We analytically compute, to the eight-and-a-half post-Newtonian order, and to linear order in the mass ratio, the radial potential describing (within the effective one-body formalism) the gravitational interaction of two bodies, thereby extending previous analytic results. These results are obtained by applying analytical gravitational self-force theory (for a particle in circular orbit around a Schwarzschild black hole) to Detweiler’s gauge-invariant redshift variable. We emphasize the increase in “transcendentality” of the numbers entering the post-Newtonian expansion coefficients as the order increases, in particular we note the appearance of $\zeta (3)$ (as well as the square of Euler’s constant $\gamma$) starting at the seventh post-Newtonian order. We study the convergence of the post-Newtonian expansion as the expansion parameter $u=GM/(c^{2}r)$ leaves the weak-field domain $u\ll 1$ to enter the strong field domain $u=O(1)$.

The Euclidean or Bunch-Davies $O(4,1)$ invariant state for quantum fields in global de Sitter space is shown to be unstable to small perturbations, even for a massive free field with no self-interactions. There are perturbations of this state with energy density that is arbitrarily small at early times, is exponentially blueshifted in the contracting phase of “eternal” de Sitter space, and becomes large enough to disturb the classical geometry through the semi-classical Einstein equations at later times. In the closely analogous case of a constant, uniform electric field, a time symmetric state equivalent to the de Sitter invariant one is constructed, which is also not a stable vacuum state under perturbations. The role of a quantum anomaly in the growth of perturbations and symmetry breaking is emphasized in both cases. In de Sitter space, the same results are obtained either directly from the renormalized stress tensor of a massive scalar field, or for massless conformal fields of any spin, more directly from the effective action and stress tensor associated with the conformal trace anomaly. The anomaly stress tensor shows that states invariant under the $O(4)$ subgroup of the de Sitter group are also unstable to perturbations of lower spatial symmetry, implying that both the $O(4,1)$ isometry group and its $O(4)$ subgroup are broken by quantum fluctuations. Potential consequences of this result for cosmology and the problem of vacuum energy are discussed.

We show that global de Sitter space is unstable to particle creation, even for a massive free field theory with no self-interactions. The $O(4,1)$ de Sitter invariant state is a definite phase coherent superposition of particle and antiparticle solutions in both the asymptotic past and future and, therefore, is not a true vacuum state. In the closely related case of particle creation by a constant, uniform electric field, a time symmetric state analogous to the de Sitter invariant one is constructed, which is also not a stable vacuum state. We provide the general framework necessary to describe the particle creation process, the mean particle number, and dynamical quantities such as the energy-momentum tensor and current of the created particles in the de Sitter and electric field backgrounds respectively in real time, establishing the connection to kinetic theory. We compute the energy-momentum tensor for adiabatic vacuum states in de Sitter space initialized at early times in global ${\mathbb{S}}^3$ sections and show that particle creation in the contracting phase results in exponentially large energy densities at later times, necessitating an inclusion of their backreaction effects and leading to large deviation of the spacetime from global de Sitter space before the expanding phase can begin.

In this paper we clarify the relation between the invariant relativistic relative velocity $V_{\mathrm{r}}$, the Møller velocity $\overline{v}$, and the nonrelativistic relative velocity $v_r$. Adopting $V_{\mathrm{r}}$ as the true physical relative velocity for pair collisions in a nondegenerate relativistic gas, we show that in the frame comoving with the gas (i) a probability density function $\mathcal{P}(V_{\mathrm{r}})$ for $V_{\mathrm{r}}$ exists, (ii) an exact formula for the mean value $⟨V_{\mathrm{r}}⟩$ exists, (iii) the thermally averaged cross section times relative velocity $⟨\sigma v_{\text{rel}}⟩$ that appears in the density evolution equation for thermal relics is reformulated only in terms of $V_{\mathrm{r}}$ and $\mathcal{P}(V_{\mathrm{r}})$ in a manifestly Lorentz invariant form, and (iv) the frame-dependent issues of the standard formulation in terms of the Møller velocity, as well as “superluminal” relative velocities, are not present in this formulation. Furthermore, considering the annihilation of dark matter into a particle-antiparticle pair $f\overline{f}$, in the cases $m_f=0$, $m_f=m$, and $m_f\gg m$, we find that the coefficients of the low velocity expansion of $⟨\sigma V_{\mathrm{r}}⟩$ admit an exact analytical representation in terms of the Meijer $G$ functions that can be reduced to combinations of modified Bessel functions of the second kind.

