The Fokker action governing the motion of compact binary systems without spins is derived in harmonic coordinates at the fourth post-Newtonian approximation (4PN) of general relativity. Dimensional regularization is used for treating the local ultraviolet (UV) divergences associated with point particles, followed by a renormalization of the poles into a redefinition of the trajectories of the point masses. Effects at the 4PN order associated with wave tails propagating at infinity are included consistently at the level of the action. A finite part procedure based on analytic continuation deals with the infrared (IR) divergencies at spatial infinity, which are shown to be fully consistent with the presence of near-zone tails. Our end result at 4PN order is Lorentz invariant and has the correct self-force limit for the energy of circular orbits. However, we find that it differs from the recently published result derived within the ADM Hamiltonian formulation of general relativity [T. Damour, P. Jaranowski, and G. Schäfer, Phys. Rev. D 89, 064058 (2014)]. More work is needed to understand this discrepancy.

Modified theories of gravity provide us with a unique opportunity to generate innovative tests of gravity. In Chameleon $f(R)$ gravity, the gravitational potential differs from the weak-field limit of general relativity (GR) in a mass dependent way. We develop a probe of gravity which compares high mass clusters, where Chameleon effects are weak, to low mass clusters, where the effects can be strong. We utilize the escape velocity edges in the radius/velocity phase space to infer the gravitational potential profiles on scales of 0.3–1 virial radii. We show that the escape edges of low mass clusters are enhanced compared to GR, where the magnitude of the difference depends on the background field value $|\overline{f_{R0}}|$. We validate our probe using N-body simulations and simulated light cone galaxy data. For a Dark Energy Spectroscopic Instrument Bright Galaxy Sample, including observational systematics, projection effects, and cosmic variance, our test can differentiate between GR and Chameleon $f(R)$ gravity models, $|\overline{f_{R0}}|=4\times {10}^{-6}$ ($2\times {10}^{-6}$) at $>5\sigma$ ($>2\sigma$), more than an order of magnitude better than current cluster-scale constraints.

We study the gravitational collapse of two thin shells of matter, in asymptotically flat spacetime or constrained to move within a spherical box. We show that this simple two-body system has surprisingly rich dynamics, which includes prompt collapse to a black hole, perpetually oscillating solutions or black hole formation at arbitrarily large times. Collapse is induced by shell crossing and the black hole mass depends sensitively on the number of shell crossings. At certain critical points, the black hole mass exhibits critical behavior, determined by the change in parity (even or odd) of the number of crossings, with or without mass-gap during the transition. Some of the features we observe are reminiscent of confined scalars undergoing “turbulent” dynamics.

The unification of general relativity with quantum theory will also require a coming together of the two quite different mathematical languages of general relativity and quantum theory, i.e., of differential geometry and functional analysis, respectively. Of particular interest in this regard is the field of spectral geometry, which studies to which extent the shape of a Riemannian manifold is describable in terms of the spectra of differential operators defined on the manifold. Spectral geometry is hard because it is highly nonlinear, but linearized spectral geometry, i.e., the task to determine small shape changes from small spectral changes, is much more tractable and may be iterated to approximate the full problem. Here, we generalize this approach, allowing, in particular, nonequal finite numbers of shape and spectral degrees of freedom. This allows us to study how well the shape degrees of freedom are encoded in the eigenvalues. We apply this strategy numerically to a class of planar domains and find that the reconstruction of small shape changes from small spectral changes is possible if enough eigenvalues are used. While isospectral nonisometric shapes are known to exist, we find evidence that generically shaped isospectral nonisometric shapes, if existing, are exceedingly rare.

