We examine the observational viability of a class of $f(\mathcal{R})$ gravity cosmological models. Particular attention is devoted to constraints from the recent observational determination of the redshift of the cosmological deceleration-acceleration transition. Making use of the fact that the Ricci scalar is a function of redshift $z$ in these models, $\mathcal{R}=\mathcal{R}(z)$, and so is $f(z)$, we use cosmography to relate a $f(z)$ test function evaluated at higher $z$ to late-time cosmographic bounds. First, we consider a model-independent procedure to build up a numerical $f(z)$ by requiring that at $z=0$ the corresponding cosmological model reduces to standard $\mathrm{\Lambda }\mathrm{CDM}$. We then infer late-time observational constraints on $f(z)$ in terms of bounds on the Taylor expansion cosmographic coefficients. In doing so we parametrize possible departures from the standard $\mathrm{\Lambda }\mathrm{CDM}$ model in terms of a two-parameter logarithmic correction. The physical meaning of the two parameters is also discussed in terms of the post-Newtonian approximation. Second, we provide numerical estimates of the cosmographic series terms by using type Ia supernova apparent magnitude data and Hubble parameter measurements. Finally, we use these estimates to bound the two parameters of the logarithmic correction. We find that the deceleration parameter in our model changes sign at a redshift consistent with what is observed.

We present simple expressions for the relativistic first and second order fractional density perturbations for Friedmann-Lemaître cosmologies with dust, in four different gauges: the Poisson, uniform curvature, total matter and synchronous-comoving gauges. We include a cosmological constant and arbitrary spatial curvature in the background. A distinctive feature of our approach is our description of the spatial dependence of the perturbations using a canonical set of quadratic differential expressions involving an arbitrary spatial function that arises as a conserved quantity. This enables us to unify, simplify and extend previous seemingly disparate results. We use the primordial matter and metric perturbations that emerge at the end of the inflationary epoch to determine the additional arbitrary spatial function that arises when integrating the second order perturbation equations. This introduces a non-Gaussianity parameter into the expressions for the second order density perturbation. In the special case of zero spatial curvature we show that the time evolution simplifies significantly, and requires the use of only two nonelementary functions, the so-called growth suppression factor at the linear level, and one new function at the second order level. We expect that the results will be useful in applications, for example, studying the effects of primordial non-Gaussianity on the large scale structure of the Universe.

In this paper, we propose a toy model of the renormalizable theory describing a massive spin-two field. Although the model is renormalizable, we show that the model contains ghosts. The coupling of the theory with gravity can be regarded as a new kind of bimetric gravity or bigravity. We show that the massive spin-two field plays the role of the cosmological constant.

We consider scenarios in which the 125 GeV resonance observed at the Large Hadron Collider is a Technicolor (TC) isosinglet scalar, the TC Higgs and explore the viable parameter space of the effective Higgs boson couplings within the TC Higgs scenario using the latest LHC data. By comparison with quantum chromodynamics, we argue that the couplings of the TC Higgs to the massive weak bosons are very close to the standard model (SM) values. The couplings to photons and gluons are model-dependent, but close to the SM values in several TC theories. The couplings of the TC Higgs to SM fermions are due to interactions beyond TC, such as extended technicolor: if such interactions successfully generate mass for the SM fermions, we argue that the couplings of the latter to the TC Higgs are also SM-like. We suggest a generic parametrization of the TC Higgs interactions with SM particles that accommodates a large class of TC models, and we perform a fit of these parameters to the Higgs LHC data. The fit reveals regions of the parameter space where the form factors have an order-one absolute value at the 95% CL, in agreement with expectations in TC theories. This indicates that the discovered Higgs boson is consistent with the TC Higgs hypothesis for several TC theories.

We present three case studies at a 100 TeV proton collider for how jet analyses can be improved using new jet (sub)structure techniques. First, we use the winner-take-all recombination scheme to define a recoil-free jet axis that is robust against pileup. Second, we show that soft drop declustering is an effective jet grooming procedure that respects the approximate scale invariance of QCD. Finally, we highlight a potential standard candle for jet calibration using the soft-dropped energy loss. This latter observable is remarkably insensitive to the scale and flavor of the jet, a feature that arises because it is infrared/collinear unsafe, but Sudakov safe.