The observational signatures of multifield inflation will generally evolve as the Universe reheats. We introduce a general analytic formalism for tracking this evolution through perturbative reheating, applicable to two-field models with arbitrary separable potentials. The various transitions, including the onset of scalar field oscillations and the reheating of each field, can happen in different orders and on arbitrary hypersurfaces. The effective equations of state of the oscillating fields are also arbitrary. Nevertheless, our results are surprisingly simple. Our formalism encapsulates and generalizes a huge range of previous calculations including two-field inflation, spectator models, the inhomogeneous end of inflation scenario and numerous generalized curvaton scenarios.

Interacting dark energy and dark matter is used to go beyond the standard cosmology. We base our arguments on Planck data and conclude that an interaction is compatible with the observations and can provide a strong argument towards consistency of different values of cosmological parameters.

We implement the effective field theory (EFT) approach to dark energy and modified gravity in the public Einstein-Boltzmann solver CAMB. The resulting code, which we dub EFTCAMB, is a powerful and versatile tool that can be used for several objectives. It can be employed to evolve the full dynamics of linear scalar perturbations of a broad range of single field dark energy and modified gravity model, once the model of interest is mapped into the EFT formalism. It offers a numerical implementation of EFT as a model-independent framework to test gravity on cosmological scales. EFTCAMB has a built-in check for the fulfillment of general stability conditions such as the absence of ghost and superluminal propagation of perturbations. It handles phantom-divide crossing models and does not contain any quasistatic approximation, but rather evolves the full dynamics of perturbations on linear scales. As we will show, the latter is an important feature in view of the accuracy and scale range of upcoming surveys. We show the reliability and applicability of our code by evolving the dynamics of linear perturbations and extracting predictions for power spectra in several models. In particular we perform a thorough analysis of $f(R)$ theories, comparing our outputs with those of an existing code for $\mathrm{\Lambda }\mathrm{CDM}$ backgrounds, and finding an agreement that can reach 0.1% for models with a Compton wavelength consistent with current cosmological data. We then showcase the flexibility of our code studying two different scenarios. First we produce new results for designer $f(R)$ models with a time-varying dark energy equation of state. Second, we extract predictions for linear observables in some parametrized EFT models with a phantom-divide crossing equation of state for dark energy.

We extend previous classifications of inflationary models by means of their behavior at large $N$, where $N$ is the number of e-foldings. In addition to the perturbative $1/N$ case, whose slow-roll parameters fall off as powers of $1/N$, we introduce the constant, nonperturbative and logarithmic classes. This covers the large majority of inflationary models. Furthermore, we calculate the running of the spectral tilt for all these classes. Remarkably, we find that the tilt’s runnings essentially cluster around the per-mil level. We comment on the implications for future experiments.

Advanced ground-based gravitational-wave detectors are capable of measuring tidal influences in binary neutron-star systems. In this work, we report on the statistical uncertainties in measuring tidal deformability with a full Bayesian parameter estimation implementation. We show how simultaneous measurements of chirp mass and tidal deformability can be used to constrain the neutron-star equation of state. We also study the effects of waveform modeling bias and individual instances of detector noise on these measurements. We notably find that systematic error between post-Newtonian waveform families can significantly bias the estimation of tidal parameters, thus motivating the continued development of waveform models that are more reliable at high frequencies.

We calculate the branching fractions of the $B_s^0\to J/\psi \varphi (1020)$ and $B_s^0\to J/\psi f_2^{\prime }(1525)$ decays using a simple model based on the framework of the factorization approach. We also evaluate the total $B_s^0\to J/\psi K^{+}{K}^{-}$ branching ratio, including the resonances and nonresonant contributions to the $K^{+}{K}^{-}$ channel, by applying the Dalitz plot analysis. The largest resonant component of the final state structure in the $B_s^0\to J/\psi K^{+}{K}^{-}$ decay is $\varphi (1020)$, accompanied by $f_2^{\prime }(1525)$ and five additional resonances. We compute the resonant contributions $B_s^0\to J/\psi \varphi (1020)(\to K^{+}{K}^{-})$, $B_s^0\to J/\psi f_2^{\prime }(1525)(\to K^{+}{K}^{-})$ and nonresonant decay then compare with data from Belle and LHCb. The overall branching fractions are obtained by applying our calculations to be $BR[B_s^0\to J/\psi \varphi (1020)]=(1.14\pm 0.17)\times 10^{-3}$, $BR[B_s^0\to J/\psi f_2^{\prime }(1525)]=(0.33\pm 0.05)\times 10^{-3}$, and $BR[B_s^0\to J/\psi K^{+}{K}^{-}]=(1.03\pm 0.09)\times 10^{-3}$.

