Great attention is given to the first star formation and the epoch of reionization as main targets of planned large radio interferometries (e.g. Square Kilometre Array). Recently, it is claimed that the supersonic relative velocity between baryons and cold dark matter can suppress the abundance of first stars and impact the cosmological reionization process. Therefore, in order to compare observed results with theoretical predictions it is important to examine the effect of the supersonic relative motion on the small-scale structure formation. In this paper, we investigate this effect on the nonlinear structure formation in the context of the spherical collapse model in order to understand the fundamental physics in a simple configuration. We show the evolution of the dark matter sphere with the relative velocity by both using N-body simulations and numerically calculating the equation of motion for the dark matter mass shell. The effects of the relative motion in the spherical collapse model appear as the delay of the collapse time of dark matter halos and the decrease of the baryon mass fraction within the dark matter sphere. Based on these results, we provide the fitting formula of the critical density contrast for collapses with the relative motion effect and calculate the mass function of dark matter halos in the Press-Schechter formalism. As a result, the relative velocity decreases the abundance of dark matter halos whose mass is smaller than ${10}^8{M}_{\odot }/h$.

The explicit form for the post-Newtonian gravitational time delay of light signals propagating on the equatorial plane of a Kerr-Newman black hole is derived. Based on the null geodesic in Kerr-Newman spacetime, we adopt the iterative method to calculate the time delay. Our result reduces to the previous formulation for the Kerr black hole if we drop the contribution from the electrical charge. Our time-delay formula for the Reissner-Nordström geometry is different from the previous publication [Phys. Rev. D 69, 023002 (2004)], in which the largest second order contribution to the time delay is missing.

We apply QCD-inspired techniques to study nonrelativistic $N$-component degenerate fermions with attractive interactions. By analyzing the singular-value spectrum of the fermion matrix in the Lagrangian, we derive several exact relations that characterize spontaneous symmetry breaking $\mathrm{U}(1)\times \mathrm{SU}(N)\to \mathrm{Sp}(N)$ through bifermion condensates. These are nonrelativistic analogues of the Banks-Casher relation and the Smilga-Stern relation in QCD. Nonlocal order parameters are also introduced and their spectral representations are derived, from which a nontrivial constraint on the phase diagram is obtained. The effective theory of soft collective excitations is derived, and its equivalence to random matrix theory is demonstrated in the $ϵ$ regime. We numerically confirm the above analytical predictions in Monte Carlo simulations.

Lattice quantum chromodynamics (QCD) studies of electromagnetic properties of hadrons and light nuclei, such as magnetic moments and polarizabilities, have proven successful with the use of background field methods. With an implementation of nonuniform background electromagnetic fields, properties such as charge radii and higher electromagnetic multipole moments (for states of higher spin) can additionally be obtained. This can be achieved by matching lattice QCD calculations to a corresponding low-energy effective theory that describes the static and quasistatic responses of hadrons and nuclei to weak external fields. With particular interest in the case of vector mesons and spin-1 nuclei such as the deuteron, we present an effective field theory of spin-1 particles coupled to external electromagnetic fields. To constrain the charge radius and the electric quadrupole moment of the composite spin-1 field, the single-particle Green’s functions in a linearly varying electric field in space are obtained within the effective theory, providing explicit expressions that can be used to match directly onto lattice QCD correlation functions. The viability of an extraction of the charge radius and the electric quadrupole moment of the deuteron from the upcoming lattice QCD calculations of this nucleus is discussed.

We consider the electron-positron annihilation process into hadrons $R_{e^{+}{e}^{-}}$ up to $\mathcal{O}({\alpha }_s^3)$, and we adopt the smearing method suggest by Poggio, Quinn, and Weinberg to confront the experimental data with theory. As a theoretical model, we use a QCD coupling constant frozen in the low-energy regime, where this coupling can be parametrized in terms of an effective dynamical gluon mass ($m_g$) which is determined through Schwinger-Dyson equations. In order to find the best fit between experimental data and theory, we perform a ${\chi }^2$ study, that, within the uncertainties of the approach, has a minimum value when $m_g/{\mathrm{\Lambda }}_{\mathrm{QCD}}$ is in the range 1.2–1.4. These values are in agreement with other phenomenological determinations of this ratio and lead to an infrared effective charge ${\alpha }_s(0)\approx 0.7$. We comment how this effective charge may affect the global duality mass scale that indicates the frontier between perturbative and nonperturbative physics.

Inclusive production of a quarkonium ${\eta }_{c,b}$ in hadron collisions at low transverse momentum can be used to extract various transverse-momentum-dependent (TMD) gluon distributions of hadrons, provided the TMD factorization for the process holds. The factorization involving unpolarized TMD gluon distributions of unpolarized hadrons has been examined with on-shell gluons at the one-loop level. In this work, we study the factorization at the one-loop level with a diagram approach in the most general case, where all TMD gluon distributions at leading twist are involved. We find that the factorization holds and the perturbative effects are represented by one perturbative coefficient. Since the initial gluons from hadrons are off shell, in general, there exists the so-called superleading region found recently. We find that the contributions from this region can come from individual diagrams at the one-loop level, but they are canceled in the sum. Our factorized result for the differential cross section is explicitly gauge invariant.

