We derive maps relating the currents and energy-momentum tensors in noncommutative (NC) gauge theories with their commutative equivalents. Some uses of these maps are discussed. Especially, in NC electrodynamics, we obtain a generalization of the Lorentz force law. Also, the same map for anomalous currents relates the Adler-Bell-Jackiw–type NC covariant anomaly with the standard commutative-theory anomaly. For the particular case of two dimensions, we discuss the implications of these maps for the Sugawara-type energy-momentum tensor.

We present here the general transformation that leaves unchanged the form of the field equations for perfect fluid cosmologies in the Dvali-Gabadadze-Porrati (DGP) brane-world model. Specifically, a prescription for relating exact solutions with different equations of state is provided, and the symmetries found can be used as algorithms for generating new cosmological models from previously known ones. We also present, implicitly, the first known exact DGP perfect fluid spacetime. A particular case of the general transformation is used to illustrate the crucial role played both by the number of scalar fields and the extra-dimensional effects in the occurrence of inflation. In particular, we see that assisted inflation does not proceed at all times for one of the two possible ways in which the brane can be embedded into the bulk.

We treat the gravitational effects of quantum stress tensor fluctuations. An operational approach is adopted in which these fluctuations produce fluctuations in the focusing of a bundle of geodesics. This can be calculated explicitly using the Raychaudhuri equation as a Langevin equation. The physical manifestation of these fluctuations are angular blurring and luminosity fluctuations of the images of distant sources. We give explicit results for the case of a scalar field on a flat background in a thermal state.

Contrary to previous claims, it is shown that the expectation values of the quantum stress tensor for a massless scalar field propagating on a two-dimensional extreme Reissner-Nordström black hole are indeed regular on the horizon.

Cosmic inflation is envisioned as the “most likely” start for the observed universe. To give substance to this claim, a framework is needed in which inflation can compete with other scenarios and the relative likelihood of all scenarios can be quantified. The most concrete scheme to date for performing such a comparison shows inflation to be strongly disfavored. We analyze the source of this failure for inflation and present an alternative calculation, based on more traditional semiclassical methods, that results in inflation being exponentially favored. We argue that reconciling the two contrasting approaches presents interesting fundamental challenges, and is likely to have a major impact on ideas about the early universe.

Copi, Huterer, Starkman, and Schwarz introduced multipole vectors in a tensor context and used them to demonstrate that the first-year Wilkinson microwave anisotropy probe (WMAP) quadrupole and octopole planes align at roughly the 99.9% confidence level. In the present article, the language of polynomials provides a new and independent derivation of the multipole vector concept. Bézout’s theorem supports an elementary proof that the multipole vectors exist and are unique (up to rescaling). The constructive nature of the proof leads to a fast, practical algorithm for computing multipole vectors. We illustrate the algorithm by finding exact solutions for some simple toy examples and numerical solutions for the first-year WMAP quadrupole and octopole. We then apply our algorithm to Monte Carlo skies to independently reconfirm the estimate that the WMAP quadrupole and octopole planes align at the 99.9% level.

Cosmic shear surveys have great promise as tools for precision cosmology, but can be subject to systematic errors including intrinsic ellipticity correlations of the source galaxies. The intrinsic alignments are believed to be small for deep surveys, but this is based on intrinsic and lensing distortions being uncorrelated. Here we show that the gravitational lensing shear and intrinsic shear need not be independent: correlations between the tidal field and the intrinsic shear cause the intrinsic shear of nearby galaxies to be correlated with the gravitational shear acting on more distant galaxies. We estimate the magnitude of this effect for two simple intrinsic-alignment models: one in which the galaxy ellipticity is linearly related to the tidal field, and one in which it is quadratic in the tidal field as suggested by tidal torque theory. The first model predicts a gravitational-intrinsic ($GI$) correlation that can be much greater than the intrinsic-intrinsic ($II$) correlation for broad redshift distributions, and that remains when galaxies pairs at similar redshifts are rejected. The second model, in its simplest form, predicts no gravitational-intrinsic correlation. In the first model, and assuming a normalization consistent with recently claimed detections of intrinsic correlations, we find that the $GI$ correlation term can exceed the usual $II$ term by $>1$ order of magnitude and the intrinsic correlation induced $B$-mode by 2 orders of magnitude. These interference effects can suppress the lensing power spectrum for a single broad redshift bin by of order $\sim 10\%$ at $z_s=1$ and $\sim 30\%$ at $z_s=0.5$. We conclude that, depending on the intrinsic-alignment model, the $GI$ correlation may be the dominant contaminant of the lensing signal and can even affect cross spectra between widely separated bins. We describe two ways to constrain this effect, one based on density-shear correlations and one based on scaling of the cross correlation tomography signal with redshift.

