Studies of the initial conditions for inflation have conflicting predictions from exponential suppression to inevitability. At the level of phase space, this conflict arises from the competing intuitions of $CPT$ invariance and thermodynamics. After reviewing this conflict, we enlarge the ensemble beyond phase space to include scalar potential data. We show how this leads to an important contribution from inflection point inflation, enhancing the likelihood of inflation to a power law, $1/N_e^3$. In the process, we emphasize the attractor dynamics of the gravity-scalar system and the existence of universality classes from inflection point inflation. Finally, we comment on the predictivity of inflation in light of these results.

In this paper we study the dynamics of gravitational collapse of a homogeneous dust sphere in a model exhibiting a linear nonminimal coupling between matter and curvature. The evolution of the scale factor and the matter density is obtained for different choices of Lagrangian density of matter, highlighting the direct physical relevance of the latter in this theory. Following a discussion of the junction conditions and boundary terms in the action functional, the matching with the outer metric and event horizon are analyzed. We find that a distinct phenomenology arises when compared with standard results for the Oppenheimer-Snyder collapse, namely the possibility of finite-density black holes and the breaking of the no-hair theorem, due to a dependence of the end state of a black hole on the initial radius of the spherical body.

We consider the implications of Lorentz-invariance violation (LIV) on cosmogenic neutrino observations, with particular focus on the constraints imposed on several well-developed models for ultrahigh energy cosmogenic neutrino production by recent results from the ANITA long-duration balloon payload, and RICE at the South Pole. Under a scenario proposed originally by Coleman and Glashow, each lepton family may attain maximum velocities that can exceed $c$, leading to energy-loss through several interaction channels during propagation. We show that future observations of cosmogenic neutrinos will provide by far the most stringent limit on LIV in the neutrino sector. We derive the implied level of LIV required to suppress observation of predicted fluxes from several mainstream cosmogenic neutrino models, and specifically those recently constrained by the ANITA and RICE experiments. We simulate via detailed Monte Carlo code the propagation of cosmogenic neutrino fluxes in the presence of LIV-induced energy losses. We show that this process produces several detectable effects in the resulting attenuated neutrino spectra, even at LIV-induced neutrino superluminality of $(u_{\nu }-c)/c\simeq {10}^{-26}$, about 13 orders of magnitude below current bounds.

We study the evolution of an inflation-generated magnetic field, due to its coupling to fluid motions, during cosmological phase transitions. We find that the magnetic field stays almost unchanged on large scales, while on small scales, the spectrum is modified in such a way that power at small scales becomes progressively suppressed. We also show that the magnetic field generates turbulent motions in the initially turbulence-free plasma. On large scales, the slope of the resulting kinetic energy spectrum is consistent with that of white noise.

The chameleon scalar field is a matter-coupled dark energy candidate whose nonlinear self-interaction partially screens its fifth force at laboratory scales. Nevertheless, small-scale experiments such as the torsion pendulum can provide powerful constraints on chameleon models. Here we develop a simple approximation for computing chameleon fifth forces in torsion pendulum experiments such as Eöt-Wash. We show that our approximation agrees well with published constraints on the quartic chameleon, and we use it to extend these constraints to a much wider range of models. Finally, we forecast the constraints which will result from the next-generation Eöt-Wash experiment, and show that this experiment will exclude a wide range of quantum-stable models.

We study the hadron-quark mixed phase in protoneutron stars, where neutrinos are trapped and lepton number becomes a conserved quantity besides the baryon number and electric charge. Considering protoneutron-star matter as a ternary system, the Gibbs conditions are applied together with the Coulomb interaction. We find that there no crystalline (“pasta”) structure appears in the regime of high lepton-number fraction; the size of pasta becomes very large and the geometrical structure becomes mechanically unstable due to the charge screening effect. Consequently the whole system is separated into two bulk regions like an amorphous state, where the surface effect is safely neglected. There, the local charge neutrality is approximately attained, so that the equation of state is effectively reduced to the one for a binary system. Hence, we conclude that there is no possibility for the density discontinuity to appear in protoneutron-star matter, which is a specific feature in a pure system. These features are important when considering astrophysical phenomena such as supernova explosions or radiation of the gravitational wave from protoneutron stars.

We deliver an exploratory lattice QCD examination of the $K^{*}(892)$ meson decay width via the $p$-wave scattering phase shift of a pion-kaon ($\pi K$) system in the isospin $I=1/2$ channel. The modified Rummukainen-Gottlieb formula for a two-particle system with arbitrary mass is employed to extract phase shifts, which clearly reveal the existence of a resonance at a mass around the $K^{*}(892)$ meson mass. The effective range formula is applied to describe the energy dependence of the phase shift and we extract the effective $K^{*}\to \pi K$ coupling constant as $g_{K^{*}\pi K}=6.38(78)$. The decay width estimated from the phase shift is about $64.9\pm 8.0\mathrm{MeV}$, which is in reasonable accordance with the experiment. Our lattice investigations are conducted on a ${20}^3\times 48$ MILC gauge configuration with the $N_f=2+1$ flavors of the asqtad-improved staggered dynamical sea quarks at $(m_{\pi }+m_K)/m_{K^{*}}\approx 0.739$ and lattice spacing $a\approx 0.15\mathrm{fm}$.