The photon spectrum in macrocoherent atomic deexcitation via radiative emission of neutrino pairs has been proposed as a sensitive probe of the neutrino mass spectrum, capable of competing with conventional neutrino experiments. In this paper we revisit this interesting proposal in order to quantify the requirements for statistical determination of some of the properties of the neutrino spectrum, in particular, the neutrino mass scale and the mass ordering. Our results are shown as the product of the experimental lifetime, the target volume, and the number density of atoms which have to be set in a coherence state with a given electric field in the target, needed for determination of these properties with a given confidence level.

Inspired by the recent diboson excess observed at the LHC and possible interpretation within a TeV-scale left-right symmetric framework, we explore its implications for low-energy experiments searching for lepton number and flavor violation. Assuming a simple type-II seesaw mechanism for neutrino masses, we show that for the right-handed (RH) gauge boson mass and coupling values required to explain the LHC anomalies, the RH contribution to the lepton number violating process of neutrinoless double beta decay ($0\nu \beta \beta$) is already constrained by current experiments for relatively low-mass (MeV-GeV) RH neutrinos. The future ton-scale $0\nu \beta \beta$ experiments could probe most of the remaining parameter space, irrespective of the neutrino mass hierarchy and uncertainties in the oscillation parameters and nuclear matrix elements. On the other hand, the RH contribution to the lepton flavor violating process of $\mu \to e\gamma$ is constrained for relatively heavier (TeV) RH neutrinos, thus providing a complementary probe of the model. Finally, a measurement of the absolute light neutrino mass scale from future precision cosmology could make this scenario completely testable.

In this erratum, we point out that the correction to the gravitational energy flux from compact binary inspirals in dynamical Chern-Simons gravity enters at third post-Newtonian order instead of second post-Newtonian order. We also correct the scalar energy flux at second post-Newtonian order by considering terms that we missed in the original paper.

Spontaneous Lorentz violation is a viable mechanism to look for Planck scale physics. In this work, we study spontaneous Lorentz violation models, in flat spacetime, where a vector field produces such a violation and matter is modeled by a complex scalar field. We show that it is possible to construct a Hamilton density for which the evolution respects the dynamical constraints. However, we also find that the initial data, as required by standard field theory, does not determine the fields evolution in a unique way. In addition, we present some examples where the physical effects of such ambiguities can be recognized. As a consequence, the proposals in which the electromagnetic and gravitational interactions emerge from spontaneous Lorentz violation are challenged.

We argue, at a very basic effective field theory level, that higher dimension operators in scalar theories that break symmetries at scales close to their ultraviolet completion cutoff include terms that favor the breaking of translation (Lorentz) invariance, potentially resulting in striped, checkerboard or general crystal-like phases. Such descriptions can be thought of as the effective low energy description of QCD-like gauge theories near their strong coupling scale where terms involving higher dimension operators are generated. Our low energy theory consists of scalar fields describing operators such as $\overline{q}q$ and $\overline{q}{F}^{(2n)}q$. Such scalars can have kinetic mixing terms that generate effective momentum dependent contributions to the mass matrix. We show that these can destabilize the translationally invariant vacuum. It is possible that in some real gauge theory such operators could become sufficiently dominant to realize such phases, and it would be interesting to look for them in lattice simulations. We present a holographic model of the same phenomena which includes renormalization group running. A key phenomenological motive to look at such states is recent work that shows that the nonlinear response in $R^2$ gravity to such short-range fluctuations can mimic a cosmological constant. Intriguingly in a cosmology with such a Starobinsky inflation term, to generate the observed value of the present day acceleration would require stripes at the electroweak scale. Unfortunately, low energy phenomenological constraints on Lorentz violation in the electron-photon system appear to strongly rule out any such possibility outside of a disconnected dark sector.

Eigenvalue distributions of properly regularized Wilson-loop operators are used to study the transition from UV behavior to IR behavior in gauge theories coupled to matter that potentially have an IR fixed point. We numerically demonstrate the emergence of scale invariance in a matrix model that describes $SU(N)$ gauge theory coupled to two flavors of massless adjoint fermions in the large $N$ limit. The eigenvalue distribution of Wilson loops of varying sizes cannot be described by a universal lattice beta function connecting the UV to the IR.

The BEC-BCS crossover for a Nambu–Jona-Lasinio (NJL) model with diquark interactions is studied in the presence of an external magnetic field. Particular attention is paid to different regularization schemes used in the literature. A thorough comparison of results is performed for the case of a cold and magnetized two-color NJL model. According to our results, the critical chemical potential for the BEC transition exhibits a clear inverse magnetic catalysis effect for magnetic fields in the range $1\lesssim eB/m_{\pi }^2\lesssim 20$. As for the BEC-BCS crossover, the corresponding critical chemical potential is very weakly sensitive to magnetic fields up to $eB\sim 9m_{\pi }^2$, showing a much smaller inverse magnetic catalysis as compared to the BEC transition, and displays a strong magnetic catalysis from this point on.