We investigate the scalar potential of a general $S_3$-symmetric three-Higgs-doublet model. The outcome of our analysis does not depend on the fermionic sector of the model. We identify a decoupling limit for the scalar spectrum of this scenario. In view of the recent LHC Higgs data, we show our numerical results only in the decoupling limit. Unitarity and stability of the scalar potential demand that many new scalars must be lurking below 1 TeV. We provide numerical predictions for $h\to \gamma \gamma$ and $h\to Z\gamma$ signal strengths, which can be used to falsify the theory.

We consider the contributions of individual new particles to the anomalous magnetic moment of the muon, utilizing the generic framework of simplified models. We also present analytic results for all possible one-loop contributions, allowing easy application of these results for more complete models which predict more than one particle capable of correcting the muon magnetic moment. Additionally, we provide a mathematica code to allow the reader to straightforwardly compute any one-loop contribution. Furthermore, we derive bounds on each new particle considered, assuming either the absence of other significant contributions to $a_{\mu }$ or that the anomaly has been resolved by some other mechanism. The simplified models we consider are constructed without the requirement of $SU(2{)}_L$ invariance, but appropriate chiral coupling choices are also considered. In summary, we found the following particles capable of explaining the current discrepancy, assuming unit couplings: 2 TeV (0.3 TeV) neutral scalar with pure scalar (chiral) couplings, 4 TeV doubly charged scalar with pure pseudoscalar coupling, 0.3–1 TeV neutral vector boson depending on what couplings are used (vector, axial, or mixed), 0.5–1 TeV singly charged vector boson depending on which couplings are chosen, and 3 TeV doubly charged vector-coupled bosons. We also derive the following $1\sigma$ lower bounds on new particle masses assuming unit couplings and that the experimental anomaly has been otherwise resolved: a doubly charged pseudoscalar must be heavier than 7 TeV, a neutral scalar than 3 TeV, a vector-coupled new neutral boson 600 GeV, an axial-coupled neutral boson 1.5 TeV, a singly charged vector-coupled $W^{\prime }$ 1 TeV, a doubly charged vector-coupled boson 5 TeV, scalar leptoquarks 10 TeV, and vector leptoquarks 10 TeV. We emphasize that the quoted numbers apply within simplified models, but the reader can easily use our mathematica code to calculate the contribution of their own model of new physics.

In this work we present the computation of the Higgs boson decay into a photon and a $Z^0$ boson at the one-loop level in the framework of the next-to-minimal supersymmetric standard model (NMSSM). The numerical evaluation of this decay width was performed within the framework of the SloopS code, originally developed for the minimal supersymmetric standard model but which was recently extended to deal with the NMSSM. Thanks to the high level of automation of SloopS, all contributions from the various sector of the NMSSM are consistently taken into account, in particular the nondiagonal chargino and sfermion contributions. We then explored the NMSSM parameter space, using HiggsBounds and HiggsSignals, to investigate to what extent these signal can be enhanced.

In this article we study the impact of the lightest vector and scalar resonance multiplets in the pion and kaon decay constants up to next-to-leading order in the $1/N_C$ expansion, i.e., up to the one-loop level. The $F_{\pi }$ and $F_K$ predictions obtained within the framework of resonance chiral theory are confronted with lattice simulation data. The vector loops (and the $\rho -\pi \pi$ coupling $G_V$ in particular) are found to play a crucial role in the determination of the chiral perturbation theory couplings $L_4$ and $L_5$ at next-to-leading order in $1/N_C$. Puzzling, values of $G_V\lesssim 40\mathrm{MeV}$ seem to be necessary to agree with current phenomenological results for $L_4$ and $L_5$. Conversely, a value of $G_V\gtrsim 60\mathrm{MeV}$ compatible with standard $\rho -\pi \pi$ determinations turns these chiral couplings negative. However, in spite of the strong anti-correlation with $L_4$, the $SU(3)$ chiral coupling $F_0$ remains stable all the time and stays within the range $78\sim 86\mathrm{MeV}$ when $G_V$ is varied in a wide range, from 40 up to 70 MeV. Finally, we would like to remark that the leading order expressions used in this article for the $\eta -{\eta }^{\prime }$ mixing, mass splitting of the vector multiplet masses and the quark mass dependence of the $\rho (770)$ mass are found in reasonable agreement with the lattice data.

