We argue that theories with multiple axions generically contain a large number of vacua that can account for the smallness of the cosmological constant. In a theory with $N$ axions, the dominant instantons with charges $Q$ determine the discrete symmetry of vacua. Subleading instantons break the leading periodicity and lift the vacuum degeneracy. For generic integer charges the number of distinct vacua is given by $\sqrt{\det (Q^{\top }Q)}\propto e^N$. Our construction motivates the existence of a landscape with a vast number of vacua in a large class of four-dimensional effective theories.

The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and momenta leading to the quadratic Hamiltonian describing linear perturbations. The final Hamiltonian is obtained without assuming any equations of motions for the background variables. This general formalism is applied to the special case of two fluids, having in mind the usual radiation and matter mix which made most of our current Universe history. Quantization is achieved using an adiabatic expansion of the basis functions. This allows for an unambiguous definition of a vacuum state up to the given adiabatic order. Using this basis, we show that particle creation is well defined for a suitable choice of vacuum and canonical variables, so that the time evolution of the corresponding quantum fields is unitary. This provides constraints for setting initial conditions for an arbitrary number of fluids and background time evolution. We also show that the common choice of variables for quantization can lead to an ill-defined vacuum definition. Our formalism is not restricted to the case where the coupling between fields is small, but is only required to vary adiabatically with respect to the ultraviolet modes, thus paving the way to consistent descriptions of general models not restricted to single-field (or fluid).

We show that simple thermodynamic conditions determine, to a great extent, the equation of state and dynamics of cosmic defects of arbitrary dimensionality. We use these conditions to provide a more direct derivation of the velocity-dependent one-scale (VOS) model for the macroscopic dynamics of topological defects of arbitrary dimensionality in a ($N+1$)-dimensional homogeneous and isotropic universe. We parametrize the modifications to the VOS model associated with the interaction of the topological defects with other fields, including, in particular, a new dynamical degree of freedom associated with the variation of the mass per unit $p$-area of the defects, and we compute the corresponding scaling solutions. The observational impact of this new dynamical degree of freedom is also briefly discussed.

An established phenomenology and theoretical interpretation of $p\text{−}p$ collision data at lower collision energies should provide a reference for $p\text{−}p$ and other collision systems at higher energies, against which claims of novel physics may be tested. The description of $p\text{−}p$ collisions at the relativistic heavy ion collider has remained incomplete even as claims for collectivity and other novelties in data from smaller systems at the large hadron collider have emerged recently. In this study we report the charge-multiplicity dependence of two-dimensional angular correlations and of single-particle (SP) densities on transverse rapidity $y_t$ and pseudorapidity $\eta$ from 200 GeV $p\text{−}p$ collisions. We define a comprehensive and self-consistent two-component ($\text{soft}+\text{hard}$) model for hadron production and report a significant $p\text{−}p$ nonjet quadrupole component as a third (angular-correlation) component. Our results have implications for $p\text{−}p$ centrality, the underlying event, collectivity in small systems and the existence of flows in high-energy nuclear collisions.

The hadronic production of a Higgs boson ($H$) in association with $b$ jets will play an important role in investigating the Higgs-boson couplings to Standard Model (SM) particles during Run II of the CERN Large Hadron Collider, and could in particular reveal the presence of anomalies in the assumed hierarchy of Yukawa couplings to the third-generation quarks. A very high degree of accuracy in the theoretical description of this process is crucial to implement the rich physics program that could lead to either direct or indirect evidence of new physics from Higgs-boson measurements. Aiming for accuracy in the theoretical modeling of $H+b$-jet production, we have interfaced the analytic next-to-leading-order QCD calculation of $Hb\overline{b}$ production with parton-shower Monte Carlo event generators in the powheg box framework. In this paper we describe the most relevant aspects of the implementation and present results for the production of $H+1b$ jet, $H+2b$ jets, and $H$ with no tagged $b$ jets, in the form of kinematic distributions of the Higgs boson, of the $b$ jets, and of the non-$b$ jets, at the 13 TeV Large Hadron Collider. The corresponding code is part of the public release of the powheg box.

The neighborhood of the QCD chiral critical point is characterized by intense fluctuations of the chiral field which could, in principle, generate pronounced experimental signatures. However, experimental uncertainties which are inherent to heavy-ion collisions, as well as the modest size and duration of the formed plasma, will severely attenuate these signatures. Using Monte Carlo techniques, we study second-order event-by-event moments of pions as a prototype for signatures of the chiral critical point based on the enhancement of the correlation length and event-by-event analysis. We test their viability against some realistic ingredients, similar to the ones found in the RHIC beam energy scan program.