Three-dimensional gravity coupled to pressureless dust is a field theory with 1 local degree of freedom. In the canonical framework, the dust-time gauge encodes this field in the metric. We find that its dynamics, up to diffeomorphism flow, is independent of spatial derivatives and is therefore ultralocal. We study this feature further by analyzing the linearized equations of motion about flat and (anti-)de Sitter backgrounds, and show that this field may be viewed as either a traceless or a transverse mode.

The holographic dual of a gravitational theory around the de Sitter background is argued to be a Euclidean conformal gravity theory in one fewer dimensions. The measure for the holographic theory naturally includes a sum over topologies as well as conformal structures.

We study mimetic $F(R)$ gravity with a potential and Lagrange multiplier constraint. In the context of these theories, we introduce a reconstruction technique which enables us to realize arbitrary cosmologies, given the Hubble rate and an arbitrarily chosen $F(R)$ gravity. We exemplify our method by realizing cosmologies that are in concordance with current observations (Planck data) and also well-known bouncing cosmologies. The attribute of our method is that the $F(R)$ gravity can be arbitrarily chosen, so we can have the appealing features of the mimetic approach combined with the known features of some $F(R)$ gravities, which unify early-time with late-time acceleration. Moreover, we study the existence and the stability of de Sitter points in the context of mimetic $F(R)$ gravity. In the case of unstable de Sitter points, it is demonstrated that graceful exit from inflation occurs. We also study the Einstein-frame counterpart theory of the Jordan-frame mimetic $F(R)$ gravity, and we discuss the general properties of the theory and exemplify our analysis by studying a quite interesting (from a phenomenological point of view) model with two scalar fields. We also calculate the observational indices of the two-scalar-field model, by using the two-scalar-field formalism. Furthermore, we extensively study the dynamical system that corresponds to the mimetic $F(R)$ gravity, by finding the fixed points and studying their stability. Finally, we modify our reconstruction method to function in the inverse way and thus yield which $F(R)$ gravity can realize a specific cosmological evolution, given the mimetic potential and the Lagrange multiplier.

If the inflationary era is preceded by a radiation-dominated era in which the inflaton too was in thermal equilibrium at some very early time, then the CMB data places an upper bound on the comoving temperature of the (decoupled) inflaton quanta. In addition, if one considers models of “just enough” inflation, where the number of e-foldings of inflation is just enough to solve the horizon and flatness problems, then we get a lower bound on the Hubble parameter during inflation, $H_{\inf }$, which is in severe conflict with the upper bound from tensor perturbations. Alternatively, imposing the upper bound on $H_{\inf }$ implies that such scenarios are compatible with the data only if the number of relativistic degrees of freedom in the thermal bath in the preinflationary Universe is extremely large (greater than ${10}^9$ or ${10}^{11}$). We are not aware of scenarios in which this can be satisfied.

It was shown recently that, without jeopardizing the success of the $\mathrm{\Lambda }$ cold dark matter model on cosmic scales, the modified Newtonian dynamics (MOND) can be derived as an emergent phenomenon when axionlike dark matter particles condense into superfluid on the galactic scales. We propose in this paper a Dirac-Born-Infeld (DBI) scalar field conformally coupled to the matter components. To maintain the success of MOND phenomenon of dark matter superfluid on the galactic scales, the fifth force introduced by the DBI scalar should be screened on the galactic scales. It turns out that the screening effect naturally leads to a simple explanation for a longstanding puzzle that the MOND critical acceleration coincides with present Hubble scale. This galactic coincidence problem is solved, provided that the screened DBI scalar also plays the role of dark energy on the cosmic scales.

The phenomenon of stochastic eternal inflation is studied for a chaotic inflation potential in a Bianchi type I spacetime background. After deriving the appropriate stochastic Klein-Gordon equation, we give details on the conditions for eternal inflation. It is shown that for eternal inflation to occur, the amount of anisotropy must be small. In fact, it is shown that eternal inflation will only take place if the shear anisotropy variables take on values within a small region of the interior of the Kasner circle. We then calculate the probability of eternal inflation occurring based on techniques from stochastic calculus.

We analyze electroweak baryogenesis during a two-step electroweak symmetry-breaking transition, wherein the baryon asymmetry is generated during the first step and preserved during the second. Focusing on the dynamics of $CP$ violation required for asymmetry generation, we discuss general considerations for successful two-step baryogenesis. Using a concrete model realization, we illustrate in detail the viability of this scenario and the implications for present and future electric dipole moment (EDM) searches. We find that $CP$ violation associated with a partially excluded sector may yield the observed baryon asymmetry while evading present and future EDM constraints.