We describe several new ways of specifying the behavior of Lemaître-Tolman (LT) models, in each case presenting the method for obtaining the LT arbitrary functions from the given data, and the conditions for existence of such solutions. In addition to our previously considered “boundary conditions,” the new ones include: a simultaneous big bang, a homogeneous density or velocity distribution in the asymptotic future, a simultaneous big crunch, a simultaneous time of maximal expansion, a chosen density or velocity distribution in the asymptotic future, only growing or only decaying fluctuations. Since these conditions are combined in pairs to specify a particular model, this considerably increases the possible ways of designing LT models with desired properties.

Slow-roll inflation is studied as an effective field theory. We find that the form of the inflaton potential consistent with Wilkinson Microwave Anisotropy Probe (WMAP) data and slow roll is $V(\varphi )=N{M}^{4}w(\frac{\varphi }{\sqrt{N}{M}_{\mathrm{Pl}}})$, where $\varphi$ is the inflaton field, $M$ is the inflation energy scale, and $N\sim 50$ is the number of e-folds since the cosmologically relevant modes crossed the Hubble radius until the end of inflation. The inflaton field scales as $\varphi =\sqrt{N}{M}_{\mathrm{Pl}}\chi$. The dimensionless function $w(\chi )$ and field $\chi$ are generically $\mathcal{O}(1)$. The WMAP value for the amplitude of scalar adiabatic fluctuations $|{\Delta }_{kad}^{(S)}{|}^2$ fixes the inflation scale $M\sim 0.77\times {10}^{16}$. This form of the potential makes manifest that the slow-roll expansion is an expansion in $1/N$. A Ginzburg-Landau realization of the slow-roll inflaton potential reveals that the Hubble parameter, inflaton mass and nonlinear couplings are of the seesaw form in terms of the small ratio $M/M_{\mathrm{Pl}}$. For example, the quartic coupling $\lambda \sim \frac{1}{N}(\frac{M}{M_{\mathrm{Pl}}}{)}^4$. The smallness of the nonlinear couplings is not a result of fine-tuning but a natural consequence of the validity of the effective field theory and slow-roll approximation. We clarify Lyth’s bound relating the tensor/scalar ratio and the value of $\varphi /M_{\mathrm{Pl}}$. The effective field theory is valid for $V(\varphi )\ll M_{\mathrm{Pl}}^4$ for general inflaton potentials allowing amplitudes of the inflaton field $\varphi$ well beyond $M_{\mathrm{Pl}}$. Hence bounds on $r$ based on the value of $\varphi /M_{\mathrm{Pl}}$ are overly restrictive. Our observations lead us to suggest that slow-roll, single field inflation may well be described by an almost critical theory, near an infrared stable Gaussian fixed point.

The flavor puzzle of the standard model is explained in split fermion models by having the fermions localized and separated in an extra dimension. Many of these models assume a certain profile for the Higgs vacuum expectation value, usually uniform, or confined to a brane, without providing a dynamical realization for it. By studying the effect of the coupling between the Higgs and the localizer fields, we obtain these scenarios as results, rather than Ansätze. Moreover, we discuss other profiles and show that they are phenomenologically viable.

The glueball-to-vacuum matrix elements of local gluonic operators in scalar, tensor, and pseudoscalar channels are investigated numerically on several anisotropic lattices with the spatial lattice spacing ranging from 0.1–0.2 fm. These matrix elements are needed to predict the glueball branching ratios in $J/\psi$ radiative decays which will help identify the glueball states in experiments. Two types of improved local gluonic operators are constructed for a self-consistent check and the finite-volume effects are studied. We find that lattice spacing dependence of our results is very weak and the continuum limits are reliably extrapolated, as a result of improvement of the lattice gauge action and local operators. We also give updated glueball masses with various quantum numbers.

We investigate the exclusive two-pion production at the $Z$-pole through the process $e^{+}{e}^{-}\to Z\to \pi \pi \gamma$. In the kinematical region where the invariant mass of the two pions is much smaller than the mass of the $Z$ boson, the process can be factorized into the convolution of a hard coefficient and a soft matrix element, the generalized distribution amplitude of two pions. We calculate the differential cross-section of charged pion pair production and neutral pion pair production and find the former to be much larger than the latter. We show that combining the measurements of charged pion pair production and neutral pion pair production at the $Z$-pole provides a convenient approach to access the $C$-odd part of the $2\pi$ distribution amplitudes.

