We construct the external metric of a slowly rotating, tidally deformed material body in general relativity. The tidal forces acting on the body are assumed to be weak and to vary slowly with time, and the metric is obtained as a perturbation of a background metric that describes the external geometry of an isolated, slowly rotating body. The tidal environment is generic and characterized by two symmetric trace-free tidal moments ${\mathcal{E}}_{ab}$ and ${\mathcal{B}}_{ab}$, and the body is characterized by its mass $M$, its radius $R$, and a dimensionless angular-momentum vector ${\chi }^a\ll 1$. The perturbation accounts for all couplings between ${\chi }^a$ and the tidal moments. The body’s gravitational response to the applied tidal field is measured in part by the familiar gravitational Love numbers $K_2^{\text{el}}$ and $K_2^{\text{mag}}$, but we find that the coupling between the body’s rotation and the tidal environment requires the introduction of four new quantities, which we designate as rotational-tidal Love numbers. All these Love numbers are gauge invariant in the usual sense of perturbation theory, and all vanish when the body is a black hole.

We study weak-field solutions having spherical symmetry in $f(T)$ gravity; to this end, we solve the field equations for a nondiagonal tetrad, starting from Lagrangian in the form $f(T)=T+\alpha T^n$, where $\alpha$ is a small constant, parametrizing the departure of the theory from general relativity. We show that the classical spherically symmetric solutions of general relativity, i.e., the Schwarzschild and Schwarzschild–de Sitter solutions, are perturbed by terms in the form $\propto r^{2-2n}$ and discuss the impact of these perturbations in observational tests.

In this work we investigate the existence of relativistic models for dark matter in the context of bimetric gravity, used here to reproduce the modified Newtonian dynamics (MOND) at galactic scales. For this purpose we consider two different species of dark matter particles that separately couple to the two metrics of bigravity. These two sectors are linked together via an internal $U(1)$ vector field, and some effective composite metric built out of the two metrics. Among possible models only certain classes of kinetic and interaction terms are allowed without invoking ghost degrees of freedom. Along these lines we explore the number of allowed kinetic terms in the theory and point out the presence of ghosts in a previous model. Finally, we propose a promising class of ghost-free candidate theories that could provide the MOND phenomenology at galactic scales while reproducing the standard cold dark matter model at cosmological scales.

We examine the impact of a nonminimal coupling of the inflaton to the Ricci scalar, $\frac{1}{2}\xi R{\varphi }^2$, on the inflationary predictions. Such a nonminimal coupling is expected to be present in the inflaton Lagrangian on fairly general grounds. As a case study, we focus on the simplest inflationary model governed by the potential $V\propto {\varphi }^2$, using the latest combined 2015 analysis of Planck and the $\mathrm{BICEP}2/Keck$ Array. We find that the presence of a coupling $\xi$ is favored at a significance of 99% C.L., assuming that nature has chosen the potential $V\propto {\varphi }^2$ to generate the primordial perturbations and a number of $e$-foldings $N=60$. Within the context of the same scenario, we find that the value of $\xi$ is different from zero at the $2\sigma$ level. When considering the cross-correlation polarization spectra from the $\mathrm{BICEP}2/Keck$ Array and Planck, a value of $r=0.038_{-0.030}^{+0.039}$ is predicted in this particular nonminimally coupled scenario. Future cosmological observations may therefore test these values of $r$ and verify or falsify the nonminimally coupled model explored here.

We consider an extension of the Standard Model with an arbitrary number $N$ of Higgs doublets (NHDM) and calculate their contribution to the oblique parameters $S$ and $T$. We examine the possible limitations on $N$ from precision measurements of these parameters. In view of the complexity of the general case of NHDM, we analyze several benchmark scenarios for the Higgs mass spectrum, identifying the lightest $CP$-even Higgs with the Higgs-like particle recently observed at the LHC with the mass of $\sim 125\mathrm{GeV}$. The rest of the Higgses are put above the mass scale of $\sim 600\mathrm{GeV}$, below which the LHC experiments do not detect any Higgs-like signals except for the former famous one. We show that, in a scenario with all the heavy Higgses degenerate at any scale, there are no limitations on the number $N$ of the Higgs doublets. However, upper limits appear for certain not completely degenerate configurations of the heavy Higgses.

