A popular three-dimensional reduction of the Bethe-Salpeter formalism for the description of bound states in quantum field theory is the Salpeter equation, derived by assuming both instantaneous interactions and free propagation of all bound-state constituents. Numerical (variational) studies of the Salpeter equation with confining interaction, however, observed specific instabilities of the solutions, likely related to the Klein paradox and rendering (part of the) bound states unstable. An analytic investigation of the problem by a comprehensive spectral analysis is feasible for the reduced Salpeter equation with only harmonic-oscillator confining interactions. There we are able to prove rigorously that the bound-state solutions correspond to real discrete spectra bounded from below and are thus free of all instabilities.

The Cornwall-Jackiw-Tomboulis (CJT) effective action at finite temperature is applied to study the symmetry nonrestoration (SNR) and inverse symmetry breaking (ISB) at high temperature in the $Z_2\times Z_2$ model. A renormalization prescription is developed for the CJT effective action in the double bubble approximation. It is shown that the triviality related feature of the model does not show up, and the temperature effects do not alter the conditions for SNR/ISB in a broad range of temperatures.

Numerical simulations of 15 orbits of an equal-mass binary black-hole system are presented. Gravitational waveforms from these simulations, covering more than 30 cycles and ending about 1.5 cycles before merger, are compared with those from quasicircular zero-spin post-Newtonian (PN) formulae. The cumulative phase uncertainty of these comparisons is about 0.05 radians, dominated by effects arising from the small residual spins of the black holes and the small residual orbital eccentricity in the simulations. Matching numerical results to PN waveforms early in the run yields excellent agreement (within 0.05 radians) over the first $\sim 15$ cycles, thus validating the numerical simulation and establishing a regime where PN theory is accurate. In the last 15 cycles to merger, however, generic time-domain Taylor approximants build up phase differences of several radians. But, apparently by coincidence, one specific post-Newtonian approximant, TaylorT4 at 3.5PN order, agrees much better with the numerical simulations, with accumulated phase differences of less than 0.05 radians over the 30-cycle waveform. Gravitational-wave amplitude comparisons are also done between numerical simulations and post-Newtonian, and the agreement depends on the post-Newtonian order of the amplitude expansion: the amplitude difference is about 6%–7% for zeroth order and becomes smaller for increasing order. A newly derived 3.0PN amplitude correction improves agreement significantly ($<1\%$ amplitude difference throughout most of the run, increasing to 4% near merger) over the previously known 2.5PN amplitude terms.

We present a new, simple method for calculating the scalar, electromagnetic, and gravitational self-forces acting on particles in orbit around a Kerr black hole. The standard “mode-sum regularization” approach for self-force calculations relies on a decomposition of the full (retarded) perturbation field into multipole modes, followed by the application of a certain mode-by-mode regularization procedure. In recent years several groups have developed numerical codes for calculating black hole perturbations directly in $2+1$ dimensions (i.e., decomposing the azimuthal dependence into $m$-modes, but refraining from a full multipole decomposition). Here we formulate a practical scheme for constructing the self-force directly from the $2+1$-dimensional $m$-modes. While the standard mode-sum method is serving well in calculations of the self-force in Schwarzschild geometry, the new scheme should allow a more efficient treatment of the Kerr problem.

We consider the late-time tails of spherical waves propagating on even-dimensional Minkowski spacetime under the influence of a long range radial potential. We show that in six and higher even dimensions there exist exceptional potentials for which the tail has an anomalously small amplitude and fast decay. Tails outside higher-dimensional Schwarzschild black holes are also discussed.

