universe in synchronous coordinates. For the scalar-scalar coupling between 1st-order perturbations, we decompose the 2nd-order perturbed Einstein equation into the respective field equations of 2nd-order scalar, vector, and tensor perturbations, and obtain their solutions with general initial conditions. In particular, the decaying modes of solution are included, the 2nd-order vector is generated even if the 1st-order vector is absent, and the solution of the 2nd-order tensor corrects that in literature. We perform general synchronous-to-synchronous gauge transformations up to 2nd order generated by a 1st-order vector field ${\xi }^{(1)\mu }$ and a 2nd-order ${\xi }^{(2)\mu }$. All the residual gauge modes of 2nd-order metric perturbations and density contrast are found, and their number is substantially reduced when the transformed 3-velocity of dust is set to zero. Moreover, we show that only ${\xi }^{(2)\mu }$ is effective in carrying out 2nd-order transformations that we consider, because ${\xi }^{(1)\mu }$ has been used in obtaining the 1st-order perturbations. Holding the 1st-order perturbations fixed, the transformations by ${\xi }^{(2)\mu }$ on the 2nd-order perturbations have the same structure as those by ${\xi }^{(1)\mu }$ on the 1st-order perturbations.

Recent measurements of the Geminga and $\mathrm{B}0656+14$ pulsars by the gamma-ray telescope HAWC (along with earlier measurements by Milagro) indicate that these objects generate significant fluxes of very high-energy electrons. In this paper, we use the very high-energy gamma-ray intensity and spectrum of these pulsars to calculate and constrain their expected contributions to the local cosmic-ray positron spectrum. Among models that are capable of reproducing the observed characteristics of the gamma-ray emission, we find that pulsars invariably produce a flux of high-energy positrons that is similar in spectrum and magnitude to the positron fraction measured by PAMELA and AMS-02. In light of this result, we conclude that it is very likely that pulsars provide the dominant contribution to the long perplexing cosmic-ray positron excess.

We discuss free Dirac fermions rotating uniformly inside a cylindrical cavity in the presence of background magnetic field parallel to the cylinder axis. We show that, in addition to the known bulk states, the system contains massive edge states with the masses inversely proportional to the radius of the cylinder. The edge states appear at quantized threshold values of the fermion mass, which depend on the details of (chiral) MIT boundary conditions imposed at the surface of the cylinder. In the limit of infinite fermion mass, the masses of the edge states remain finite but, generally, nonzero as contrasted to the masses of the bulk states which become infinitely large. The presence of magnetic field affects the spectrum of both bulk and edge modes, and the masses of the edge states may vanish at certain quantized values of magnetic field. The moment of inertia of Dirac fermions is nonmonotonically increasing, oscillating function of magnetic field. The oscillations are well pronounced in a low-temperature domain and disappear at high temperatures. We also show that the edge modes alone do not support the anomalous transport phenomena such as chiral magnetic and chiral vortical effects.

Testing, in a nontrivial, model-independent way, the hypothesis that the three-massive-neutrinos paradigm properly describes nature is among the main goals of the current and the next generation of neutrino oscillation experiments. In the coming decade, the DUNE and Hyper-Kamiokande experiments will be able to study the oscillation of both neutrinos and antineutrinos with unprecedented precision. We explore the ability of these experiments, and combinations of them, to determine whether the parameters that govern these oscillations are the same for neutrinos and antineutrinos, as prescribed by the $CPT$-theorem. We find that both DUNE and Hyper-Kamiokande will be sensitive to unexplored levels of leptonic $CPT$-violation. Assuming the parameters for neutrino and antineutrino oscillations are unrelated, we discuss the ability of these experiments to determine the neutrino and antineutrino mass-hierarchies, atmospheric-mixing octants, and $CP$-odd phases, three key milestones of the experimental neutrino physics program. Additionally, if the $CPT$-symmetry is violated in nature in a way that is consistent with all present neutrino and antineutrino oscillation data, we find that DUNE and Hyper-Kamiokande have the potential to ultimately establish leptonic $CPT$-invariance violation.

We propose an extension of the standard model introducing large $SU(2{)}_L$ multiplet fields which are quartet and septet scalars and quintet Majorana fermions. These multiplets can induce the neutrino masses via interactions with the $SU(2)$ doublet leptons. We then find the neutrino masses are suppressed by a small vacuum expectation value of the quartet/septet and an inverse of the quintet fermion mass, relaxing the Yukawa hierarchies among the standard model fermions. We also discuss collider physics at the Large Hadron Collider, considering the production of charged particles in these multiplets, and due to the effects of violating the custodial symmetry, some specific signatures can be found. Then, we discuss the detectability of these signals.

