Using the observation data of type Ia supernovae, cosmic microwave background, and baryon acoustic oscillations, we establish two concrete $f(T)$ models with a nonminimal torsion-matter coupling extension. We study in detail the cosmological implication of our models and find they are successful in describing the observation of the Universe and its large-scale structure and evolution. In other words, these models do not change the successful aspects of the $\mathrm{\Lambda }\mathrm{CDM}$ scenario under the error band of fitting values as describing the evolution history of the Universe including the radiation-dominated era, the matter-dominated era, and the present accelerating expansion. Meanwhile, the significant advantage of these models is that they could avoid the cosmological constant problem of $\mathrm{\Lambda }\mathrm{CDM}$. A joint analysis is performed by using the data of cosmic microwave $\text{background}+\text{baryon}$ acoustic $\text{oscillations}+\text{joint}$ light-curve analysis, which leads to ${\mathrm{\Omega }}_{m0}=0.255\pm 0.010$, ${\mathrm{\Omega }}_{b0}{h}^2=0.0221\pm 0.0003$ and $H_0=68.54\pm 1.27$ for model I and ${\mathrm{\Omega }}_{m0}=0.306\pm 0.010$, ${\mathrm{\Omega }}_{b0}{h}^2=0.0225\pm 0.0003$ and $H_0=60.97\pm 0.44$ for model II at $1\sigma$ confidence level. The evolution of the decelaration parameter $q(a)$ and the effective equation of state $w_{DE}(a)$ are displayed. Furthermore, the resulting age of the Universe from our models is consistent with the ages of the oldest globular clusters. As for the fate of the Universe, model I and model II result in a de Sitter accelerating phase and a power-law one, respectively, even though $w_{DE0}<-1$ makes model I look like a phantom at the present time.

We consider domain walls in the $Z_3$ symmetric next-to-minimal supersymmetric standard model. The spontaneous $Z_3$ discrete symmetry breaking produces domain walls, and the stable domain walls are problematic. Thus, we assume the $Z_3$ symmetry is slightly but explicitly broken and the domain walls decay. Such a decay causes a large late-time entropy production. We study its cosmological implications on unwanted relics such as the moduli, gravitino, lightest superparticle, and axion.

We consider the possibility that the Universe is made of a dark fluid described by a quadratic equation of state $P=K{\rho }^2$, where $\rho$ is the rest-mass density and $K$ is a constant. The energy density $\epsilon =\rho c^2+K{\rho }^2$ is the sum of two terms: a rest-mass term $\rho c^2$ that mimics “dark matter” ($P=0$) and an internal energy term $u=K{\rho }^2=P$ that mimics a “stiff fluid” ($P=\epsilon$) in which the speed of sound is equal to the speed of light. In the early universe, the internal energy dominates and the dark fluid behaves as a stiff fluid ($P\sim \epsilon$, $\epsilon \propto a^{-6}$). In the late universe, the rest-mass energy dominates and the dark fluid behaves as pressureless dark matter ($P\simeq 0$, $\epsilon \propto a^{-3}$). We provide a simple analytical solution of the Friedmann equations for a universe undergoing a stiff matter era, a dark matter era, and a dark energy era due to the cosmological constant. This analytical solution generalizes the Einstein–de Sitter solution describing the dark matter era, and the $\mathrm{\Lambda }\mathrm{CDM}$ model describing the dark matter era and the dark energy era. Historically, the possibility of a primordial stiff matter era first appeared in the cosmological model of Zel’dovich where the primordial universe is assumed to be made of a cold gas of baryons. A primordial stiff matter era also occurs in recent cosmological models where dark matter is made of relativistic self-gravitating Bose-Einstein condensates (BECs). When the internal energy of the dark fluid mimicking stiff matter is positive, the primordial universe is singular like in the standard big bang theory. It expands from an initial state with a vanishing scale factor and an infinite density. We consider the possibility that the internal energy of the dark fluid is negative (while, of course, its total energy density is positive), so that it mimics anti-stiff matter. This happens, for example, when the BECs have an attractive self-interaction with a negative scattering length. In that case, the primordial universe is nonsingular and bouncing like in loop quantum cosmology. At $t=0$, the scale factor is finite and the energy density is equal to zero. The universe first has a phantom behavior where the energy density increases with the scale factor, then a normal behavior where the energy density decreases with the scale factor. For the sake of generality, we consider a cosmological constant of arbitrary sign. When the cosmological constant is positive, the Universe asymptotically reaches a de Sitter regime where the scale factor increases exponentially rapidly with time. This can account for the accelerating expansion of the Universe that we observe at present. When the cosmological constant is negative (anti–de Sitter), the evolution of the Universe is cyclic. Therefore, depending on the sign of the internal energy of the dark fluid and on the sign of the cosmological constant, we obtain analytical solutions of the Friedmann equations describing singular and nonsingular expanding, bouncing, or cyclic universes.