The viscous inhomogeneities of a relativistic plasma determine a further class of entropic modes whose amplitude must be sufficiently small since curvature perturbations are observed to be predominantly adiabatic and Gaussian over large scales. When the viscous coefficients only depend on the energy density of the fluid the corresponding curvature fluctuations are shown to be almost adiabatic. After addressing the problem in a gauge-invariant perturbative expansion, the same analysis is repeated at a nonperturbative level by investigating the nonlinear curvature inhomogeneities induced by the spatial variation of the viscous coefficients. It is demonstrated that the quasiadiabatic modes are suppressed in comparison with a bona fide adiabatic solution. Because of its anomalously large tensor to scalar ratio the quasiadiabatic mode cannot be a substitute for the conventional adiabatic paradigm so that, ultimately, the present findings seems to exclude the possibility of a successful accelerated dynamics solely based on relativistic viscous fluids. If the dominant adiabatic mode is not affected by the viscosity of the background a sufficiently small fraction of entropic fluctuations of viscous origin cannot be a priori ruled out.

We discuss Born-Infeld type fields (tachyon fields) in classical and quantum cosmology. We first partly review and partly extend the discussion of the classical solutions and focus in particular on the occurrence of singularities. For quantization, we employ geometrodynamics. In the case of constant potential, we discuss both Wheeler-DeWitt quantization and reduced quantization. We are able to give various solutions and discuss their asymptotics. For the case of general potential, we transform the Wheeler-DeWitt equation to a form where it leads to a difference equation. Such a difference equation was previously found in the quantization of black holes. We give explicit results for the cases of constant potential and inverse squared potential and point out special features possessed by solutions of the difference equation.

We consider the space-condensate inflation model to study the primordial gravitational waves generated in the early Universe. We calculate the energy spectrum of gravitational waves induced by the space-condensate inflation model for the full frequency range with the assumption that the phase transition between two consecutive regimes is abrupt during the evolution of the Universe. The suppression of the energy spectrum is found in our model for the decreasing frequency of gravitational waves depending on the model parameter. To realize the suppression of the energy spectrum of the primordial gravitational waves, we study the existence of the early phase transition during inflation for the space-condensate inflation model.

We study the matter bispectrum of the large-scale structure by comparing different perturbative and phenomenological models with measurements from $N$-body simulations obtained with a modal bispectrum estimator. Using shape and amplitude correlators, we directly compare simulated data with theoretical models over the full three-dimensional domain of the bispectrum, for different redshifts and scales. We review and investigate the main perturbative methods in the literature that predict the one-loop bispectrum: standard perturbation theory, effective field theory, resummed Lagrangian and renormalized perturbation theory, calculating the latter also at two loops for some triangle configurations. We find that effective field theory (EFT) succeeds in extending the range of validity furthest into the mildly nonlinear regime, albeit at the price of free extra parameters requiring calibration on simulations: EFT is found to be accurate to 5% up to a scale of $k_{\max }^{*}\simeq 0.4h/\mathrm{Mpc}$ at $z=1$, compared with $k_{\max }^{*}\simeq 0.2h/\mathrm{Mpc}$ at $z=1$ for most other one-loop perturbative methods. For the more phenomenological halo model, we confirm that despite its validity in the deeply nonlinear regime it has a deficit of power on intermediate scales, which worsens at higher redshifts (the maximum deficit in the amplitude correlator is $\sim 20\%$ at $z=1$, and up to 40% at $z=2$); this issue is ameliorated, but not solved, by combined halo-perturbative models. We show from simulations that in this transition region there is a strong squeezed bispectrum component that is significantly underestimated in the halo model at earlier redshifts. We thus propose a phenomenological method for alleviating this deficit, which we develop into a simple phenomenological “three-shape” benchmark model based on the three fundamental shapes we have obtained from studying the halo model. When calibrated on the simulations, this three-shape benchmark model accurately describes the bispectrum on all scales and redshifts considered, providing a prototype bispectrum Halofit-like methodology that could be used to describe and test parameter dependencies.

We propose a new scenario of Affleck-Dine baryogenesis where a flat direction in the MSSM generates $B-L$ asymmetry just after the end of inflation. The resulting amount of baryon asymmetry is independent of low-energy supersymmetric models but is dependent on inflation models. We consider the hybrid and chaotic inflation models and find that reheating temperature is required to be higher than that in the conventional scenario of Affleck-Dine baryogenesis. In particular, nonthermal gravitino-overproduction problem is naturally avoided in the hybrid inflation model. Our results imply that Affleck-Dine baryogenesis can be realized in a broader range of supersymmetry and inflation models than expected in the literature.

