Some analysis of the supernovae type Ia observational data seems to indicate that the Universe today is dominated by a phantom field, for which all energy conditions are violated. Such phantom field may imply a singularity in a future finite time, called big rip. Studying the evolution of scalar perturbations for such a field, we show that if the pressure is negative enough, the Universe can become highly inhomogeneous and this phantom menace may be avoided.

We explore the moduli space of heterotic strings in two dimensions. In doing so, we introduce new lines of compactified theories with Spin(24) gauge symmetry and discuss compactifications with Wilson lines. The phase structure of $d=2$ heterotic string theory is examined by classifying the hypersurfaces in moduli space which support massless quanta or discrete states. Finally, we compute the torus amplitude over much of the moduli space.

We consider the standard model (SM) extended by the flavor symmetry $D_5$ and search for a minimal model leading to viable phenomenology. We find that it contains four Higgs fields apart from the three generations of fermions whose left-handed and left-handed conjugate parts do not transform in the same way under $D_5$. We provide two numerical fits for the case of Dirac and Majorana neutrinos to show the viability of our low energy model. The fits can accommodate all data with the neutrinos being normally ordered. For Majorana neutrinos two of the right-handed neutrinos are degenerate. Concerning the Higgs sector we find that all potentials constructed with three SM-like Higgs doublets transforming as $\underline{\mathbf{1}}+\underline{\mathbf{2}}$ under $D_5$ have a further unwanted global $U(1)$ symmetry. Therefore we consider the case of four Higgs fields forming two $D_5$ doublets and show that this potential leads to viable solutions in general, however it does not allow spontaneous $CP$ violation (SCPV) for an arbitrary vacuum expectation value (VEV) configuration. Finally, we discuss extensions of our model to grand unified theories (GUTs) as well as embeddings of $D_5$ into the continuous flavor symmetries $SO(3{)}_f$ and $SU(3{)}_f$.

We examine the energetics of $Q$ balls in Maxwell-Chern-Simons theory in two space dimensions. Whereas gauged $Q$ balls are unallowed in this dimension in the absence of a Chern-Simons term due to a divergent electromagnetic energy, the addition of a Chern-Simons term introduces a gauge field mass and renders finite the otherwise-divergent electromagnetic energy of the $Q$ ball. Similar to the case of gauged $Q$ balls, Maxwell-Chern-Simons $Q$ balls have a maximal charge. The properties of these solitons are studied as a function of the parameters of the model considered, using a numerical technique known as relaxation. The results are compared to expectations based on qualitative arguments.

We treat two possible phenomenological effects of quantum fluctuations of spacetime geometry: spectral line broadening and angular blurring of the image of a distance source. A geometrical construction will be used to express both effects in terms of the Riemann tensor correlation function. We apply the resulting expressions to study some explicit examples in which the fluctuations arise from a bath of gravitons in either a squeezed state or a thermal state. In the case of a squeezed state, one has two limits of interest: a coherent state which exhibits classical time variation but no fluctuations, and a squeezed vacuum state, in which the fluctuations are maximized.

The strategy of obtaining the familiar Kerr-Newman solution in general relativity is based on either using the metric ansatz in the Kerr-Schild form, or applying the method of complex coordinate transformation to a nonrotating charged black hole. In practice, this amounts to an appropriate rescaling of the mass parameter in the metric of uncharged black holes. Using a similar approach, we assume a special metric ansatz in $N+1$ dimensions and present a new analytic solution to the Einstein-Maxwell system of equations. It describes rotating charged black holes with a single angular momentum in the limit of slow rotation. We also give the metric for a slowly rotating charged black hole with two independent angular momenta in five dimensions. Finally, we compute the gyromagnetic ratio of these black holes which corresponds to the value $g=N-1$.

By using virial theorem, Helmholtz and Kelvin showed that the contraction of a bound self-gravitating system must be accompanied by release of radiation energy irrespective of the details of the contraction process. This happens because the total Newtonian energy of the system $E_N$ (and not just the Newtonian gravitational potential energy $E_g^N$) decreases for such contraction. In the era of general relativity (GR) too, it is justifiably believed that gravitational contraction must release radiation energy. However no GR version of (Newtonian) Helmholtz- Kelvin (HK) process has ever been derived. Here, for the first time, we derive the GR version of the appropriate virial theorem and Helmholtz Kelvin mechanism by simply equating the well known expressions for the gravitational mass and the inertial mass of a spherically symmetric static fluid. Simultaneously, we show that the GR counterparts of global “internal energy”, “gravitational potential energy” and “binding energy” are actually different from what have been used so far. Existence of this GR HK process asserts that, in Einstein gravity too, gravitational collapse must be accompanied by emission of radiation irrespective of the details of the collapse process.