The QCD phase diagram in the temperature vs quark chemical potential plane is studied in the presence of a magnetic field, using the linear sigma model coupled to quarks. It is shown that the decrease of the couplings with increasing field strength obtained in this model leads to the critical temperature for the phase transition to decrease with increasing field intensity (inverse magnetic catalysis). This happens provided that plasma screening is properly accounted for. It is also found that with increasing field strength the location of the critical end point in the phase diagram moves toward lower values of the critical quark chemical potential and larger values of the critical temperature. In addition, the critical end point approaches the temperature axis for large values of the magnetic field. We argue that a similar behavior is to be expected in QCD, since the physical impact of the magnetic field, regardless of strength, is to produce a spatial dimension reduction, whereby virtual quark-antiquark pairs are closer on average and thus the strength of their interaction decreases due to asymptotic freedom.

We perform a systematical and analytical study of lepton mixing which can be derived from the subgroups of $SU(3)$ under the assumption that neutrinos are Dirac particles. We find that type D groups can predict lepton mixing patterns compatible with the experimental data at the $3\sigma$ level. The lepton mixing matrix turns out to be of the trimaximal form, and the Dirac $CP$ violating phase is trivial. Moreover, we extend the flavor symmetry to the quark sector. The Cabibbo mixing between the first two generations of quarks can be generated by type D groups. Since all the finite subgroups of $U(3)$ that are not the subgroups of $SU(3)$ have not been classified, an exhaustive scan over all finite discrete groups up to order 2000 is performed with the help of the computer algebra system gap. We find that only 90 (10) groups for Dirac (Majorana) neutrinos can generate the lepton mixing angles in the experimentally preferred ranges. The lepton mixing matrix is still the trimaximal pattern and the Dirac $CP$ phase remains trivial. The smallest groups that lead to viable mixing angles are [162, 10], [162, 12], and [162, 14]. For quark flavor mixing, the correct order of magnitude of the Cabibbo-Kobayashi-Maskawa matrix elements cannot be generated. Only the Cabibbo mixing is allowed even if we impose very loose constraints $0.1\le |V_{us}|\le 0.3$ and $|V_{ub}|\le |V_{cb}|<|V_{us}|$. The group $\mathrm{\Delta }(6\times 7^2)$ can predict a Cabibbo angle ${\theta }_q=\pi /14$ in good agreement with the best fit value. The observed Cabibbo mixing angle can easily be accommodated if the first two left-handed quark fields are assigned to a doublet. The groups that can give rise to both phenomenologically viable lepton mixing angles and acceptable Cabibbo angles are discussed, and the groups $\mathrm{\Delta }(6\times 9^2)$, [648, 259], [648, 260], [648, 266], and $\mathrm{\Delta }(6\times {14}^2)$ are especially promising in the case of the triplet assignment for both quark and lepton sectors. The three groups [496, 19], [496, 21], and [496, 23] are interesting candidates for flavor symmetry if the left-handed lepton and quark fields are assigned to triplet and doublet plus singlet, respectively.