Measurements of the muon charge asymmetry in inclusive $pp\to W+X$ production at $\sqrt{s}=7\mathrm{TeV}$ are presented. The data sample corresponds to an integrated luminosity of $4.7{\mathrm{fb}}^{-1}$ recorded with the CMS detector at the LHC. With a sample of more than 20 million $W\to \mu \nu$ events, the statistical precision is greatly improved in comparison to previous measurements. These new results provide additional constraints on the parton distribution functions of the proton in the range of the Bjorken scaling variable $x$ from ${10}^{-3}$ to ${10}^{-1}$. These measurements and the recent CMS measurement of associated $W+\text{charm}$ production are used together with the cross sections for inclusive deep inelastic $e^{\pm }p$ scattering at HERA in a next-to-leading-order QCD analysis. The determination of the valence quark distributions is improved, and the strange-quark distribution is probed directly through the leading-order process $g+s\to W+c$ in proton-proton collisions at the LHC.

The Gaussian curvature of the two-surface $r=0$, $t=\text{const}$ is calculated for the Kerr–de Sitter and Kerr–Newman–de Sitter solutions, yielding nonzero analytical expressions for both cases. The results obtained on the one hand exclude the possibility for that surface to be a disk and, on the other hand, permit one to establish a correct geometrical interpretation of that surface for each of the two solutions.

We study oscillating string solutions in the Klebanov-Witten and its non-Abelian $T$-dual background dualized along an SU(2) isometry. We find the string energy as the function of the oscillation number and angular momentum. We show that for a particular set of $T$-dual coordinates both the backgrounds have equal string states. We also study the string states where the strings are expanding and contracting in the $T$-dual coordinate direction. We expect the presence of the superconformal field theory dual operators whose anomalous dimensions depend on the $T$-dual coordinate.

We study $\mathcal{N}=(0,2)$ deformed (2, 2) two-dimensional sigma models. Such hete-rotic models were discovered previously on the world sheet of non-Abelian strings supported by certain four-dimensional $\mathcal{N}=1$ theories. We study geometric aspects and holomorphic properties of these models and derive a number of exact expressions for the $\beta$ functions in terms of the anomalous dimensions analogous to the NSVZ $\beta$ function in four-dimensional gauge theories. Instanton calculus provides a straightforward method for the derivation verified at two loops by explicit calculations. Obtained two-loop anomalous dimensions give an explicit expression for one of the $\beta$ functions valid to three loops. The fixed point in the ratio of the couplings found previously at one loop is not shifted at two loops. We also consider the $\mathcal{N}=(0,2)$ supercurrent supermultiplet (the so-called hypercurrent) and its anomalies, as well as the “Konishi anomaly.” This gives us another method for finding exact $\beta$ functions. We prove that despite the chiral nature of the models under consideration, quantum loops preserve isometries of the target space.

We present a simple class of warped-product vacuum (Ricci-flat) solutions to ten- and eleven-dimensional supergravity, where the internal space is flat and noncompact and the warp factor supports de Sitter (dS) and anti–de Sitter (AdS) vacua, in addition to trivial Minkowski vacua with compact internal spaces. We outline the construction of consistent Kaluza-Klein reductions and show that, although our vacuum solutions are nonsupersymmetric, these are closely related to the bosonic part of well-known maximally supersymmetric reductions on spheres. We comment on the stability of our solutions, noting that ${(\mathrm{A})\mathrm{dS}}_3$ vacua pass routine stability tests.

We construct and study a generalized one-parameter class of scheme transformations, denoted $S_{R,m,k_1}$ with $m\ge 2$, with the property that an $S_{R,m,k_1}$ scheme transformation eliminates the $\ell$-loop terms in the beta function of a gauge theory from loop order $\ell =3$ to order $\ell =m+1$, inclusive. These scheme transformations are applied to the higher-loop calculation of the infrared zero of the beta function of an asymptotically free gauge theory with multiple fermions. We show that scheme transformations in this generalized class satisfy a set of criteria for physical acceptability over a larger range of numbers of fermions than previously studied scheme transformations. We also present an interesting modification of a different type of scheme transformation that removes the three-loop term in the beta function.

We examine the higher-dimensional action in which gravity is coupled to the exponential nonlinear electrodynamic field and a scalar dilaton field. We construct a new class of $n$-dimensional static and spherically symmetric black hole solutions of this theory in the presence of the dilaton potential with two Liouville-type terms. In the presence of two Liouville-type dilaton potentials, the asymptotic behavior of the obtained black holes is neither flat nor (A)dS. Due to the nonlinear nature of the electrodynamic field, the electric field has finite value near the origin where $r\to 0$ and goes to zero as $r\to \infty$. Interestingly enough, we find that in the absence of the dilaton field, the electric field has a finite value at $r=0$, while as soon as the dilaton field is taken into account, the electric field diverges as $r\to 0$. This implies that the presence of the dilaton field changes the behavior of the electric field near the origin. In the limiting case where the nonlinear parameter $\beta$ goes to infinity, our solutions reduce to dilaton black holes of Einstein-Maxwell-dilaton gravity in higher dimensions. We compute the conserved and thermodynamic quantities of the solutions and show that these quantities satisfy the first law of black hole thermodynamics on the horizon.