We compute the energy of $2+1$ Minkowski space from a covariant action principle. Using Ashtekar and Varadarajan’s characterization of $2+1$ asymptotic flatness, we first show that the $2+1$ Einstein-Hilbert action with Gibbons-Hawking boundary term is both finite on shell (apart from past and future boundary terms) and stationary about solutions under arbitrary smooth asymptotically flat variations of the metric. Thus, this action provides a valid variational principle and no further boundary terms are required. We then obtain the gravitational Hamiltonian by direct computation from this action. The result agrees with the Hamiltonian of Ashtekar and Varadarajan up to an overall additive constant. This constant is such that $2+1$ Minkowski space is assigned the energy $E_{{\mathrm{Mink}}_{2+1}}=-\frac{1}{4G}$, while the upper bound on the energy becomes $E\le 0$. Any variational principle with a boundary term built only from the extrinsic and intrinsic curvatures of the boundary is shown to lead to the same result. Interestingly, our result is not the $\Lambda \to 0$ limit of the corresponding energy $E_{{\mathrm{AdS}}_{2+1}}=-\frac{1}{8G}$ of $2+1$ anti-de Sitter (AdS) space.

Backreactions are considered in a de Sitter spacetime whose cosmological constant is generated by the potential of a scalar field. The leading order gravitational effect of nonlinear matter fluctuations is analyzed and it is found that the initial value problem for the perturbed Einstein equations possesses linearization instabilities. We show that these linearization instabilities can be avoided by assuming strict de Sitter invariance of the quantum states of the linearized fluctuations. We furthermore show that quantum anomalies do not block the invariance requirement. This invariance constraint applies to the entire spectrum of states, from the vacuum to the excited states (should they exist), and is in that sense much stronger than the usual Poincare invariance requirement of the Minkowski vacuum alone. Thus to leading order in their effect on the gravitational field, the quantum states of the matter and metric fluctuations must be de Sitter invariant.

The fourth order Weyl gravity theory of Mannheim and Kazanas is based on replacing the Einstein-Hilbert action with the square of the Weyl tensor, and on modifying the matter action of the standard model of particle physics to make it conformally invariant. This theory has been suggested as a model of both dark matter and dark energy. We show that the theory contains two uncoupled sectors: a trivial sector containing no dynamics on which the conformal symmetry acts, and a dynamical sector in which all the fields are conformal invariants. We deduce that in the limit of weak fields and slow motions the theory does not agree with the predictions of general relativity, and is therefore ruled out by Solar System observations.

Kerr-Schild solutions of the Einstein-Maxwell field equations, containing semi-infinite axial singular lines, are investigated. It is shown that axial singularities break up the black hole, forming holes in the horizon. As a result, a tubelike region appears which allows matter to escape from the interior without crossing the horizon. It is argued that axial singularities of this kind, leading to very narrow beams, can be created in black holes by external electromagnetic or gravitational excitations and may be at the origin of astrophysically observable effects such as jet formation.

We obtain a new exact black hole solution in Einstein-Gauss-Bonnet gravity with a cosmological constant which bears a specific relation to the Gauss-Bonnet coupling constant. The spacetime is a product of the usual 4-dimensional manifold with a ($n-4$)-dimensional space of constant negative curvature, i.e., its topology is locally ${\mathcal{M}}^n\approx {\mathcal{M}}^4\times {\mathcal{H}}^{n-4}$. The solution has two parameters and asymptotically approximates to the field of a charged black hole in anti-de Sitter spacetime. The most interesting and remarkable feature is that the Gauss-Bonnet term acts like a Maxwell source for large $r$ while at the other end it regularizes the metric and weakens the central singularity.

We show that heavy quarckonium states, similar to light mesons, form Regge trajectories in $(n,M^2)$ and $(M^2,J)$ planes and the slope of these trajectories is independent on the quantum numbers of the mesons. This fact can be useful for the prediction of the masses of heavy quarkonia and the determination of the quantum numbers of the newly discovered states.

The quadratic divergences of the Higgs mass may be cancelled either accidentally or by the exchange of some new particles. Alternatively its impact on naturalness may be weakened by raising the Higgs mass, which requires changing the standard model below its natural cutoff. We show in detail how this can be achieved, while preserving perturbativity and consistency with the electroweak precision tests, by extending the standard model to include a second Higgs doublet that has neither a vev nor couplings to quarks and leptons. This inert doublet model yields a perturbative and completely natural description of electroweak physics at all energies up to 1.5 TeV. The discrete symmetry that yields the inert doublet is unbroken, so that dark matter may be composed of neutral inert Higgs bosons, which may have escaped detection at LEP2. Predictions are given for multilepton events with missing transverse energy at the Large Hadron Collider, and for the direct detection of dark matter.