We study lattice QCD at nonvanishing chemical potential using the complex Langevin equation. We compare the results with multiparameter reweighting both from $\mu =0$ and phase-quenched ensembles. We find a good agreement for lattice spacings below $\approx 0.15\mathrm{fm}$. On coarser lattices the complex Langevin approach breaks down. Four flavors of staggered fermions are used on $N_t=4$, 6 and 8 lattices. For one ensemble we also use two flavors to investigate the effects of rooting.

The role of instanton-like objects in the QCD vacuum on the mass spectrum of low-lying light hadrons is explored in lattice QCD. Using overimproved stout-link smearing, tuned to preserve instanton-like objects in the QCD vacuum, the evolution of the mass spectrum under smearing is examined. The calculation is performed using a ${20}^3\times 40$ dynamical fat-link-irrelevant-clover (FLIC) fermion action ensemble with lattice spacing 0.126 fm. Through the consideration of a range of pion masses, the effect of the vacuum instanton content is compared at a common pion mass. While the qualitative features of ground-state hadrons are preserved on instanton-dominated configurations, the excitation spectrum experiences significant changes. The underlying physics revealed shows little similarity to the direct-instanton-interaction predictions of the instanton liquid model.

We present a detailed assessment of how well a future electron-ion collider could constrain helicity parton distributions in the nucleon and, therefore, unveil the role of the intrinsic spin of quarks and gluons in the proton’s spin budget. Any remaining deficit in this decomposition will provide the best indirect constraint on the contribution due to the total orbital angular momenta of quarks and gluons. Specifically, all our studies are performed in the context of global QCD analyses based on realistic pseudodata and in the light of the most recent data obtained from polarized proton-proton collisions at BNL-RHIC that have provided evidence for a significant gluon polarization in the accessible, albeit limited range of momentum fractions. We also present projections on what can be achieved on the gluon’s helicity distribution by the end of BNL-RHIC operations. All estimates of current and projected uncertainties are performed with the robust Lagrange multiplier technique.

Viscous modifications to the thermal distributions of quark-antiquarks and gluons have been studied in a quasiparticle description of the quark-gluon-plasma medium created in relativistic heavy-ion collision experiments. The model is described in terms of quasipartons that encode the hot QCD medium effects in their respective effective fugacities. Both shear and bulk viscosities have been taken in to account in the analysis, and the modifications to thermal distributions have been obtained by modifying the energy-momentum tensor in view of the nontrivial dispersion relations for the gluons and quarks. The interactions encoded in the equation of state induce significant modifications to the thermal distributions. As an implication, the dilepton production rate in the $q\overline{q}$ annihilation process has been investigated. The equation of state is found to have a significant impact on the dilepton production rate along with the viscosities.

We propose a three loop radiative neutrino mass scenario with an isolated doubly charged singlet scalar $k^{\pm \pm }$ without couplings to the charged leptons, while two other singly charged scalars $h_1^{\pm }$ and $h_2^{\pm }$ attach to them. In this setup, the lepton flavor violation originating from $k^{\pm \pm }$ exchanges is suppressed and the model is less constrained, where some couplings can take sizable values. As reported in our previous work [1], the loop suppression factor at the three loop level would be too strong and realized neutrino masses in a three loop scenario could be smaller than the observed minuscule values. The sizable couplings can help us to enhance neutrino masses without drastically large scalar trilinear couplings appearing in a neutrino mass matrix, which tends to drive the vacuum stability to become jeopardized at the one loop level. Now the doubly charged scalar $k^{\pm \pm }$ has less constraint via lepton flavor violation and the vacuum can be quite stable, and thus a few hundred GeV mass in $k^{\pm \pm }$ is possible, which is within the LHC reach and this model can be tested in the near future. Note that the other $h_1^{\pm }$ and $h_2^{\pm }$ should be heavy at least around a few TeV. We suitably arrange the charges of an additional global $U(1)$ symmetry, where the decay constant of the associated Nambu-Goldstone boson can be around a TeV scale consistently. Also, this model is indirectly limited through a global analysis on results of the LHC Higgs search and issues on a dark matter candidate, the lightest Majorana neutrino. After $h_1^{\pm }$ and $h_2^{\pm }$ are decoupled, this particle couples to the standard model particles only through two charge parity even scalars in theory and thus information on this scalar sector is important. Consistent solutions are found, but a part of them is now on the edge.