We perform a next-to-next-to-leading order (NNLO) analysis of nuclear parton distribution functions (nPDFs) using neutral current charged-lepton (${\ell }^{\pm }+\text{nucleus}$) deeply inelastic scattering (DIS) data and Drell-Yan (DY) cross-section ratios ${\sigma }_{\mathrm{DY}}^A/{\sigma }_{\mathrm{DY}}^{A^{\prime }}$ for several nuclear targets. We study in detail the parametrizations and the atomic mass (A) dependence of the nuclear PDFs at this order. The present nuclear PDFs global analysis provides us a complete set of nuclear PDFs, $f_i^{(A,Z)}(x,Q^2)$, with a full functional dependence on $x$, A, ${\mathrm{Q}}^2$. The uncertainties of the obtained nuclear modification factors for each parton flavour are estimated using the well-known Hessian method. The nuclear charm quark distributions are also added into the analysis. We compare the parametrization results with the available data and the results of other nuclear PDFs groups. We found our nuclear PDFs to be in reasonably good agreement with them. The estimates of errors provided by our global analysis are rather smaller than those of other groups. In general, a very good agreement is achieved. We also briefly review the recent heavy-ion collisions data including the first experimental data from the LHC $\text{proton}+\text{lead}$ and $\text{lead}+\text{lead}$ run which can be used in the global fits of nuclear PDFs. We highlight different aspects of the high luminosity Pb–Pb and p–Pb data which have been recorded by the CMS Collaboration.

We discuss a quantum deformation of the Green-Schwarz superstring on flat space, arising as a contraction limit of the corresponding deformation of ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$. This contraction limit turns out to be equivalent to a previously studied limit that yields the so-called mirror model—the model obtained from the light cone gauge fixed ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ string by a double Wick rotation. Reversing this logic, the ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ superstring is the double Wick rotation of a quantum deformation of the flat space superstring. This quantum deformed flat space string realizes symmetries of the timelike $\kappa$-Poincaré type and is T dual to ${\mathrm{dS}}_5\times {\mathrm{H}}^5$, indicating interesting relations between symmetry algebras under T duality. Our results directly extend to ${\mathrm{AdS}}_2\times {\mathrm{S}}^2\times {\mathrm{T}}^6$ and ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{T}}^4$ and beyond string theory to many (semi)symmetric space coset sigma models, such as a deformation of the four-dimensional Minkowski sigma model with timelike $\kappa$-Poincaré symmetry. We also discuss possible null and spacelike deformations.

We construct the six-dimensional quantum chromodynamics (QCD) Lagrangian in a linear covariant gauge and subsequently renormalize it at two loops in the modified minimal subtraction ($\overline{\mathrm{MS}}$) scheme. The coupling constant corresponding to the gauge interaction is asymptotically free for all numbers of quark fields, $N_f$. Analyzing the $\beta$ functions yields a rich spectrum of fixed points. For instance, the conformal window in the six-dimensional theory is at $N_f=16$ for the $SU(3)$ color group. The critical theory structure is similar to that of an $O(N)$ scalar theory in eight dimensions. Using the large-$N$ expansion the latter is shown to be in the same universality class as the Heisenberg ferromagnet. Similarly using the large-$N_f$ expansion, six-dimensional QCD is shown to be in the same class as the two-dimensional non-Abelian Thirring model and four-dimensional QCD. Abelian gauge theories are also renormalized at high loops in six and eight dimensions. It is shown that the gauge parameter only appears in the electron anomalous dimension at one loop, similar to four dimensions.

Electrodynamics with a local and linear constitutive law is used as a framework for models violating Lorentz covariance. The constitutive tensor of such a construction is irreducibly decomposed into three independent pieces. The principal part is the anisotropic generalization of the standard electrodynamics. The two other parts, axion and skewon, represent nonclassical modifications of electrodynamics. We derive the expression for the photon propagator in the Minkowski spacetime endowed with a skewon field. For a relatively small (antisymmetric) skewon field, a modified Coulomb law is exhibited.