Two twisted doublets, one containing the up and down quarks and the other containing the strange quark with an $SU(2)$-flavor partner, are used for studies in the meson sector. The relevant chiral perturbation theory is presented, and quenched QCD simulations (where the partner of the strange quark is not active) are performed. Pseudoscalar meson masses and decay constants are computed; the vector and scalar mesons are also discussed. A comparison is made to the case of an untwisted strange quark, and some effects due to quenching, discretization, and the definition of maximal twist are explored.

We study thermodynamics of strongly coupled lattice QCD with two colors of massless staggered fermions as a function of the baryon chemical potential $\mu$ in $3+1$ dimensions using a new cluster algorithm. We find evidence that the model undergoes a weak first order phase transition at $\mu =0$ which becomes second order at a finite $\mu$. Symmetry considerations suggest that the universality class of these phase transitions should be governed by a $O(N)\times O(2)$ field theory with collinear order, with $N=3$ at $\mu =0$ and $N=2$ at $\mu \ne 0$. The universality class of the second order phase transition at $\mu \ne 0$ appears to be governed by the decoupled $XY$ fixed point present in the $O(2)\times O(2)$ field theory. Finally we show that the quantum ($T=0$) phase transition as a function of $\mu$ is a second order mean field transition.

We determine the next-to-leading logarithmic (NLL) QCD corrections to the cross section $\sigma (e^{+}{e}^{-}\to t\overline{t}H)$ for center-of-mass (c.m.) energies up to 500 GeV. The dynamics is dominated by nonrelativistic effects, and the summation of terms singular in the relative $t\overline{t}$ velocity is mandatory to all orders in the strong coupling constant ${\alpha }_s$ using an effective theory. The summations lead to an enhancement of the tree-level predictions by about a factor of 2 and are important for the determination of the top Yukawa coupling. We also study the impact of polarization of the electron-positron beams and provide a fast approximation formula for the known $\mathcal{O}({\alpha }_s)$ QCD fixed-order prediction.

Two kinds of asymmetry arise from the interference of the Born amplitude and the box-type amplitude corresponding to two virtual photon exchange, namely, charge-odd and single-spin asymmetries. In the case of unpolarized particles the charge-odd correlation is calculated. It can be measured in a combination of electron-muon and positron-muon experiments. The forward-backward asymmetry is the corresponding quantity which can be measured for the crossed processes. In the case of a polarized muon the single-spin asymmetry for annihilation and scattering channels has been calculated. The additional structure function arising from the interference is shown to suffer from infrared divergencies. The background due to electroweak interaction is discussed.

We report a study of the processes $e^{+}{e}^{-}\to \eta \gamma$ and $e^{+}{e}^{-}\to {\eta }^{\prime }\gamma$ at a center-of-mass energy of 10.58 GeV, using a $232{\mathrm{fb}}^{-1}$ data sample collected with the BABAR detector at the PEP-II collider at SLAC. We observe ${20}_{-5}^{+6}\eta \gamma$ and ${50}_{-7}^{+8}{\eta }^{\prime }\gamma$ events over small backgrounds, and measure the cross sections $\sigma (e^{+}{e}^{-}\to \eta \gamma )={4.5}_{-1.1}^{+1.2}\pm 0.3\mathrm{fb}$ and $\sigma (e^{+}{e}^{-}\to {\eta }^{\prime }\gamma )=5.4\pm 0.8\pm 0.3\mathrm{fb}$. The corresponding transition form factors at $q^2=112{\mathrm{GeV}}^2$ are $q^2|F_{\eta }(q^2)|=0.229\pm 0.030\pm 0.008\mathrm{GeV}$, and $q^2|F_{{\eta }^{\prime }}(q^2)|=0.251\pm 0.019\pm 0.008\mathrm{GeV}$, respectively.

We present measurements of the branching fraction and time-dependent $CP$ asymmetries in $B^0\to J/\psi {\pi }^0$ decays based on $(231.8\pm 2.6)\times {10}^6{\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the SLAC PEP-II asymmetric-energy $B$ factory. We obtain a branching fraction $\mathcal{B}(B^0\to J/\psi {\pi }^0)=(1.94\pm 0.22(\mathrm{stat})\pm 0.17(\mathrm{syst}))\times {10}^{-5}$. We also measure the $CP$ asymmetry parameters $C=-0.21\pm 0.26(\mathrm{stat})\pm 0.06(\mathrm{syst})$ and $S=-0.68\pm 0.30(\mathrm{stat})\pm 0.04(\mathrm{syst})$.