We derive a closed-form solution for the Green’s function for the wave equation of a static (with respect to an undragged, static observer at infinity) scalar charge in the Kerr space-time. We employ our solution to obtain an analytic expression for the self-force on such a charge, comparing our results to those of L. M. Burko and Y. T. Liu, Phys. Rev. D 64, 024006 (2001).

Because of nonperturbative quantum gravitational effects, the classical big bang singularity is replaced by a quantum big bounce of the mean scale factor in loop quantization of Bianchi-I spacetime. An important issue is to understand the various differences in the physical properties of the spacetime across the bounce. We investigate this issue in the context of various geometrical structures, identified by the Kasner exponents of the metric, which arise on approach to the singularity in the classical theory. Using an effective spacetime description of the Bianchi-I model in loop quantum cosmology with dust, radiation and stiff matter, we find that as in the classical theory, geometrical structures such as a cigar or a pancake form, but they are finite and nonsingular. Depending on the initial conditions of the matter and anisotropies, different geometric structures are possible in the pre- and post-bounce phases in physical evolution. Thus, quantum gravitational effects can cause a Kasner transition in Bianchi-I spacetime, which is not possible at the classical level. Interestingly, we find that not all transitions are allowed at the level of effective dynamics in loop quantum cosmology. We find the selection rules and underlying conditions for all allowed and forbidden transitions. The selection rules suggest that for a given set of initial conditions on anisotropies, the occurrence of Kasner transitions follows a distinct pattern, and certain transitions are more favored than others.

We study static, spherically symmetric solutions in a recently proposed ghost-free model of nonlinear massive gravity. We focus on a branch of solutions where the helicity-0 mode can be strongly coupled within certain radial regions, giving rise to the Vainshtein effect. We truncate the analysis to scales below the gravitational Compton wavelength, and consider the weak field limit for the gravitational potentials, while keeping all nonlinearities of the helicity-0 mode. We determine analytically the number and properties of local solutions that exist asymptotically on large scales, and of local (inner) solutions that exist on small scales. We find two kinds of asymptotic solutions, one of which is asymptotically flat, while the other one is not, and also two types of inner solutions, one of which displays the Vainshtein mechanism, while the other exhibits a self-shielding behavior of the gravitational field. We analyze in detail in which cases the solutions match in an intermediate region. The asymptotically flat solutions connect only to inner configurations displaying the Vainshtein mechanism, while the nonasymptotically flat solutions can connect with both kinds of inner solutions. We show furthermore that there are some regions in the parameter space where global solutions do not exist, and characterize precisely in which regions of the phase space the Vainshtein mechanism takes place.

In four-dimensional spacetime, moons around black holes generate low-amplitude tides, and the energy extracted from the hole’s rotation is always smaller than the gravitational radiation lost to infinity. Thus, moons orbiting a black hole inspiral and eventually merge. However, it has been conjectured that in higher-dimensional spacetimes orbiting bodies generate much stronger tides, which backreact by tidally accelerating the body outward. This effect, analogous to the tidal acceleration experienced by the Earth–Moon system, would determine the evolution of the binary. Here, we put this conjecture to the test, by studying matter coupled to a massless scalar field in orbit around a singly spinning rotating black hole in higher dimensions. We show that in dimensions larger than five the energy extracted from the black hole through superradiance is larger than the energy carried out to infinity. Our numerical results are in excellent agreement with analytic approximations and lend strong support to the conjecture that tidal acceleration is the rule, rather than the exception, in higher dimensions. Superradiance dominates the energy budget and moons “outspiral”; for some particular orbital frequency, the energy extracted at the horizon equals the energy emitted to infinity and “floating orbits” generically occur. We give an interpretation of this phenomenon in terms of the membrane paradigm and of tidal acceleration due to energy dissipation across the horizon.

The computation of probabilities in an eternally inflating universe requires a regulator or “measure.” The scale factor time measure truncates the Universe when a congruence of timelike geodesics has expanded by a fixed volume factor. This definition breaks down if the generating congruence is contracting—a serious limitation that excludes from consideration gravitationally bound regions such as our own. Here we propose a closely related regulator which is well defined in the entire spacetime. The new scale factor cutoff restricts to events with a scale factor below a given value. Since the scale factor vanishes at caustics and crunches, this cutoff always includes an infinite number of disconnected future regions. We show that this does not lead to divergences. The resulting measure combines desirable features of the old scale factor cutoff and of the light-cone time cutoff, while eliminating some of the disadvantages of each.