We investigate the effect of the inclusion of relativistic Coulomb terms in a confined-isospin-density-dependent-mass (CIDDM) model of strange quark matter (SQM). We found that if we include the Coulomb term in scalar density form, the SQM equation of state (EOS) at high densities is stiffer but if we include the Coulomb term in vector density form it is softer than that of the standard CIDDM model. We also investigate systematically the role of each term of the extended CIDDM model. Compared with what was reported by Chu and Chen [Astrophys. J. 780, 135 (2014)], we found the stiffness of SQM EOS is controlled by the interplay among the oscillator harmonic, isospin asymmetry and Coulomb contributions depending on the parameter’s range of these terms. We have found that the absolute stable condition of SQM and the mass of $2M_{\odot }$ pulsars can constrain the parameter of oscillator harmonic ${\kappa }_1\approx 0.53$ in the case the Coulomb term is excluded. If the Coulomb term is included, for the models with their parameters are consistent with SQM absolute stability condition, the $2.0M_{\odot }$ constraint more prefers the maximum mass prediction of the model with the scalar Coulomb term than that of the model with the vector Coulomb term. On the contrary, the high densities EOS predicted by the model with the vector Coulomb is more compatible with the recent perturbative quantum chromodynamics result [1] than that predicted by the model with the scalar Coulomb. Furthermore, we also observed the quark composition in a very high density region depends quite sensitively on the kind of Coulomb term used.

We reexamine the $d=3$ dynamical gluon mass problem in pure-glue non-Abelian $SU(N)$ gauge theories, paying particular attention to the observed (in Landau gauge) violation of positivity for the spectral function of the gluon propagator. This is expressed as a large bulge in the propagator at small momentum, due to the $d=3$ avatar of asymptotic freedom. Mass is defined through $m^{-2}=\mathrm{\Delta }(p=0)$, where $\mathrm{\Delta }(p)$ is the scalar function for the gluon propagator in some chosen gauge; it is not a pole mass and is generally gauge dependent, except in the gauge-invariant pinch technique (PT). We truncate the PT equations with a recently proposed method called the vertex paradigm that automatically satisfies the QED-like Ward identity relating the three-gluon PT vertex function with the PT propagator. The mass is determined by a homogeneous Bethe-Salpeter equation involving this vertex and propagator. This gap equation also encapsulates the Bethe-Salpeter equation for the massless scalar excitations, essentially Nambu-Goldstone fields, that necessarily accompany gauge-invariant gluon mass. The problem is to find a good approximate value for $m$ and at the same time explain the bulge, which by itself leads, in the gap equation for the gluon mass, to excessively large values for the mass. Our point is not to give a high-accuracy determination of $m$ but to clarify the way in which the propagator bulge and a fairly accurate estimate of $m$ can coexist, and we use various approximations that illustrate the underlying mechanisms. The most critical point is to satisfy the Ward identity. In the PT we estimate a gauge-invariant dynamical gluon mass of $m\approx N{g}^2/(2.48\pi )$. We translate these results to the Landau gauge using a background-quantum identity involving a dynamical quantity $\kappa$ such that $m=\kappa m_L$, where $m_L^{-2}\equiv {\mathrm{\Delta }}_L(p=0)$. Given our estimates for $m$, $\kappa$, the relation is fortuitously well satisfied for $SU(2)$ lattice data.

We discuss the effect that small fluctuations of the local anisotropy of pressure and of the energy density may have on the occurrence of cracking in spherical compact objects, satisfying a polytropic equation of state. Two different kinds of polytropes are considered. For both, it is shown that departures from equilibrium may lead to the appearance of cracking, for a wide range of values of the parameters defining the polytrope. Prospective applications of the obtained results to some astrophysical scenarios are pointed out.

We consider an extension of Wheeler-DeWitt minisuperpace cosmology with additional interaction terms that preserve the linear structure of the theory. General perturbative methods are developed and applied to known semiclassical solutions for a closed Universe filled with a massless scalar. The exact Feynman propagator of the free theory is derived by means of a conformal transformation in minisuperspace. As an example, a stochastic interaction term is considered, and first order perturbative corrections are computed. It is argued that such an interaction can be used to describe the interaction of the cosmological background with the microscopic d.o.f. of the gravitational field. A Helmoltz-like equation is considered for the case of interactions that do not depend on the internal time, and the corresponding Green’s kernel is obtained exactly. The possibility of linking this approach to fundamental theories of quantum gravity is investigated.