We discuss a representation of the $Z_3$ gauge-Higgs lattice field theory at finite density in terms of dual variables, i.e., loops of flux and surfaces. In the dual representation the complex action problem of the conventional formulation is resolved and Monte Carlo simulations at arbitrary chemical potential become possible. A suitable algorithm based on plaquette occupation numbers and link fluxes is introduced and we analyze the model at zero temperature and finite density both in the weak and strong coupling phases. We show that at zero temperature the model has different first order phase transitions as a function of the chemical potential both for the weak and strong coupling phases. The exploratory study demonstrates that alternative degrees of freedom may successfully be used for Monte Carlo simulations in several systems with gauge and matter fields.

A generalized inverse seesaw model, in which the $9\times 9$ neutrino mass matrix has vanishing (1,1) and (1,3) submatrices, is proposed. This is similar to the universal two-zero texture which gives vanishing (1,1) and (1,3) elements of the $3\times 3$ mass matrices in both the charged lepton and neutrino sectors. We consider the $Z_6\times Z_6$ group to realize such texture zeros in the framework of the generalized inverse seesaw model. We also analyze the universal two-zero texture in the general case and propose two Ansätze to reduce the number of free parameters. Taking account of the new result of ${\theta }_{13}$ from the Daya Bay experiment, we constrain the parameter space of the universal two-zero texture in the general case and in the two Ansätze, respectively. We find that one of the Ansätze works well.

We derive bounds on the Dirac Yukawa couplings of the neutrinos in seesaw models using the recent Large Hadron Collider (LHC) data on Higgs decays for the case where the Standard Model singlet heavy leptons needed for the seesaw mechanism have masses in the 100 GeV range. Such scenarios with large Yukawa couplings are natural in inverse seesaw models since the small neutrino mass owes its origin to a small Majorana mass of a new set of singlet fermions. Large Yukawas with sub-TeV mass right-handed neutrinos are also possible for certain textures in Type-I seesaw models, so that the above bounds also apply to them. We find that the current Higgs data from the LHC can put bounds on both electron- and muon-type Yukawa couplings of order ${10}^{-2}$.

We study the implications of the experimental results on the $\mu \to e\gamma$ decay rate and the muon anomalous magnetic moment on muonic lepton flavor violating processes, such as $\mu \to 3e$ and $\mu N\to eN$. We use a model-independent approach in this analysis, where these processes are considered to be loop induced by exchanging spin-$1/2$ and spin-0 particles. We explore two complementary cases—those with no cancellation mechanism in amplitudes and those with an internal (built-in) cancellation mechanism. Our main results are as follows: (a) Bounds from rates are used to constrain parameters, such as coupling constants and masses. These constraints can be easily updated by simple scalings, if the experimental situations change. (b) The muon $g-2$ data favors nonchiral interactions. (c) In $\mu \to 3e$ and $\mu N\to eN$ processes, $Z$-penguin diagrams may play some role, while box diagram contributions to $\mu \to 3e$ are usually highly constrained. (d) In the first case (without any built-in cancellation mechanism), using the recent $\mu \to e\gamma$ bound, we find that $\mu \to 3e$ and $\mu N\to eN$ rates are usually bounded below the present experimental limits by two to three orders of magnitude in general. Furthermore, by comparing $\Delta a_{\mu }$ and $\mathcal{B}(\mu \to e\gamma )$ data, the couplings of $\mu$ and $e$ are found to be highly hierarchical. Additional suppression mechanisms should be called for. (e) In the second case (with a built-in cancellation mechanism), mixing angles can provide additional suppression factors to satisfy the $\Delta a_{\mu }$ and $\mathcal{B}(\mu \to e\gamma )$ bounds. While the $\mu \to 3e$ rate remains suppressed, the bounds on $\mu N\to eN$ rates, implied from the latest $\mu \to e\gamma$ bound, can be relaxed significantly and can be just below the present experimental limits.

We study, in a $d$-dimensional space-time, the nonanalyticity of the thermal free energy in the scalar ${\varphi }^4$ theory as well as in QED. We find that the infrared divergent contributions induce, when $d$ is even, a nonanalyticity in the coupling $\alpha$ of the form $(\alpha {)}^{(d-1)/2}$ whereas when $d$ is odd the nonanalyticity is only logarithmic.

We illustrate the power and efficiency of a recently uncovered Mellin-space approach to AdS/CFT correlation functions by providing a universal formula for the four-scalar graviton-exchange Witten diagram for arbitrary CFT-dual scaling dimensions. Our result keeps the space-time dimension generic as well, and is expressed as a combination of just 11 hypergeometric functions. Such hypergeometric functions are related to scalar-exchange diagrams. In particular, if reverse engineered in terms of $D$ functions, this might be viewed as a first step toward proving a long-standing conjecture by Dolan, Nirschl and Osborn pertaining to four-point correlators of chiral primary operators at strong coupling. Most importantly, the technology developed herein marks an additional development toward the long-anticipated computation of the four-point function of the $\mathcal{N}=4$ sYM stress tensor.