A recent variant of the inflationary paradigm is that the primordial curvature perturbations come from quantum fluctuations of a scalar field, subdominant and effectively massless during inflation, called the “curvaton,” instead of the fluctuations of the inflaton field. We consider the situation where the primordial curvature perturbations generated by the quantum fluctuations of an inflaton and of a curvaton field are of the same order of magnitude. We compute the total curvature perturbation and its spectrum in this case and we discuss the observational consequences.

Littlest Higgs model predicts some extra particles beyond the Standard Model. Among them, an extra neutral gauge boson $A_H$ is lightest and its mass could be a few hundred GeV. We study production and decay of $A_H$ at future $e^{+}{e}^{-}$ linear collider and compare them with those of $Z^{\prime }$ bosons in supersymmetric $E_6$ models. We find that, if the extra gauge boson mass is smaller than $\sqrt{s}$ of the linear collider, the forward-backward asymmetries of $b$- and $c$-quarks at the $A_H$ pole differ significantly from those given by the $Z^{\prime }$ bosons, and are useful to test the littlest Higgs model and SUSY $E_6$ models.

We show that the low-energy effective superpotential of an $\mathcal{N}=1$ $\mathrm{U}(N)$ gauge theory with matter in the adjoint and arbitrary even tree-level superpotential has, in the classically unbroken case, the same functional form as the effective superpotential of a $\mathrm{U}(N)$ gauge theory with matter in the fundamental and the same tree-level interactions, up to some rescalings of the couplings. We also argue that the same kind of reasoning can be applied to other cases as well.

We study the neutralino relic density and the neutralino-proton elastic scattering cross sections in the minimal supersymmetric standard model (MSSM) with $CP$-violating phases. We include all the final states to the neutralino pair annihilation cross section at the tree level, taking into account the mixing between the $CP$-even and $CP$-odd neutral Higgs fields. We show that variations of the relic density and the elastic scattering cross sections with the $CP$-violating phases are significant. In particular, interferences between the major contributions in the neutralino annihilation cross section can cause considerable enhancement of the relic density.

Asymmetries in the hadroproduction of charm particles directly probe power corrections to the QCD factorization theorems. In this paper, the heavy-quark recombination mechanism, a power correction that explains charm meson asymmetries, is extended to charm baryons. In this mechanism, a light quark participates in the hard-scattering that creates a charm quark and they hadronize together into a charm baryon. This provides a natural and economical explanation for the ${\Lambda }_c^{+}/{\Lambda }_c^{-}$ asymmetries measured in $\pi N$ and $pN$ collisions.

The Collins mechanism provides a nonperturbative explanation for the large single-spin asymmetries found in hard semi-inclusive reactions involving a transversely polarized nucleon. However, there are seemingly convincing reasons to suspect that the mechanism vanishes, and indeed it does vanish in the naive parton model where a quark is regarded as an essentially free particle. We give an intuitive analysis which highlights the difference between the naive picture and the realistic one and shows how the Collins mechanism arises when the quark is described as an off-shell particle by a field in interaction.

Using the soft-collinear effective theory we derive the factorization theorem for the decays $B\to M_1{M}_2$ with $M_{1,2}=\pi ,K,\rho ,K^{*}$, at leading order in $\Lambda /E_M$ and $\Lambda /m_b$. The results derived here apply even if ${\alpha }_s(E_M\Lambda )$ is not perturbative, and we prove that the physics sensitive to the $E\Lambda$ scale is the same in $B\to M_1{M}_2$ and $B\to M$ form factors. We argue that $c\overline{c}$ penguins could give long-distance effects at leading order. Decays to two transversely polarized vector mesons are discussed. Analyzing $B\to \pi \pi$ we find predictions for $B^0\to {\pi }^0{\pi }^0$ and $|V_{ub}|f_{+}^{B\to \pi }(0)$ as a function of $\gamma$.