We consider multiparticle contributions to nucleon two- and three-point functions from the perspective of chiral dynamics. Lattice nucleon interpolating operators, which have definite chiral transformation properties, can be mapped into chiral perturbation theory. Using the most common of such operators, we determine pion-nucleon and pion-delta couplings to nucleon two- and three-point correlation functions at leading order in the low-energy expansion. The couplings of pions to nucleons and deltas in two-point functions are consistent with simple phase-space considerations, in accordance with the Lehmann spectral representation. An argument based on available phase space on a torus is utilized to derive the scaling of multiple-pion couplings. While multipion states are indeed suppressed, this suppression scales differently with particle number compared to that in infinite volume. For nucleon three-point correlation functions, we investigate the axial-vector current at vanishing momentum transfer. The effect of pion-nucleon and pion-delta states on the extraction of the nucleon axial charge is assessed. We show that couplings to finite volume multiparticle states could potentially lead to overestimation of the axial charge. Hence pion-nucleon excited states cannot explain the trend seen in lattice QCD calculations of the nucleon axial charge.

In $2+1$ flavor lattice QCD, the spectrum of the nucleon is presented for both parities using local meson-baryon-type interpolating fields in addition to the standard three-quark nucleon interpolators. The role of local five-quark operators in extracting the nucleon excited-state spectrum via correlation matrix techniques is explored on dynamical gauge fields with $m_{\pi }=293\mathrm{MeV}$, leading to the observation of a state in the region of the noninteracting S-wave $N\pi$ scattering threshold in the negative-parity sector. Furthermore, the robustness of the variational technique is examined by studying the spectrum on a variety of operator bases. Fitting a single-state ansatz to the eigenstate-projected correlators provides robust energies for the low-lying spectrum that are essentially invariant despite being extracted from qualitatively different bases.

We investigate existing and future hadron-collider constraints on the top dipole chromomagnetic and chromoelectric moments, two quantities that are expected to be modified in the presence of new physics. We focus first on recent measurements of the inclusive top pair production cross section at the Tevatron and at the Large Hadron Collider. We then analyze the role of top-antitop events produced at very large invariant masses, in the context of the forthcoming 13–14 TeV runs of the LHC, and at a future 100 TeV proton-proton collider. In this latter case, the selection of semileptonic decays to hard muons allows to tag top quarks boosted to the multi-TeV regime, strongly reducing the QCD backgrounds and leading to a significant improvement in the sensitivity to anomalous top couplings.

In this paper, we reconsider the single-interval Rényi entropy of a free compact scalar on a torus. In this case, the contribution to the entropy could be decomposed into a classical part and a quantum part. The classical part includes the contribution from all the saddle points, while the quantum part is universal. After considering a different monodromy condition from the one in the literature, we reevaluate the classical part of the Rényi entropy. Moreover, we expand the entropy in the low-temperature limit and find the leading thermal correction term, which is consistent with the universal behavior suggested in [J. Cardy and C. P. Herzog, Phys. Rev. Lett. 112, 171603 (2014)]. Furthermore, we investigate the large-interval behavior of the entanglement entropy and show that the universal relation between the entanglement entropy and thermal entropy holds in this case.

We derive an analytical expression for extracting the gravitational waveforms at null infinity using the Weyl scalar ${\psi }_4$ measured at a finite radius. Our expression is based on a series solution in orders of $1/r$ to the equations for gravitational perturbations about a spinning black hole. We compute this expression to order $1/r^2$ and include the spin parameter $a$ of the Kerr background. We test the accuracy of this extraction procedure by measuring the waveform for a merging black-hole binary at ten different extraction radii (in the range $r/M=75–190$ and for three different resolutions in the convergence regime. We find that the extraction formula provides a set of values for the radiated energy and momenta that at finite extraction radii converges towards the expected values with increasing resolution, which is not the case for the “raw” waveform at finite radius. We also examine the phase and amplitude errors in the waveform as a function of observer location and again observe the benefits of using our extraction formula. The leading corrections to the phase are $\mathcal{O}(1/r)$ and to the amplitude are $\mathcal{O}(1/r^2)$. This method provides a simple and practical way of estimating the waveform at infinity, and may be especially useful for scenarios such as well separated binaries, where the radiation zone is far from the sources, that would otherwise require extended simulation grids in order to extrapolate the raw waveform to infinity. Thus this method saves important computational resources and provides an estimate of errors.