In the present paper we analyze the spectrum of quasinormal modes for massive scalar and Dirac fields, allowing for both tardyonic (${\mu }^2>0$) and tachyonic (${\mu }^2<0$) masses, in the expanding and rotating cosmological background. The spectrum found shows a number of peculiar features, which are absent in the Minkowski space-time. A hypothetical particle that moves faster than light, a tachyon, is known to be classically unstable in the Minkowski space-time. This instability has its analog at the quantum level: small vacuum fluctuations of the field lead to the unbounded growth of the amplitude, so that the appearance of the real tachyons in the spectrum means that there is catastrophic instability in the theory. It has been conjectured a long time ago that possibly the lightest particles with nonzero mass, the neutrino, may be a tachyon. Here we shall show that in the rotating and expanding Universe tachyons are stable if their mass is less than some constant, which is related to the Universe’s rotation and expansion scales. The current upper bound on the rotation scale gives us a very small upper bound on the tachyon’s mass which is many orders less than the mass of the electron. This might explain why only very light particles have the chance of becoming tachyons. It is shown that the spectrum of the “normal” (${\mu }^2>0$) Dirac field has a discontinuity as a function of the $z$ component of the wave vector $k_z$ at $k_z=0$.

We develop a model-independent test of general relativity that allows for the constraint of the gravitational wave (GW) polarization content with GW detections of binary compact object inspirals. We first consider three modified gravity theories (Brans-Dicke theory, Rosen’s theory, and Lightman-Lee theory) and calculate the response function of ground-based detectors to gravitational waves in the inspiral phase. This allows us to see how additional polarizations predicted in these theories modify the general relativistic prediction of the response function. We then consider general power-law modifications to the Hamiltonian and radiation-reaction force and study how these modify the time-domain and Fourier response function when all polarizations are present. From these general arguments and specific modified gravity examples, we infer an improved parameterized post-Einsteinian template family with complete polarization content. This family enhances general relativity templates through the inclusion of new theory parameters, reducing to the former when these parameters acquire certain values, and recovering modified gravity predictions for other values, including all polarizations. We conclude by discussing detection strategies to constrain these new, polarization theory parameters by constructing certain null channels through the combination of output from multiple detectors.

We present the performance of searches for gravitational-wave bursts associated with external astrophysical triggers as a function of the search sky region. We discuss both the case of Gaussian noise and real noise of gravitational wave detectors for arbitrary detector networks. We demonstrate the ability to reach Gaussian limited sensitivity in real non-Gaussian data, and show the conditions required to attain it. We find that a single sky position search is $\sim 20\%$ more sensitive than an all-sky search of the same data.

We perform a joint analysis of dwarf galaxy data from the Fermi Gamma-ray Space Telescope in search of dark matter annihilation into a gamma-ray line. We employ a novel statistical method that takes into account the spatial and spectral information of individual photon events from a sample of seven dwarf galaxies. Dwarf galaxies show no evidence of a gamma-ray line between 10 GeV and 1 TeV. The subsequent upper limit on the annihilation cross section to a two-photon final state is ${3.9}_{-3.7}^{+7.1}\times {10}^{-26}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ at 130 GeV, where the errors reflect the systematic uncertainty in the distribution of dark matter within the dwarf galaxies.

If fermion condensation is a main source of electroweak symmetry breaking, an ultra-heavy Higgs doublet of mass $\sim {10}^8\mathrm{GeV}$ can yield naturally small Dirac neutrino masses. We show that such a scenario can lead to a new leptogenesis mechanism based on the decays of the ultra-heavy Higgs. Given its very large mass, the requisite Higgs doublet can be considered an elementary particle and would point to a cutoff scale $\sim {10}^{10}\mathrm{GeV}$. We outline how our scenario can also naturally lead to composite asymmetric dark matter. Some potential signals of this scenario are discussed.

The first experimental evidence for direct $CP$ violation in charm-quark decays has recently been presented by the LHCb collaboration in the difference between the $D\to K^{+}{K}^{-}$ and $D\to {\pi }^{+}{\pi }^{-}$ time-integrated $CP$ asymmetries. We estimate the size of the effects that can be expected within the Standard Model and find that at leading order in $1/m_c$ they are an order of magnitude smaller. However, tree-level annihilation type amplitudes are known to be large experimentally. This implies that certain formally $1/m_c$-suppressed penguin amplitudes could plausibly account for the LHCb measurement. Simultaneously, the flavor-breaking parts of these amplitudes could explain the large difference between the $D\to K^{+}{K}^{-}$ and $D\to {\pi }^{+}{\pi }^{-}$ decay rates.