We further study the previously proposed ansatz, $\mathrm{T}\mathrm{r}(M_{\nu })=0$, for a prediagonal light Majorana type neutrino mass matrix. If $CP$ violation is neglected this enables one to use the existing data on squared mass differences to estimate (up to a discrete ambiguity) the neutrino masses themselves. If it is assumed that only the conventional $CP$ phase is present, the ansatz enables us to estimate this phase in addition to all three masses. If it is assumed that only the two Majorana $CP$ phases are present, the ansatz enables us to present a one parameter family of solutions for the masses and phases. This enables us to obtain a simple “global” view of lepton number violation effects. Furthermore using an SO(10) motivation for the ansatz suggests an amusing toy (clone) model in which the heavy neutrinos have the same mixing pattern and mass ratios as the light ones. In this case only their overall mass scale is not known (although it is constrained by the initial motivation). Using this toy model we make a rough estimate of the magnitude of the baryon to photon ratio induced by the leptogenesis mechanism. Solutions close to the $CP$ conserving cases seem to be favored.

We generalize to arbitrary dimension the construction of a covariant and supersymmetric constraint for the massless super Poincaré algebra, which was given for the 11-dimensional case in a previous work. We also contrast it with a similar construction appropriate to the massive case. Finally we show that the constraint uniquely fixes the representation of the algebra.

Domain walls in $1+2$ dimensions are studied to clarify some general features of topological-charge anomalies in supersymmetric theories, by extensive use of a superfield supercurrent. For domain walls quantum modifications of the supercharge algebra arise not only from the short-distance anomaly but also from another source of long-distance origin, induced spin in the domain-wall background, and the latter dominates in the sum. A close look into the supersymmetric trace identity, which naturally accommodates the central-charge anomaly and its superpartners, shows an interesting consequence of the improvement of the supercurrent: Via an improvement the anomaly in the central-charge can be transferred from induced spin in the fermion sector to an induced potential in the boson sector. This fact reveals a dual character, both fermionic and bosonic, of the central-charge anomaly, which reflects the underlying supersymmetry. The one-loop superfield effective action is also constructed to verify the anomaly and Bogomol’nyi-Prasad-Sommerfield (BPS) saturation of the domain-wall spectrum.

Results of a detailed examination of the cascade nucleosynthesis resulting from the putative hadronic decay, evaporation, or annihilation of a primordial relic during the big bang nucleosynthesis (BBN) era are presented. It is found that injection of energetic nucleons around cosmic time ${10}^3\mathrm{s}$ may lead to an observationally favored reduction of the primordial ${}^7\mathrm{L}\mathrm{i}/\mathrm{H}$ yield by a factor 2–3. Moreover, such sources also generically predict the production of the ${}^6\mathrm{L}\mathrm{i}$ isotope with magnitude close to the as yet unexplained high ${}^6\mathrm{L}\mathrm{i}$ abundances in low-metallicity stars. The simplest of these models operates at a fractional contribution to the baryon density ${\Omega }_b{h}^2\gtrsim 0.025$, slightly larger than that inferred from standard BBN. Though further study is required, such sources, as, for example, due to the decay of the next-to-lightest supersymmetric particle into GeV gravitinos or the decay of an unstable gravitino in the TeV range of abundance ${\Omega }_{\tilde{G}}{h}^2\sim 5\times {10}^{-4}$ show promise to explain both the ${}^6\mathrm{L}\mathrm{i}$ and ${}^7\mathrm{L}\mathrm{i}$ abundances in low-metallicity stars.

Measurements of the Cosmic Microwave Background (CMB) temperature anisotropy and the temperature-polarization cross correlation by Wilkinson Microwave Anistropy Probe (WMAP) suggest a reionization redshift of $z\sim 17\pm 5$. On the other hand, observations of high redshift galaxies indicate a presence of a significant fraction of neutral hydrogen at redshift $z\sim 6-7$. We show that cosmic strings with tensions well within, but not far from, current observation bounds could cause early star formation at a level sufficient to explain the high reionization redshift.

We study the $N_f$-flavor Gross-Neveu model in $2+1$ dimensions with a baryon chemical potential $\mu$, using both analytical and numerical methods. In particular, we study the self-consistent Boltzmann equation in the Fermi liquid framework using the quasiparticle interaction calculated to $O(1/N_f)$, and find solutions for zero sound propagation for almost all $\mu >{\mu }_c$, the critical chemical potential for chiral symmetry restoration. Next we present results of a numerical lattice simulation, examining temporal correlation functions of mesons defined using a point-split interpolating operator, and finding evidence for phononlike behavior characterized by a linear dispersion relation in the long wavelength limit. We argue that our results provide the first evidence for a collective excitation in a lattice simulation.