We present a measurement of the inclusive electron spectrum in $B\to X_{u}e\nu$ decays near the kinematic limit for $B\to X_{c}e\nu$ transitions, using a sample of $88\times {10}^6$ $B\overline{B}$ pairs recorded by the BABAR detector at the ${\rm Y}(4S)$ resonance. Partial branching fraction measurements are performed in five overlapping intervals of the electron momentum; for the interval of $2.0–2.6\mathrm{GeV}/c$ we obtain $\Delta \mathcal{B}(B\to X_{u}e\nu )=(0.572\pm {0.041}_{\mathrm{stat}}\pm {0.065}_{\mathrm{syst}})\times {10}^{-3}$. Combining this result with shape function parameters extracted from BABAR measurements of moments of the inclusive photon spectrum in $B\to X_s\gamma$ decays and moments of the hadron-mass and lepton-energy spectra in $B\to X_c\ell \nu$ decays we determine $|V_{ub}|=(4.44\pm {0.25}_{\exp -0.38SF}^{+0.42}\pm {0.22}_{\mathrm{theory}})\times {10}^{-3}$. Here the first error represents the combined statistical and systematic experimental uncertainties of the partial branching fraction measurement, the second error refers to the uncertainty of the determination of the shape function parameters, and the third error is due to theoretical uncertainties in the QCD calculations.

It is suggested that Schwinger’s (1951) vacuum persistence probability against pair production by an intense but constant electric field is a very good approximation to the corresponding quantity if the field does not vary appreciably over space-time distances less than $m^{-1}(m^2/e|E|)$. This general result appears to be in agreement with a variety of previous calculations, both numerical and analytical.

We report on searches for $B^{-}\to D_s^{-}\varphi$ and $B^{-}\to D_s^{*-}\varphi$. In the context of the standard model, these decays are expected to be highly suppressed since they proceed through annihilation of the $b$ and $\overline{u}$ quarks in the $B^{-}$ meson. Our results are based on $234\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at SLAC. We find no evidence for these decays, and we set Bayesian 90% confidence level upper limits on the branching fractions $\mathcal{B}(B^{-}\to D_s^{-}\varphi )<1.9\times {10}^{-6}$ and $\mathcal{B}(B^{-}\to D_s^{*-}\varphi )<1.2\times {10}^{-5}$. These results are consistent with standard model expectations.

We collect some arguments for treating a D-brane with overcritical electric field as a well-posed initial condition for a D-brane decay. Within the field theoretical toy model of Minahan and Zwiebach we give an estimate for the condensates of the related infinite tower of tachyonic excitations.

We analyze large $N$ phase transitions for $U(N)$ $q$-deformed two-dimensional Yang-Mills theory on the sphere. We determine the phase diagram of the model and we show that, for small values of the deformation parameter, the theory exhibits a phase transition which is smoothly connected to the Douglas-Kazakov phase transition. For large values of the deformation parameter the phase transition is absent. By explicitly computing the one-instanton suppression factor in the weakly coupled phase, we also show that the transition is triggered by instanton effects. Finally, we present the solution of the model in the strongly coupled phase. Our analysis suggests that, on certain backgrounds, nonperturbative topological string theory has new phase transitions at small radius. From the point of view of gauge theory, it suggests a mechanism to smooth out large $N$ phase transitions.

We first investigate the attractor solution associated with assisted inflation in heterotic M theory to see if it is stable. By perturbing the solutions we find a solitary stable fixed point with the general path through phase space dependent upon the Calabi-Yau data and the number of five-branes. We then go on to examine the effect of including nonperturbative corrections to the inflaton potential arising from boundary-brane instantons as well as higher order brane interaction terms. The result is that assisted inflation is only possible if we allow fine tuning of the superpotential, and that generic nonperturbative superpotentials will prevent this kind of inflation from occurring.

We analyze high-energy scattering for noncommutative field theories using the dual gravity description. We find that the Froissart-Martin bound still holds, but that cross sections stretch in the noncommutative directions in a way dependent on the infrared cutoff. This puzzling behavior suggests new aspects of UV/IR mixing.

For the evolution of density fluctuation in nonlinear cosmological dynamics, adhesion approximation (AA) is proposed as a phenomenological model, which is especially useful for describing nonlinear evolution. However, the origin of the artificial viscosity in AA is not clarified. Recently, Buchert and Domínguez report if the velocity dispersion of the dust fluid is regarded as isotropic, it works on a principle similar to viscosity or effective pressure, and they consider isotropic velocity dispersion as the origin of the artificial viscosity in AA. They name their model the Euler-Jeans-Newton (EJN) model. In this paper, we focus on the velocity distribution in AA and the EJN model and examine the time evolution in both models. We find the behavior of AA differs from that of the EJN model, i.e., although the peculiar velocity in the EJN model oscillates, that in AA is monotonically decelerated due to viscosity without oscillation. Therefore it is hard to regard viscosity in AA as effective pressure in the EJN model.