We investigate and classify Fermi surface behavior for a set of fermionic modes in a family of backgrounds holographically dual to $\mathcal{N}=4$ super-Yang-Mills theory at zero temperature with two distinct chemical potentials. We numerically solve fluctuation equations for every spin-$1/2$ field in five-dimensional maximally supersymmetric gauged supergravity not mixing with gravitini. Different modes manifest two, one, or zero Fermi surface singularities, all associated with non-Fermi liquids, and we calculate dispersion relations and widths of excitations. We study two limits where the zero-temperature entropy vanishes. In one limit, a Fermi surface approaches a marginal Fermi liquid, which we demonstrate analytically, and conductivity calculations show a hard gap with the current dual to the active gauge field superconducting, while the other is insulating. In the other limit, conductivities reveal a soft gap with the roles of the gauge fields reversed.

In the paper a generalization of the ($1+1$)-dimensional model by Chodos et al. [Phys. Rev. D 61, 045011 (2000)] has been performed to the case of ($2+1$)-dimensional spacetime. The model includes four-fermion interactions both in the fermion-antifermion (or chiral) and fermion-fermion (or superconducting) channels. We study temperature $T$ and chemical potential $\mu$ induced phase transitions in the leading order of large-$N$ expansion technique, where $N$ is a number of fermion fields. It is shown that at sufficiently large values of $\mu$ and arbitrary relations between coupling constants, the superconducting phase appears in the system both at $T=0$ and $T>0$. In particular, at $T=0$ and sufficiently weak attractive interaction in the chiral channel, the Cooper pairing occurs for arbitrary couplings in the superconducting channel even at infinitesimal values of $\mu$.

We demonstrate that in the supersymmetric extensions of a class of generalized (or K) field theories introduced recently, the static energy satisfies a Bogomoln’yi-Prasad-Sommerfield bound in each topological sector. Further, the corresponding soliton solutions saturate the bound. We also find strong indications that the Bogomoln’yi-Prasad-Sommerfield bound shows up in the supersymmetry algebra as a central extension, as is the case in the well-known supersymmetric field theories with standard kinetic terms.

It has been suggested that certain derivatively coupled nonrenormalizable scalar field theories might restore the perturbative unitarity of high-energy hard scatterings by classicalization, i.e., formation of multiparticle states of soft quanta [2]. Here we apply the semiclassical method of calculating the multiparticle production rates to the scalar Dirac-Born-Infeld theory, which is suggested to classicalize. We find that the semiclassical method is applicable for the energies in the final state above the cutoff scale of the theory, $L_{*}^{-1}$. We encounter that the cross section of the process $2\to N$ ceases to be exponentially suppressed for the particle number in the final state $N$ smaller than a critical particle number $N_{\mathrm{crit}}\sim (E{L}_{*}{)}^{4/3}$. It coincides with the typical particle number produced in two-particle collisions at high energies predicted by classicalization arguments.

We investigate chiral symmetry breaking in the ($2+1$)-dimensional Thirring model as a function of the coupling as well as the Dirac flavor number $N_{\mathrm{f}}$ with the aid of the functional renormalization group. For small enough flavor number $N_{\mathrm{f}}<N_{\mathrm{f}}^{\mathrm{cr}}$, the model exhibits a chiral quantum phase transition for sufficiently large coupling. We compute the critical exponents of this second order transition as well as the fermionic and bosonic mass spectrum inside the broken phase within a next-to-leading order derivative expansion. We also determine the quantum critical behavior of the many-flavor transition which arises due to a competition between vector and chiral-scalar channels and which is of second order as well. Due to the problem of competing channels, our results rely crucially on the RG technique of dynamical bosonization. For the critical flavor number, we find $N_{\mathrm{f}}^{\mathrm{cr}}\simeq 5.1$ with an estimated systematic error of approximately one flavor.

We construct a well-defined lattice-regularized quantum theory formulated in terms of fundamental fermion and gauge fields, the same type of degrees of freedom as in the Standard Model. The theory is explicitly invariant under local Lorentz transformations and, in the continuum limit, under diffeomorphisms. It is suitable for describing large nonperturbative and fast-varying fluctuations of metrics. Although the quantum curved space turns out to be, on the average, flat and smooth owing to the noncompressibility of the fundamental fermions, the low-energy Einstein limit is not automatic: one needs to ensure that composite metrics fluctuations propagate to long distances as compared to the lattice spacing. One way to guarantee this is to stay at a phase transition. We develop a lattice mean-field method and find that the theory typically has several phases in the space of the dimensionless coupling constants, separated by the 2nd order phase transition surface. For example, there is a phase with a spontaneous breaking of chiral symmetry. The effective low-energy Lagrangian for the ensuing Goldstone field is explicitly diffeomorphism invariant. We expect that the Einstein gravitation is achieved at the phase transition. A bonus is that the cosmological constant is probably automatically zero.