The best laboratory constraints on strongly coupled chameleon fields come not from tests of gravity per se but from precision measurements of the Casimir force. The chameleonic force between two nearby bodies is more akin to a Casimir-like force than a gravitational one: The chameleon force behaves as an inverse power of the distance of separation between the surfaces of two bodies, just as the Casimir force does. Additionally, experimental tests of gravity often employ a thin metallic sheet to shield electrostatic forces; however, this sheet masks any detectable signal due to the presence of a strongly coupled chameleon field. As a result of this shielding, experiments that are designed to specifically test the behavior of gravity are often unable to place any constraint on chameleon fields with a strong coupling to matter. Casimir force measurements do not employ a physical electrostatic shield and as such are able to put tighter constraints on the properties of chameleons fields with a strong matter coupling than tests of gravity. Motivated by this, we perform a full investigation on the possibility of testing chameleon models with both present and future Casimir experiments. We find that present-day measurements are not able to detect the chameleon. However, future experiments have a strong possibility of detecting or rule out a whole class of chameleon models.

Data analysis for the proposed Laser Interferometer Space Antenna (LISA) will be complicated by the huge number of sources in the LISA band. In the frequency band $\sim {10}^{-4}-2\times {10}^{-3}\mathrm{Hz}$, galactic white dwarf binaries (GWDBs) are sufficiently dense in frequency space that it will be impossible to resolve most of them, and “confusion noise” from the unresolved Galactic binaries will dominate over instrumental noise in determining LISA’s sensitivity to other sources in that band. Confusion noise from unresolved extreme-mass-ratio inspirals (EMRIs) could also contribute significantly to LISA’s total noise curve. To date, estimates of the effect of LISA’s confusion noise on matched-filter searches and their detection thresholds have generally approximated the noise as Gaussian, based on the central limit theorem. However in matched-filter searches, the appropriate detection threshold for a given class of signals may be located rather far out on the tail of the signal-to-noise probability distribution, where a priori it is unclear whether the Gaussian approximation is reliable. Using the Edgeworth expansion and the theory of large deviations, we investigate the probability distribution of the usual matched-filter detection statistic, far out on the tail of the distribution. We apply these tools to four somewhat idealized versions of LISA data searches: searches for EMRI signals buried in GWDB confusion noise, and searches for massive black hole binary signals buried in (i) GWDB noise, (ii) EMRI noise, and (iii) a sum of EMRI noise and Gaussian noise. Assuming reasonable short-distance cutoffs in the populations of confusion sources (since the very closest and hence strongest sources will be individually resolvable), modifications to the appropriate detection threshold, due to the non-Gaussianity of the confusion noise, turn out to be quite small for realistic cases. The smallness of the correction is partly due to the fact that these three types of sources evolve on quite different time scales, so no single background source closely resembles any search template. We also briefly discuss other types of LISA searches where the non-Gaussianity of LISA’s confusion backgrounds could perhaps have a much greater impact on search reliability and efficacy.

The physical representation of the general double–Reissner–Nordström solution is obtained by rewriting the $N=2$ Bretón–Manko–Aguilar electrostatic metric in the Varzugin–Chistyakov parametrization $(M_i,Q_i,R)$. A concise analytical formula is derived for the interaction force between two arbitrary Reissner–Nordström constituents, and an example of the equilibrium configuration involving two oppositely charged particles which confirms earlier Bonnor’s prediction of the existence of such configurations is given.

The linearly polarized Gowdy $T^3$ model is paradigmatic for studying technical and conceptual issues in the quest for a quantum theory of gravity since, after a suitable and almost complete gauge fixing, it becomes an exactly soluble midisuperspace model. Recently, a new quantization of the model, possessing desired features such as a unitary implementation of the gauge group and of the time evolution, has been put forward and proven to be essentially unique. An appropriate setting for making contact with other approaches to canonical quantum gravity is provided by the Schrödinger representation, where states are functionals on the configuration space of the theory. Here we construct this functional description, analyze the time evolution in this context and show that it is also unitary when restricted to physical states, i.e. states which are solutions to the remaining constraint of the theory.

Previously, we developed a general method to construct invariant conserved currents and charges in gravitational theories with Lagrangians that are invariant under spacetime diffeomorphisms and local Lorentz transformations. This approach is now generalized to the case when the local Lorentz group is replaced by an arbitrary local gauge group. The particular examples include the Maxwell and Yang-Mills fields coupled to gravity with Abelian and non-Abelian local internal symmetries and the metric-affine gravity in which the local Lorentz spacetime group is extended to the local general linear group.