We have studied the quasifree dissociation of quarkonia through a complex potential that

To know the total width of the recently discovered Higgs boson particle, it is important to measure the invisible decay width of the Higgs boson. However, the signal for this measurement at the LHC, i.e., a charged lepton pair and missing energy in the final state, cannot be definitely understood as the product of the intermediate produced $Z$ and $H$ bosons due to the possible interaction between dark matter and a $Z$ boson or quarks, which can be described by representative effective operators. First, we consider the relic abundance, the LUX direct detection experiment, and the result of searching for Higgs boson invisible decay at the LEP and LHC to find the allowed parameter region for the effective operators. Then we investigate the transverse momentum distribution of the missing energy and propose two observables that can be used to distinguish the different underlying processes. Moreover, with these two observables, we may be able to determine the masses of invisible particles.

Spin-charge separation, a crucial ingredient in 2D models of strongly correlated systems, is mostly considered in condensed matter applications. In this paper we present a relativistic field-theoretic model in which charged particles of spin $1/2$ emerge by soldering spinless charges and magnetic vortices in a confinement quantum phase transition modeled as a tensor Higgs mechanism. The model involves two gauge fields, a vector one and a two-form gauge field interacting by the topological $BF$-term. When this tensor gauge symmetry is spontaneously broken charges are soldered to the ends of magnetic vortices and thus confined by a linear potential. If the vector potential has a topological $\theta$-term with value $\theta =\pi$, the constituents of this “meson” acquire spin $1/2$ in this transition.

We consider Einstein-Maxwell-dilaton gravity with charged dust and interaction of the form $P(\chi )F_{\mu \nu }{F}^{\mu \nu }$, where $P(\chi )$ is an arbitrary function of the dilaton field $\chi$ that can be normal or phantom. For any regular $P(\chi )$, static configurations are possible with arbitrary functions $g_{00}=\exp (2\gamma (x^i))$ ($i=1$, 2, 3) and $\chi =\chi (\gamma )$, without any assumption of spatial symmetry. The classical Majumdar-Papapetrou system is restored by putting $\chi =\text{const}$. Among possible solutions are black-hole (BH) and quasi-black-hole (QBH) ones. Some general results on BH and QBH properties are deduced and confirmed by examples. It is found, in particular, that asymptotically flat BHs and QBHs can exist with positive energy densities of matter and both scalar and electromagnetic fields.

We discuss the possibility of using fast radio bursts (FRBs)—if cosmological—as a viable cosmic probe. We find that the contribution of the host galaxies to the detected dispersion measures can be inapparent for the FRBs that are not from galaxy centers or star-forming regions. The inhomogeneity of the intergalactic medium (IGM), however, causes significant deviation of the dispersion measure from that predicted in the simplified homogeneous IGM model for an individual event. Fortunately, with sufficient FRBs along different sightlines but within a very narrow redshift interval (e.g., $\mathrm{\Delta }z\sim 0.05$), the mean obtained from averaging observed dispersion measures does not suffer such a problem and hence may be used as a cosmic probe. We show that in the optimistic case (e.g., about 20 FRBs in each $\mathrm{\Delta }z$ have been measured; the most distant FRBs were at redshift $\ge 3$; the host galaxies and the FRB sources contribute little to the detected dispersion measures) and with all the uncertainties (i.e., the inhomogeneity of the IGM, the contribution and uncertainty of host galaxies, and the evolution and error of $f_{\mathrm{IGM}}$) considered, FRBs could help constrain the equation of state of dark energy.

The discovery of the Higgs boson at the LHC supports the hypothesis that the Standard Model provides an effective parametrization of all subatomic experimental data up to the Planck scale. String theory, which provides a viable perturbative approach to quantum gravity, requires for its consistency the existence of additional gauge symmetries beyond the Standard Model. The construction of heterotic string models with a viable light $Z^{\prime }$ is, however, highly constrained. We outline the construction of standardlike heterotic string models that allow for an additional Abelian gauge symmetry that may remain unbroken down to low scales. We present a string inspired model, consistent with the string constraints.