We analyze the phenomenology of a model of neutrino masses inspired by unification in ${\mathrm{E}}_6$ in which the exotic neutrinos can be present at low scales. The model introduces vector-like isosinglet down-type quarks, vector-like isodoublet leptons, neutrino singlets and two $Z^{\prime }$ bosons. The seesaw mechanism can be achieved with exotic neutrino masses as low as 100 GeV and Yukawa couplings of order ${10}^{-3}$. We find that the lightest $Z^{\prime }$ boson mass is required to be above 2.8 TeV, the exotic quark masses are required to be above 1.3 TeV (810 GeV) if they are collider stable (promptly decaying), and the exotic lepton mass bounds remain at the LEP value of 102 GeV. The model also presents a type-II two-Higgs-doublet model (2HDM) along with two heavy singlet scalars. The 2HDM naturally has the alignment limit enforced thanks to the large vacuum expectation values of the exotic scalars, thereby avoiding most constraints.

We show that the Casimir effect may lead to a deconfinement phase transition induced by the presence of boundaries in confining gauge theories. Using first-principle numerical simulations we demonstrate this phenomenon in the simplest case of the compact lattice electrodynamics in two spatial dimensions. We find that the critical temperature of the deconfinement transition in the vacuum between two parallel dielectric/metallic wires is a monotonically increasing function of the separation between the wires. At infinite separation the wires do not affect the critical temperature while at small separations the vacuum between the wires loses the confinement property due to modification of vacuum fluctuations of virtual monopoles.

Forward Drell-Yan production at high energy can provide important constraints on gluon densities at small $x$, in the saturation regime. In this work, we focus on the nuclear modification of this process, which could be measured at the LHC in the near future. For this, we employ the color dipole approach, using the optical Glauber model to relate the dipole cross section of a nucleus to the one of a proton. Combining these results with our earlier results for forward $J/\psi$ production, we compute the ratio of the nuclear modification factors of these two processes. This observable was recently suggested as a way to distinguish between initial and final state effects in forward particle production.

We determine the nucleon neutral weak electromagnetic form factors $G_{E,M}^{Z,p(n)}$ by combining results from light-front holographic QCD and lattice QCD calculations. We deduce nucleon electromagnetic form factors from light-front holographic QCD which provides a good parametrization of the experimental data of the nucleon electromagnetic form factors in the entire momentum transfer range and isolate the strange quark electromagnetic form factors $G_{E,M}^s$ using lattice QCD. From these calculations, we obtain precise estimates of the neutral weak form factors in the momentum transfer range of $0{\mathrm{GeV}}^2\le Q^2\le 0.5{\mathrm{GeV}}^2$. From the lattice QCD calculation, we present $Q^2$-dependence of the strange quark form factors. We also deduce the neutral weak Dirac and Pauli form factors $F_{1,2}^{Z,p(n)}$ of the proton and the neutron.

Tests of lepton-universality as rate ratios in $b\to s\ell \ell$ transitions can be predicted very accurately in the Standard Model. The deficits with respect to expectations reported by the LHCb experiment in muon-to-electron ratios of the $B\to K^{(*)}\ell \ell$ decay rates thus point to genuine manifestations of lepton nonuniversal new physics. In this paper, we analyze these measurements in the context of effective field theory. First, we discuss the interplay of the different operators in $R_K$ and $R_{K^{*}}$ and provide predictions for $R_{K^{*}}$ in the Standard Model and in new-physics scenarios that can explain $R_K$. We also provide approximate numerical formulas for these observables in bins of interest as functions of the relevant Wilson coefficients. Secondly, we perform frequentist fits to $R_K$ and $R_{K^{*}}$. The Standard Model disagrees with these measurements at $3.7\sigma$ significance. We find excellent fits in scenarios with combinations of ${\mathcal{O}}_{9(10)}^{\ell }=\overline{s}{\gamma }^{\mu }{b}_L\ell {\gamma }_{\mu }({\gamma }_5)\ell$ operators, with pulls relative to the Standard Model in the region of $4\sigma$. An important conclusion of our analysis is that a lepton-specific contribution to ${\mathcal{O}}_{10}$ is important to understand the data. Under the hypothesis that new-physics couples selectively to the muons, we also present fits to other $b\to s\mu \mu$ data with a conservative error assessment and comment on more general scenarios. Finally, we discuss new lepton universality ratios that, if new physics is the origin of the observed discrepancy, should contribute to the statistically significant discovery of new physics in the near future.

We perform a comprehensive analysis of electroweak, QED, and mixed QCD-electroweak corrections underlying the precise measurement of the $W$-boson mass $M_W$ at hadron colliders. By applying a template fitting technique, we detail the impact on $M_W$ of next-to-leading order electroweak and QCD corrections, multiple photon emission, lepton pair radiation, and factorizable QCD-electroweak contributions. As a by-product, we provide an up-to-date estimate of the main theoretical uncertainties of perturbative nature. Our results can serve as a guideline for the assessment of the theoretical systematics at the Tevatron and LHC and allow a more robust precision measurement of the $W$-boson mass at hadron colliders.