We consider the extended supersymmetric Pati-Salam model which, for $\mu >0$ and universal boundary conditions, succeeds to yield experimentally acceptable $b$-quark masses by moderately violating Yukawa unification. It is known that this model can lead to new shifted or new smooth hybrid inflation. We show that a successful two-stage inflationary scenario can be realized within this model based only on renormalizable superpotential interactions. The cosmological scales exit the horizon during the first stage of inflation, which is of the standard hybrid type and takes place along the trivial flat direction with the inflaton driven by radiative corrections. Spectral indices compatible with the recent data can be achieved in global supersymmetry or minimal supergravity by restricting the number of e-foldings of our present horizon during the first inflationary stage. The additional e-foldings needed for solving the horizon and flatness problems are naturally provided by a second stage of inflation, which occurs mainly along the built-in new smooth hybrid inflationary path appearing right after the destabilization of the trivial flat direction at its critical point. Monopoles are formed at the end of the first stage of inflation and are, subsequently, diluted by the second stage of inflation to become utterly negligible in the present universe for almost all (for all) the allowed values of the parameters in the case of global supersymmetry (minimal supergravity).

We study the cosmology of a toy modified theory of gravity in which gravity shuts off at short distances, as in the fat graviton scenario of Sundrum. In the weak-field limit, the theory is perturbatively local, ghost-free, and unitary, although likely suffers from nonperturbative instabilities. We derive novel self-inflationary solutions from the vacuum equations of the theory, without invoking scalar fields or other forms of stress energy. The modified perturbation equation expressed in terms of the Newtonian potential closely resembles its counterpart for inflaton fluctuations. The resulting scalar spectrum is therefore slightly red, akin to the simplest scalar-driven inflationary models. A key difference, however, is that the gravitational wave spectrum is generically not scale invariant. In particular the tensor spectrum can have a blue tilt, a distinguishing feature from standard inflation.

A “bubble universe” nucleating in an eternally inflating false vacuum will experience, in the course of its expansion, collisions with an infinite number of other bubbles. In an idealized model, we calculate the rate of collisions around an observer inside a given reference bubble. We show that the collision rate violates both the homogeneity and the isotropy of the bubble universe. Each bubble has a center which can be related to “the beginning of inflation” in the parent false vacuum, and any observer not at the center will see an anisotropic bubble collision rate that peaks in the outward direction. Surprisingly, this memory of the onset of inflation persists no matter how much time elapses before the nucleation of the reference bubble.

Recently H. Georgi suggested that a scale-invariant unparticle $\mathcal{U}$ sector with an infrared fixed point at high energy can couple with the standard model matter via a higher-dimensional operator suppressed by a high cutoff scale. Intense phenomenological search of this unparticle sector in the collider and flavor physics context has already been made. Here we explore its impact in cosmology, particularly its possible role in the supernovae cooling. We found that the energy-loss rate (and thus the cooling) is strongly dependent on the effective scale ${\Lambda }_{\mathcal{U}}$ and the anomalous dimension $d_{\mathcal{U}}$ of this unparticle theory.

We compute the full $\mathcal{O}({\alpha }_s)$ SUSY-QCD corrections to dark matter annihilation in the Higgs-funnel, resumming potentially large $\mu \tan \beta$ and $A_b$ contributions and keeping all finite $\mathcal{O}(m_b,s,1/{tan}^2\beta )$ terms. We demonstrate numerically that these corrections strongly influence the extraction of SUSY mass parameters from cosmological data and must therefore be included in common analysis tools such as darksusy or micromegas.

We compute the rates of semileptonic $B_A\to B_B{l}^{-}{l}^{-}$ ($l=e$ or $\mu$) hyperon transitions in a model where intermediate states involve loops of baryons and a Majorana neutrino. These rates turn out to be well below present experimental bounds and other theoretical estimates. From the experimental upper limit on the ${\Xi }^{-}\to p{\mu }^{-}{\mu }^{-}$ decay, we derive the bound $⟨m_{\mu \mu }⟩\le 22\mathrm{TeV}$ for the effective Majorana mass of the muon neutrino. Also, an estimate of background contributions for these decays due to the allowed $B_A\to B_B{l}^{-}{l}^{-}\overline{\nu }\overline{\nu }$ decays is provided.