The original models of causal dynamical triangulations construct space-time by arranging a set of simplices in layers separated by a fixed timelike distance. The importance of the foliation structure in the $2+1$ dimensional model is studied by considering variations in which this property is relaxed. It turns out that the fixed-lapse condition can be equivalently replaced by a set of global constraints that have geometrical interpretation. On the other hand, the introduction of new types of simplices that puncture the foliating sheets in general leads to different low-energy behavior compared to the original model.

Wisdom has recently unveiled a new relativistic effect, called “spacetime swimming”, where quasirigid free bodies in curved spacetimes can “speed up”, “slow down” or “deviate” their falls by performing local cyclic shape deformations. We show here that for fast enough cycles this effect dominates over a nonrelativistic related one, named here “space swinging”, where the fall is altered through nonlocal cyclic deformations in Newtonian gravitational fields. We expect, therefore, to clarify the distinction between both effects leaving no room to controversy. Moreover, the leading contribution to the swimming effect predicted by Wisdom is enriched with a higher order term and the whole result is generalized to be applicable in cases where the tripod is in large redshift regions.

The effect of weak gravitational lensing on the cosmic microwave background (CMB) temperature anisotropies and polarization will provide access to cosmological information that cannot be obtained from the primary anisotropies alone. We compare the information content of the lensed $B$-mode polarization power spectrum, properly accounting for the non-Gaussian correlations between the power on different scales, with that of the unlensed CMB fields and the lensing potential. The latter represent the products of an (idealized) optimal analysis that exploits the lens-induced non-Gaussianity to reconstruct the fields. Compressing the non-Gaussian lensed CMB into power spectra is wasteful and leaves a tight degeneracy between the equation of state of dark energy and neutrino mass that is much stronger than in the more optimal analysis. Despite this, a power-spectrum analysis will be a useful first step in analyzing future $B$-mode polarization data. For this reason, we also consider how to extract accurate parameter constraints from the lensed $B$-mode power spectrum. We show with simulations that for cosmic-variance-limited measurements of the lensed $B$-mode power, including the non-Gaussian correlations in existing likelihood approximations gives biased parameter results. We develop a more refined likelihood approximation that performs significantly better. This new approximation should also be of more general interest in the wider context of parameter estimation from Gaussian CMB data.

Observational consequences of inflationary cosmology in the holographic dual of the Randall-Sundrum type II braneworld scenario, as motivated by the anti-de Sitter/conformal field theory correspondence, are investigated. High energy corrections to the standard four-dimensional Friedmann equation induce a corresponding modification to the form of the single-field inflationary consistency equation based on Einstein gravity. The degree of departure from the standard expression is determined by the ratio, $r$, of the primordial tensor and scalar perturbation amplitudes and the coefficient, $c$, of the conformal anomaly in the dual gauge theory. It is found that a necessary condition for detecting such a correction with the next generation of cosmic microwave background (CMB) polarization experiments is that $r\ge 0.06$. The bound is tightened to $r>0.3$ for values of the central charge that are compatible with known compactifications of type IIB string theory as parametrized in terms of $F$-theory compactification on Calabi-Yau four-folds. This is close to the present upper bounds inferred from combined observations of the CMB anisotropy power spectrum and high redshift surveys. We conclude that if such modifications to the inflationary consistency equation are to be observable, the gravitational wave background should be detected in the near future. A further consequence of the nonstandard dynamics at high energies is that the initial state of the universe is a quiescent singularity with a finite density and pressure.

We study the motion of a Bogomol’nyi-Prasad-Sommerfield $D3$-brane in the $NS5$-brane ring background. The radion field becomes tachyonic in this geometrical setup. We investigate the potential of this geometrical tachyon in the cosmological scenario for inflation as well as dark energy. We evaluate the spectra of scalar and tensor perturbations generated during tachyon inflation and show that this model is compatible with recent observations of cosmic microwave background due to an extra freedom of the number of $NS5$-branes. It is not possible to explain the origin of both inflation and dark energy by using a single tachyon field, since the energy density at the potential minimum is not negligibly small because of the amplitude of scalar perturbations set by cosmic microwave background anisotropies. However, the geometrical tachyon can account for dark energy when the number of $NS5$-branes is large, provided that inflation is realized by another scalar field.

We show that in theories of gravity that add quadratic curvature invariants to the Einstein-Hilbert action there exist expanding vacuum cosmologies with positive cosmological constant which do not approach the de Sitter universe. Exact solutions are found which inflate anisotropically. This behavior is driven by the Ricci curvature invariant and has no counterpart in the general-relativistic limit. These examples show that the cosmic no-hair theorem does not hold in these higher-order extensions of general relativity and raises new questions about the ubiquity of inflation in the very early universe and the thermodynamics of gravitational fields.