We explore the possibility of very long-lived gravitational-wave transients (and detector artifacts) lasting hours to weeks. Such very long signals are both interesting in their own right and as a potential source of systematic error in searches for persistent signals, e.g., from a stochastic gravitational-wave background. We review possible mechanisms for emission on these time scales and discuss computational challenges associated with their detection: namely, the substantial volume of data involved in a search for very long transients can require vast computer memory and processing time. These computational difficulties can be addressed through a form of data compression known as coarse graining, in which information about narrow frequency bins is discarded in order to reduce the computational requirements of a search. Using data compression, we demonstrate an efficient radiometer (cross-correlation) algorithm for the detection of very long transients. In the process, we identify features of a very long transient search (related to the rotation of the Earth) that make it more complicated than a search for shorter transient signals. We implement suitable solutions.

In a previous work [Amendola et al., Phys. Rev. D 86, 063515 (2012)], principal component analysis based methods to constrain the dark energy equation of state using type Ia supernovae and other low redshift probes were extended to spectroscopic tests of the stability fundamental couplings, which can probe higher redshifts. Here we use them to quantify the gains in sensitivity obtained by combining spectroscopic measurements expected from ESPRESSO at the Very Large Telescope and the high-resolution ultrastable spectrograph for the E-ELT (European Extremely Large Telescope; known as ELT-HIRES) with future supernova surveys. In addition to simulated low and intermediate redshift supernova surveys, we assess the dark energy impact of high-redshift supernovae detected by the James Webb Space Telescope and characterized by the E-ELT or the Thirty Meter Telescope. Our results show that a detailed characterization of the dark energy properties beyond the acceleration phase (i.e., deep in the matter era) is viable and may reach as deep as redshift 4.

Rubano and Barrow have discussed the emergence of a dark energy, with late-time cosmic acceleration arising from a self-interacting homogeneous scalar field with a potential of hyperbolic power type. Here, we study the evolution of this scalar-field potential back in the inflationary era. Using the hyperbolic power potential in the framework of inflation, we find that the main slow-roll parameters, like the scalar spectral index, the running of the spectral index and the tensor-to-scalar fluctuation ratio can be computed analytically. Finally, in order to test the viability of this hyperbolic scalar-field model at the early stages of the Universe, we compare the predictions of that model with the latest observational data, namely Planck 2015.

Late-time power law expansion has been proposed as an alternative to the standard cosmological model and shown to be consistent with some low-redshift data. We test power law expansion against the standard flat $\mathrm{\Lambda }\mathrm{CDM}$ cosmology using goodness-of-fit and model comparison criteria. We consider type Ia supernova (SN Ia) data from two current compilations (JLA and Union2.1) along with a current set of baryon acoustic oscillation (BAO) measurements that includes the high-redshift Lyman-$\alpha$ forest measurements from BOSS quasars. We find that neither power law expansion nor $\mathrm{\Lambda }\mathrm{CDM}$ is strongly preferred over the other when the SN Ia and BAO data are analyzed separately but that power law expansion is strongly disfavored by the combination. We treat the $R_{\mathrm{h}}=ct$ cosmology (a constant rate of expansion) separately and find that it is conclusively disfavored by all combinations of data that include SN Ia observations and a poor overall fit when systematic errors in the SN Ia measurements are ignored, despite a recent claim to the contrary. We discuss this claim and some concerns regarding hidden model dependence in the SN Ia data.

We point out that the (pseudo)conformal universe scenario may be realized as the decay of a conformally invariant, metastable vacuum, which proceeds via spontaneous nucleation and subsequent growth of a bubble of a putative new phase. We study perturbations about the bubble and show that their leading late-time properties coincide with those inherent in the original models with homogeneously rolling backgrounds. In particular, the perturbations of a spectator dimension-zero field have a flat power spectrum.