We present a twin Higgs model based on left-right symmetry with a tree level quartic. This is made possible by extending the symmetry of the model to include two $Z_2$ parities, each of which is sufficient to protect the Higgs from getting a quadratically divergent mass squared. Although both parities are broken explicitly, the symmetries that protect the Higgs from getting a quadratically divergent mass are broken only collectively. The quadratic divergences of the Higgs mass are thus still protected at one loop. We find that the fine-tuning in this model is reduced substantially compared to the original left-right twin Higgs model. This mechanism can also be applied to the mirror twin Higgs model to get a significant reduction of the fine-tuning, while keeping the mirror photon massless.

If quarks are composite particles, then excited states are expected to play a rôle in the Large Hadron Collider phenomena. Concentrating on virtual effects, and using a large part of the compact muon solenoid detection criteria, we present here a realistic examination of their effect in diphoton production at the CERN LHC. For various luminosities, we present the 99% confidence limit (CL) achievable in $\Lambda -M_{q*}$ parameter space where $\Lambda$ is the compositeness scale and $M_{q^{*}}$ the mass of the state. For a $q^{*}$ of mass 0.5 TeV, $\Lambda \le 1.55(2.95)$ can be excluded at 99% CL with 30 $(200){\mathrm{fb}}^{-1}$ integrated luminosity.

We study the properties of $g^1$, the first excited state of the gluon in representative variants of the Randall-Sundrum (RS) model with the standard model (SM) fields in the bulk. We find that measurements of the coupling to light quarks (from the inclusive cross section for $pp\to g^1\to t\overline{t}$), the coupling to bottom quarks (from the rate of $pp\to g^{1}b$), as well as the overall width can provide powerful discriminants between the models. In models with large brane kinetic terms, the $g^1$ resonance can even potentially be discovered decaying into dijets against the large QCD background. We also derive bounds based on existing Tevatron searches for resonant $t\overline{t}$ production and find that they require $M_{g^1}\gtrsim 950\mathrm{GeV}$. In addition, we explore the pattern of interference between the $g^1$ signal and the nonresonant SM background, defining an asymmetry parameter for the invariant mass distribution. The interference probes the relative signs of the couplings of the $g^1$ to light quark pairs and to $t\overline{t}$, and thus provides an indication that the top is localized on the other side of the extra dimension from the light quarks, as is typical in the RS framework.

We study signals at the Large Hadron Collider (LHC) for Kaluza-Klein (KK) excitations of the electroweak gauge bosons in the framework with the standard model (SM) gauge and fermion fields propagating in a warped extra dimension. Such a framework addresses both the Planck-weak and flavor hierarchy problems of the SM. Unlike the often studied $Z^{\prime }$ cases, in this framework, there are three neutral gauge bosons due to the underlying $SU(2{)}_L\times SU(2{)}_R\times U(1{)}_X$ gauge group in the bulk. Furthermore, couplings of these KK states to light quarks and leptons are suppressed, whereas those to top and bottom quarks are enhanced compared to the SM gauge couplings. Therefore, the production of light quark and lepton states is suppressed relative to other beyond the SM constructions, and the fermionic decays of these states are dominated by the top and bottom quarks, which are, though, overwhelmed by KK gluons dominantly decaying into them. However, as we emphasize in this paper, decays of these states to longitudinal $W$, $Z$ and Higgs are also enhanced similarly to the case of top and bottom quarks. We show that the $W$, $Z$ and Higgs final states can give significant sensitivity at the LHC to $\sim 2(3)\mathrm{TeV}$ KK scale with an integrated luminosity of $\sim 100{\mathrm{fb}}^{-1}$ ($\sim 1{\mathrm{ab}}^{-1}$). Since current theoretical framework(s) favor KK masses $\gtrsim 3\mathrm{TeV}$, a luminosity upgrade of LHC is likely to be crucial in observing these states.