The possible different phases of homogeneous cold quark matter in the presence of a finite magnetic field and chemical potential are obtained within the SU(3) NJL model for two parameter sets often used in the literature. Although the general pattern is the same in both cases, the number of intermediate phases is parameter dependent. The chiral susceptibilities, as usually defined, are different not only for the $s$ quark as compared with the two light quarks, but also for the $u$ and $d$ quarks, yielding nonidentical crossover lines for the light quark sector. The results for stellar matter, imposing charge neutrality and $\beta$ equilibrium, are also presented for the same sets of parameters. The corresponding phase diagrams show some differences with respect to the symmetric cases. It is found that for stellar matter the inverse catalysis effect is less pronounced and the transition to the fully chiral symmetry-restored phase occurs at higher chemical potentials.

The discovery of the primordial B-mode polarization by the BICEP2 experiment indicates inflation with a relatively high energy scale. Taking this indication into account, we propose consistent scenarios to account for the observed baryon and dark matter densities in gravity- and gauge-mediated supersymmetry breaking models. The baryon asymmetry is explained by the Afflck-Dine mechanism, which requires relatively low reheating temperature to avoid a sizable baryonic isocurvature perturbation. The low reheating temperature then requires nonthermal production of dark matter to account for the correct relic density of dark matter. Our scenarios can account for the observations of baryon and dark matter density in gravity and gauge mediation and predict some parameters, including the mass of dark matter.

The recent discovery of a light $CP$-even Higgs in a region of masses consistent with the predictions of models with low-energy supersymmetry have intensified the discussion of naturalness in these situations. The focus point solution alleviates the minimal supersymmetric extension of the Standard Model (MSSM) fine-tuning problem. In a previous work, we showed the general form of the MSSM focus point solution, for different values of the messenger scale and of the ratio of gaugino and scalar masses. Here we study the possibility of inducing a light stop as a result of the renormalization group running from high energies. This scenario is highly predictive and leads to observables that may be constrained by future collider and flavor physics data.

Within the minimal supersymmetric extension of the Standard Model (MSSM) the associated production of neutral Higgs bosons with top and bottom quarks belongs to the most important Higgs-boson production processes at the LHC. At large values of $\mathrm{tg}\beta$, in particular, bottom-Higgs associated production constitutes the dominant production channel within the MSSM. We have calculated the next-to-leading-order supersymmetric QCD corrections to neutral Higgs production through the parton processes $q\overline{q}$, $gg\to t\overline{t}/b\overline{b}+h/H/A$ and present results for the total cross sections. The genuine SUSY-QCD corrections are of moderate size for small $\mathrm{tg}\beta$, but can be sizable for large $\mathrm{tg}\beta$. In the latter case the bulk of these corrections can be absorbed into effective bottom Yukawa couplings.

An emission line with energy of $E\sim 3.5\mathrm{keV}$ has been observed in galaxy clusters by two experiments. The emission line is consistent with the decay of a dark matter particle with a mass of $\sim 7\mathrm{keV}$. In this work we discuss the possibility that the dark particle responsible for the emission is a real scalar ($\rho$) which arises naturally in a $U(1{)}_X$ Stueckelberg extension of minimal supersymmetric standard model (MSSM). In the MSSM Stueckelberg extension $\rho$ couples only to other scalars carrying a $U(1{)}_X$ quantum number. Under the assumption that there exists a vectorlike leptonic generation carrying both $SU(2{)}_L\times U(1{)}_Y$ and $U(1{)}_X$ quantum numbers, we compute the decay of the $\rho$ into two photons via a triangle loop involving scalars. The relic density of the $\rho$ arises via the decay $H^0\to h^0+\rho$ at the loop level involving scalars, and via the annihilation processes of the vectorlike scalars into $\rho +h^0$. It is shown that the galactic data can be explained within a multicomponent dark matter model where the 7 keV dark matter is a subdominant component constituting only 1%–10% of the matter relic density, with the rest being supersymmetric dark matter such as the neutralino. Thus, the direct detection experiments remain viable searches for weakly interacting massive particles. The fact that the dark scalar $\rho$ with no interactions with the standard model particles arises from a Stueckelberg extension of a hidden $U(1{)}_X$ implies that the 3.5 keV galactic line emission is a signal from the hidden sector.