White dwarfs (WD) capture dark matter (DM) as they orbit within their host halos. These captured particles may subsequently annihilate, heating the stellar core and preventing the WD from cooling. The potential wells of WDs are considerably deeper and core temperatures significantly cooler than those of main sequence stars. Consequently, DM evaporation is less important in WDs and DM with masses $M_{\chi }\gtrsim 100\mathrm{keV}$, and annihilation cross sections orders of magnitude below the canonical thermal cross section ($⟨{\sigma }_{\mathrm{a}}\mathrm{v}⟩\gtrsim 10^{-46}{\mathrm{cm}}^3/\mathrm{s}$) can significantly alter WD cooling in particular astrophysical environments. We consider WDs in globular clusters (GCs) and dwarf galaxies. If the parameters of the DM particle are known, then the temperature of the coolest WD in a GC can be used to constrain the DM density of the cluster’s halo (potentially even ruling out the presence of a halo if the inferred density is of order the ambient Galactic density). Recently, several direct detection experiments have seen signals whose origins might be due to low mass DM. In this paper, we show that if these claims from CRESST, DAMA, CDMS-Si, and CoGeNT could be interpreted as DM, then observations of NGC 6397 limit the fraction of DM in that cluster to be $f_{\mathrm{DM}}\lesssim 10^{-3}$. This would be an improvement over existing constraints of 3 orders of magnitude and would clearly rule out a significant DM halo for this cluster. More generally, we show how such observations constrain combinations of DM and GC properties. Building on previous work, we also show how observations of WDs in dwarf galaxies, such as Segue I, can provide novel constraints on low-mass DM or DM with very low contemporary annihilation cross sections as may be realized in models in which $s$-wave annihilation is suppressed and $p$-wave annihilation dominates. This paper provides further motivation for high-quality observations of stellar populations as a probe of dark matter.

We explore the implications of the $t\text{−}b\text{−}\tau$ (and $b\text{−}\tau$) Yukawa coupling unification condition on the fundamental parameter space and sparticle spectroscopy in the minimal gauge mediated supersymmetry breaking model. We find that this scenario prefers values of the $CP$-odd Higgs mass $m_A\gtrsim 1\mathrm{TeV}$, with all colored sparticle masses above 3 TeV. These predictions will be hard to test at LHC13 but they may be testable at the high-energy LHC (HE-LHC) 33 TeV or a 100 TeV collider. Both the $t\text{−}b\text{−}\tau$ and the $b\text{−}\tau$ Yukawa coupling unification prefer a relatively light gravitino with mass $\lesssim 30\mathrm{eV}$, which makes it a candidate hot dark matter particle. However, it cannot account for more than 15% of the observed dark matter density.

We examine a simple composite Higgs model (CHM) with vector resonances in addition to the Standard Model (SM) fields in perturbation theory by using the $K$-matrix method to implement unitarity constraints. We find that the $W_L{W}_L$ scattering amplitude has an additional scalar pole (analogous to the $\sigma$ meson of QCD) as in generic strongly interacting extensions of the SM. The mass and width of this dynamically generated scalar resonance are large and the mass behaves contrary to the vector one, so that when the vector resonance is lighter, the scalar one is heavier, and vice versa. We also attempt an interpretation of this new resonance. Altogether, the presence of the vector state with the symmetries of the CHM improve the low-energy unitarity behavior also in the scalar-isoscalar channel.

We study the possible significance of four-quark states in the isosinglet scalar mesons ($J^{PC}=0^{++}$, $I=0$) by performing two-flavor full lattice QCD simulations on an $8^3\times 16$ lattice using the improved gauge action and the clover-improved Wilson quark action. In particular, we evaluate the propagators of molecular and tetraquark operators together with singly disconnected diagrams. In the computation of the singly disconnected diagrams we employ the $Z_2$-noise method with the truncated eigenmode approach. We show that the quark loops given by the disconnected diagrams play an essential role in propagators of tetraquark and molecular operators.

Canonical partition functions and Lee-Yang zeros of QCD at finite density and high temperature are studied. Recent lattice simulations confirm that the free energy of QCD is a quartic function of quark chemical potential at temperature slightly above pseudocritical temperature $T_c$, as in the case with a gas of free massless fermions. We present analytic derivation of the canonical partition functions and Lee-Yang zeros for this type of free energy using the saddle point approximation. We also perform lattice QCD simulation in a canonical approach using the fugacity expansion of the fermion determinant and carefully examine its reliability. By comparing the analytic and numerical results, we conclude that the canonical partition functions follow the Gaussian distribution of the baryon number, and the accumulation of Lee-Yang zeros of these canonical partition functions exhibit the first-order Roberge-Weiss phase transition. We discuss the validity and applicable range of the result and its implications both for theoretical and experimental studies.