We consider the model of gravity coupled to the Klein-Gordon time field. We do not deparametrize the theory using the scalar field before quantization, but quantize all degrees of freedom. Several new results for loop quantum gravity are obtained: (i) a Hilbert space for the gravity-matter system and a nonstandard representation of the scalar field thereon is constructed, (ii) a new operator for the scalar constraint of the coupled system is defined and investigated, (iii) methods for solving the constraint are developed. Commutators of the new quantum constraint operators correspond to the quantization of the Poisson bracket. This, however, poses problems for finding solutions. Hence the states we consider—and perhaps the whole setup—still needs some improvement. As a side result we describe a representation of the gravitational degrees of freedom in which the flux is diagonal. This representation is related to the BF theory vacuum of Dittrich and Geiller.

By using the scaling symmetry in the reduced action formalism, we derive the novel Smarr relation which holds even for the hairy rotating ${\mathrm{AdS}}_3$ black holes. Then, by using the Smarr relation we argue that the hairy rotating ${\mathrm{AdS}}_3$ black holes are stable thermodynamically, compared to the nonhairy ones.

In a series of recent papers Kallosh, Linde, and collaborators provide a unified description of single-field inflation with several types of potentials ranging from power law to supergravity, in terms of just one parameter $\alpha$. These so-called $\alpha$ attractors predict a spectral index $n_s$ and a tensor-to-scalar ratio $r$, which are fully compatible with the latest Planck data. The only common feature of all $\alpha$ attractors is a noncanonical kinetic term with a pole, and a potential analytic around the pole. In this paper, starting from the same Einstein frame with a noncanonical scalar kinetic energy, we explore the case of nonanalytic potentials. We find the functional form that corresponds to quasiscale-invariant gravitational models in the Jordan frame characterized by a universal relation between $r$ and $n_s$ that fits the observational data but is clearly distinct from the one of the $\alpha$ attractors. It is known that the breaking of the exact classical scale invariance in the Jordan frame can be attributed to one-loop corrections. Therefore we conclude that there exists a class of nonanalytic potentials in the noncanonical Einstein frame that is physically equivalent to a class of models in the Jordan frame, with scale invariance softly broken by one-loop quantum corrections.

Recent measurements of the cosmic microwave background (CMB) anisotropies by Planck provide a sensitive probe of dark matter annihilation during the cosmic dark ages, and specifically constrain the annihilation parameter $f_{\mathrm{eff}}⟨\sigma v⟩/m_{\chi }$. Using new results (paper II) for the ionization produced by particles injected at arbitrary energies, we calculate and provide $f_{\mathrm{eff}}$ values for photons and $e^{+}{e}^{-}$ pairs injected at keV-TeV energies; the $f_{\mathrm{eff}}$ value for any dark matter model can be obtained straightforwardly by weighting these results by the spectrum of annihilation products. This result allows the sensitive and robust constraints on dark matter annihilation presented by the Planck collaboration to be applied to arbitrary dark matter models with $s$-wave annihilation. We demonstrate the validity of this approach using principal component analysis. As an example, we integrate over the spectrum of annihilation products for a range of Standard Model final states to determine the CMB bounds on these models as a function of dark matter mass, and demonstrate that the new limits generically exclude models proposed to explain the observed high-energy rise in the cosmic ray positron fraction. We make our results publicly available at http://nebel.rc.fas.harvard.edu/epsilon.

Any injection of electromagnetically interacting particles during the cosmic dark ages will lead to increased ionization, heating, production of Lyman-$\alpha$ photons and distortions to the energy spectrum of the cosmic microwave background, with potentially observable consequences. In this paper we describe numerical results for the low-energy electrons and photons produced by the cooling of particles injected at energies from keV to multi-TeV scales, at arbitrary injection redshifts (but focusing on the post-recombination epoch). We use these data, combined with existing calculations modeling the cooling of these low-energy particles, to estimate the resulting contributions to ionization, excitation and heating of the gas, and production of low-energy photons below the threshold for excitation and ionization. We compute corrected deposition-efficiency curves for annihilating dark matter, and demonstrate how to compute equivalent curves for arbitrary energy-injection histories. These calculations provide the necessary inputs for the limits on dark matter annihilation presented in the accompanying paper I, but also have potential applications in the context of dark matter decay or deexcitation, decay of other metastable species, or similar energy injections from new physics. We make our full results publicly available at http://nebel.rc.fas.harvard.edu/epsilon, to facilitate further independent studies. In particular, we provide the full low-energy electron and photon spectra, to allow matching onto more detailed codes that describe the cooling of such particles at low energies.