Nuclear reactors provide intense sources of electron antineutrinos, characterized by few-MeV energy $E$ and unoscillated spectral shape $\mathrm{\Phi }(E)$. High-statistics observations of reactor neutrino oscillations over medium-baseline distances $L\sim O(50)\mathrm{km}$ would provide unprecedented opportunities to probe both the long-wavelength mass-mixing parameters ($\delta m^2$ and ${\theta }_{12}$) and the short-wavelength ones ($\mathrm{\Delta }{m}_{ee}^2$ and ${\theta }_{13}$), together with the subtle interference effects associated with the neutrino mass hierarchy (either normal or inverted). In a given experimental setting—here taken as in the JUNO project for definiteness—the achievable hierarchy sensitivity and parameter accuracy depend not only on the accumulated statistics but also on systematic uncertainties, which include (but are not limited to) the mass-mixing priors and the normalizations of signals and backgrounds. We examine, in addition, the effect of introducing smooth deformations of the detector energy scale, $E\to E^{\prime }(E)$, and of the reactor flux shape, $\mathrm{\Phi }(E)\to {\mathrm{\Phi }}^{\prime }(E)$, within reasonable error bands inspired by state-of-the-art estimates. It turns out that energy-scale and flux-shape systematics can noticeably affect the performance of a JUNO-like experiment, both on the hierarchy discrimination and on precision oscillation physics. It is shown that a significant reduction of the assumed energy-scale and flux-shape uncertainties (by, say, a factor of 2) would be highly beneficial to the physics program of medium-baseline reactor projects. Our results also shed some light on the role of the inverse-beta decay threshold, of geoneutrino backgrounds, and of matter effects in the analysis of future reactor oscillation data.

We consider six-dimensional supergravity compactified on orbifolds with Wilson lines and bulk flux. Torus Wilson lines are decomposed into Wilson lines around the orbifold fixed points, and twisted boundary conditions of matter fields are related to fractional localized flux. Both, orbifold singularities and flux lead to chiral fermions in four dimensions. We show that in addition to the standard bulk and fixed point anomalies the Green-Schwarz term also cancels the four-dimensional anomaly induced by the flux background. The two axions contained in the antisymmetric tensor field both contribute to the cancellation of the four-dimensional anomaly and the generation of a vector boson mass via the Stueckelberg mechanism. An orthogonal linear combination of the axions remains massless and couples to the gauge field in the standard way. Furthermore, we construct convenient expressions for the wave functions of the zero modes and relate their multiplicity and behavior at the fixed points to the bulk flux quanta and the Wilson lines.

We study spherical scalar collapse toward a black hole formation and examine the asymptotic dynamics near the central singularity of the formed black hole. It is found that, in the vicinity of the singularity, due to the strong backreaction of a scalar field on the geometry, the mass function inflates and the Kretschmann scalar grows faster than in the Schwarzschild geometry. In collapse, the Misner-Sharp mass is a locally conserved quantity, not providing information on the black hole mass that is measured at asymptotically flat regions.

We consider a way of eliminating the unwanted scalar graviton from Horava-Lifshitz gravity that is achieved via introduction of certain additional constraints. We perform canonical analysis of both projectable and nonprojectable versions of the theory. We obtain the structure of constraints in each case, and analyze its dependence on the values of the coupling constants involved in the additional constraints. In the nonprojectable theory, the scalar graviton is absent when the coupling constants have certain values, while for other values the scalar graviton appears. The projectable theory is free from the scalar graviton regardless of the values of the coupling constants, even though the structure of the constraints does depend on the value of a coupling constant.