Using large scale Monte Carlo calculations in a simple three dimensional lattice fermion model, we establish the existence of a second order quantum phase transition between a massless fermion phase and a massive one, both of which have the same symmetries. This shows that fermion masses can arise due to dynamics without the need for spontaneous symmetry breaking. Universality suggests that this alternate origin of the fermion mass should be of fundamental interest.

We study the inhomogeneous solitonic modulation of a chiral condensate within the effective Nambu–Jona-Lasinio model when a constant external magnetic field is present. The self-consistent Pauli-Villars regularization scheme is adopted to manipulate the ultraviolet divergence encountered in the thermodynamic quantities. In order to efficiently determine the chiral restoration lines, a new kind of Ginzburg-Landau expansion approach is proposed here. At zero temperature, we find that both the upper and lower boundaries of the solitonic modulation oscillate with the magnetic field in the $\mu –B$ phase diagram which is actually the de Hass–van Alphan (dHvA) oscillation. It is very interesting to find out how the tricritical Lifshitz point $(T_L,{\mu }_L)$ evolves with the magnetic field: There are also dHvA oscillations in the $T_L–B$ and ${\mu }_L–B$ curves, though the tricritical temperature $T_L$ increases monotonically with the magnetic field.

We consider the possibility that the diphoton excess at 750 GeV is caused by a new scalar resonance produced in photon fusion. This scenario is parametrized by only one relevant effective couplings and is thus minimal. We show that this setup can reproduce both the production rate and width of the resonance, and is not in conflict with the 8 TeV limits on the diphoton cross section. The scenario also predicts event rates for $WW$, $ZZ$, $Z\gamma$ final states. We suggest for one to perform precision measurements by studying light-by-light scattering with intact protons detected in forward detectors. We construct a simple model that shows that the required couplings can be achieved with new vectorlike, uncolored fermions (with a strong Yukawa coupling to the resonance) which may also account for the required width.

We interpret the diphoton anomaly as a heavy scalar $H_3$ in the so-called 331 model. The scalar is responsible for breaking the $SU(3{)}_C\otimes SU(3{)}_L\otimes U(1{)}_X$ gauge symmetry down to the standard model electroweak gauge group. It mainly couples to the standard model gluons and photons through quantum loops involving heavy quarks and leptons. Those quarks and leptons, together with the SM quarks and leptons, form the fundamental representation of the 331 model. We use the low energy theorem to calculate the effective couplings of $H_{3}gg$, $H_3\gamma \gamma$, $H_{3}ZZ$, $H_{3}WW$ and $H_{3}Z\gamma$. The analytical results can be applied to new physics models satisfying the low energy theorem. We show that the heavy quark and lepton contribution cannot produce enough diphoton pairs. It is crucial to include the contribution of charged scalars to explain the diphoton excess. The extra neutral $Z^{\prime }$ boson could also explain the 2 TeV diboson excess observed at the LHC Run-I.

The mass of the dark matter particle is unknown, and may be as low as $\sim 10^{-22}\mathrm{eV}$. The lighter part of this range, below $\sim \mathrm{eV}$, is relatively unexplored both theoretically and experimentally but contains an array of natural dark matter candidates. An example is the relaxion, a light boson predicted by cosmological solutions to the hierarchy problem. One of the few generic signals such light dark matter can produce is a time-oscillating, equivalence-principle-violating force. We propose searches for this using accelerometers, and consider in detail the examples of torsion balances, atom interferometry, and pulsar timing. These approaches have the potential to probe large parts of unexplored parameter space in the next several years. Thus such accelerometers provide radically new avenues for the direct detection of dark matter.