We investigate modified theories of gravity in the context of teleparallel geometries. It is well known that modified gravity models based on the torsion scalar are not invariant under local Lorentz transformations while modifications based on the Ricci scalar are. This motivates the study of a model depending on the torsion scalar and the divergence of the torsion vector. We derive the teleparallel equivalent of $f(R)$ gravity as a particular subset of these models and also show that this is the unique theory in this class that is invariant under local Lorentz transformation. Furthermore one can show that $f(T)$ gravity is the unique theory admitting second-order field equations.

In this paper we analyze a quartic tensor model with one interaction for a tensor of arbitrary rank. This model has a critical point where a continuous limit of infinitely refined random geometries is reached. We show that the critical point corresponds to a phase transition in the tensor model associated to a breaking of the unitary symmetry. We analyze the model in the two phases and prove that, in a double scaling limit, the symmetric phase corresponds to a theory of infinitely refined random surfaces, while the broken phase corresponds to a theory of infinitely refined random nodal surfaces. At leading order in the double scaling limit planar surfaces dominate in the symmetric phase, and planar nodal surfaces dominate in the broken phase.

We study in detail the $f$-mode secular instability for rapidly rotating neutron stars, putting emphasis on supramassive models which do not have a stable nonrotating counterpart. Such neutron stars are thought to be the generic outcome of the merger of two standard-mass neutron stars. In addition, we take into account the effects of a strong magnetic field and $r$-mode instability, that can drain a substantial amount of angular momentum. We find that the gravitational wave signal emitted by supramassive neutron stars can reach above the Advanced LIGO sensitivity at distance of about 20 Mpc, and the detectability is substantially enhanced for the Einstein Telescope. The event rate will be of the same order as the merging rates, while the analysis of the signal will carry information for the equation of state of the postmerging neutron stars and the strength of the magnetic fields.

We use the proper time formalism to study a (non-self-interacting) massive Klein-Gordon theory in the two dimensional de Sitter space. We determine the exact Green’s function of the theory by solving the DeWitt-Schwinger equation as well as by calculating the operator matrix element. We point out how the one parameter family of arbitrariness in the Green’s function arises in this method.

We present LUXCalc, a new utility for calculating likelihoods and deriving weakly interacting massive particle (WIMP)-nucleon coupling limits from the recent results of the LUX direct search dark matter experiment. After a brief review of WIMP-nucleon scattering, we derive LUX limits on the spin-dependent WIMP-nucleon couplings over a broad range of WIMP masses, under standard assumptions on the relevant astrophysical parameters. We find that, under these and other common assumptions, LUX excludes the entire spin-dependent parameter space consistent with a dark matter interpretation of DAMA’s anomalous signal, the first time a single experiment has been able to do so. We also revisit the case of spin-independent couplings, and demonstrate good agreement between our results and the published LUX results. Finally, we derive constraints on the parameters of an effective dark matter theory in which a spin-1 mediator interacts with a fermionic WIMP and Standard Model fermions via axial-vector couplings. A detailed appendix describes the use of LUXCalc with standard codes to place constraints on generic dark matter theories.

The dynamics of symplectic gauge fields provides a consistent framework for fundamental interactions based on spin-3 gauge fields. One remarkable property is that symplectic gauge fields only have minimal couplings with gravitational fields and not with any other field of the Standard Model. Interactions with ordinary matter and radiation can only arise from radiative corrections. In spite of the gauge nature of symplectic fields they acquire a mass by the Coleman-Weinberg mechanism which generates Higgs-like mass terms where the gravitational field is playing the role of a Higgs field. Massive symplectic gauge fields weakly interacting with ordinary matter are natural candidates for the dark matter component of the Universe.