We propose to construct a chirally broken model based on the infrared fixed point of a conformal system by raising the mass of some flavors while keeping the others massless. In the infrared limit, the massive fermions decouple, and the massless fermions break chiral symmetry. The running coupling of this system “walks,” and the energy range of walking can be tuned by the mass of the heavy flavors. Renormalization group considerations predict that the spectrum of such a system shows hyperscaling. We have studied a model with four light and eight heavy flavors coupled to $SU(3)$ gauge fields and verified the above expectations. We determined the mass of several hadronic states and found that some of them are in the 2–3 TeV range if the scale is set by the pseudoscalar decay constant $F_{\pi }\approx 250\mathrm{GeV}$. The $0^{++}$ scalar state behaves very differently from the other hadronic states. In most of our simulations, it is nearly degenerate with the pion, and we estimate its mass to be less than half of the vector resonance mass.

We compute the momentum diffusion coefficients of heavy quarks, ${\kappa }_{\parallel }$ and ${\kappa }_{\perp }$, in a strong magnetic field $B$ along the directions parallel and perpendicular to $B$, respectively, at the leading order in QCD coupling constant ${\alpha }_s$. We consider a regime relevant for the relativistic heavy ion collisions, ${\alpha }_{s}eB\ll T^2\ll eB$, so that thermal excitations of light quarks are restricted to the lowest Landau level (LLL) states. In the vanishing light-quark mass limit, we find ${\kappa }_{\perp }^{\mathrm{LO}}\propto {\alpha }_s^{2}TeB$ in the leading order that arises from screened Coulomb scatterings with ($1+1$)-dimensional LLL quarks, while ${\kappa }_{\parallel }$ gets no contribution from the scatterings with LLL quarks due to kinematic restrictions. We show that the first nonzero leading order contributions to ${\kappa }_{\parallel }^{\mathrm{LO}}$ come from the two separate effects: (1) the screened Coulomb scatterings with thermal gluons, and (2) a finite light-quark mass $m_q$. The former leads to ${\kappa }_{\parallel }^{\mathrm{LO},\text{gluon}}\propto {\alpha }_s^2{T}^3$ and the latter to ${\kappa }_{\parallel }^{\mathrm{LO},\text{massive}}\propto {\alpha }_s({\alpha }_{s}eB{)}^{1/2}{m}_q^2$. Based on our results, we propose a new scenario for the large value of heavy-quark elliptic flow observed in RHIC and LHC. Namely, when ${\kappa }_{\perp }\gg {\kappa }_{\parallel }$, an anisotropy in drag forces gives rise to a sizable amount of the heavy-quark elliptic flow even if heavy quarks do not fully belong to an ellipsoidally expanding background fluid.

We revisit the bottomonium spectrum motivated by the recently exciting experimental progress in the observation of new bottomonium states, both conventional and unconventional. Our framework is a nonrelativistic constituent quark model which has been applied to a wide range of hadronic observables from the light to the heavy quark sector, and thus the model parameters are completely constrained. Beyond the spectrum, we provide a large number of electromagnetic, strong and hadronic decays in order to discuss the quark content of the bottomonium states and give more insights about a better way to determine their properties experimentally.

An NLO QCD analysis of the final HERMES data on pion multiplicities is presented and a new set of pion fragmentation functions is extracted from the best fit to the data. We have studied the so-called $[x,z]$ and $[Q^2,z]$ presentations of their data, as given by HERMES, which, in principle, should simply be two different ways of presenting the experimental data. We have based our extraction on an excellent fit to the $[Q^2,z]$ presentation of the data.

In this work we provide simple and precise parametrizations of the existing $\pi K$ scattering data from threshold up to 1.6 GeV, which are constrained to satisfy forward dispersion relations as well as three additional threshold sum rules. We also provide phenomenological values of the threshold parameters and of the resonance poles that appear in elastic scattering.

The mass and decay constant of the $X(5568)$ state newly observed by the D0 Collaboration are computed within the two-point sum rule method using the diquark-antidiquark interpolating current. In calculations, the vacuum condensates up to eight dimensions are taken into account. The obtained result for the mass of the $X(5568)$ state is in a nice agreement with the experimental data.