A major contribution to the uncertainty of finite-order perturbative QCD predictions is the perceived ambiguity in setting the renormalization scale ${\mu }_r$. For example, by using the conventional way of setting ${\mu }_r\in [m_t/2,2m_t]$, one obtains the total $t\overline{t}$ production cross section ${\sigma }_{t\overline{t}}$ with the uncertainty $\Delta {\sigma }_{t\overline{t}}/{\sigma }_{t\overline{t}}\sim (\genfrac{}{}{0ex}{}{+3\%}{-4\%})$ at the Tevatron and LHC even for the present next-to next-to-leading-order level. The principle of maximum conformality (PMC) eliminates the renormalization scale ambiguity in precision tests of Abelian QED and non-Abelian QCD theories. By using the PMC, all nonconformal $\{{\beta }_i\}$ terms in the perturbative expansion series are summed into the running coupling constant, and the resulting scale-fixed predictions are independent of the renormalization scheme. The correct scale displacement between the arguments of different renormalization schemes is automatically set, and the number of active flavors $n_f$ in the $\{{\beta }_i\}$ function is correctly determined. The PMC is consistent with the renormalization group property that a physical result is independent of the renormalization scheme and the choice of the initial renormalization scale ${\mu }_r^{\mathrm{init}}$. The PMC scale ${\mu }_r^{\mathrm{PMC}}$ is unambiguous at finite order. Any residual dependence on ${\mu }_r^{\mathrm{init}}$ for a finite-order calculation will be highly suppressed since the unknown higher-order $\{{\beta }_i\}$ terms will be absorbed into the PMC scales’ higher-order perturbative terms. We find that such renormalization group invariance can be satisfied to high accuracy for ${\sigma }_{t\overline{t}}$ at the next-to next-to-leading-order level. In this paper we apply PMC scale setting to predict the $t\overline{t}$ cross section ${\sigma }_{t\overline{t}}$ at the Tevatron and LHC colliders. It is found that ${\sigma }_{t\overline{t}}$ remains almost unchanged by varying ${\mu }_r^{\mathrm{init}}$ within the region of $[m_t/4,4m_t]$. The convergence of the expansion series is greatly improved. For the ($q\overline{q}$) channel, which is dominant at the Tevatron, its next-to-leading-order (NLO) PMC scale is much smaller than the top-quark mass in the small $x$ region, and thus its NLO cross section is increased by about a factor of 2. In the case of the ($gg$) channel, which is dominant at the LHC, its NLO PMC scale slightly increases with the subprocess collision energy $\sqrt{s}$, but it is still smaller than $m_t$ for $\sqrt{s}\lesssim 1\mathrm{TeV}$, and the resulting NLO cross section is increased by $\sim 20\%$. As a result, a larger ${\sigma }_{t\overline{t}}$ is obtained in comparison to the conventional scale setting method, which agrees well with the present Tevatron and LHC data. More explicitly, by setting $m_t=172.9\pm 1.1\mathrm{GeV}$, we predict ${\sigma }_{\mathrm{Tevatron},1.96\mathrm{TeV}}={7.626}_{-0.257}^{+0.265}\mathrm{pb}$, ${\sigma }_{\mathrm{LHC},7\mathrm{TeV}}={171.8}_{-5.6}^{+5.8}\mathrm{pb}$ and ${\sigma }_{\mathrm{LHC},14\mathrm{TeV}}={941.3}_{-26.5}^{+28.4}\mathrm{pb}$.

We investigate the possible molecules composed of two heavy flavor baryons such as “$A_Q{B}_Q$” ($Q=b$, $c$) within the one-pion-exchange model (OPE). Our results indicate that the long-range $\pi$ exchange force is strong enough to form molecules such as $[{\Sigma }_Q{\Xi }_Q^{\prime }{]}_{S=1}^{I=1/2}$ ($Q=b$, $c$), $[{\Sigma }_Q{\Lambda }_Q{]}_{S=1}^{I=1}$ ($Q=b$, $c$), $[{\Sigma }_b{\Xi }_b^{\prime }{]}_{S=1}^{I=3/2}$, and $[{\Xi }_b{\Xi }_b^{\prime }{]}_{S=1}^{I=0}$ where the $S\mathrm{\text{−}}D$ mixing plays an important role. In contrast, the $\pi$ exchange does not form the spin-singlet $A_Q{B}_Q$ bound states. If we consider the heavier scalar and vector meson exchanges as well as the pion exchange, some loosely bound spin-singlet $S$-wave states appear while results of the spin-triplet $A_Q{B}_Q$ system do not change significantly, which implies the pion exchange plays an dominant role in forming the spin-triplet molecules. Moreover, we perform an extensive coupled channel analysis of the ${\Lambda }_Q{\Lambda }_Q$ system within the OPE and one-boson-exchange framework and find that there exist loosely bound states of ${\Lambda }_Q{\Lambda }_Q$ ($Q=b$, $c$) with quantum numbers $I(J^P)=0(0^{+})$, $0(0^{-})$, and $0(1^{-})$. The binding solutions of ${\Lambda }_Q{\Lambda }_Q$ system mainly come from the coupled-channel effect in the flavor space. Besides the OPE force, the medium- and short-range attractive force also plays a significant role in the formation of the loosely bound ${\Lambda }_c{\Lambda }_c$ and ${\Lambda }_b{\Lambda }_b$ states. Once produced, they will be very stable because such a system decays via weak interaction with a very long lifetime around ${10}^{-13}–{10}^{-12}\mathrm{s}$.

We perform a global analysis of neutrino oscillation data, including high-precision measurements of the neutrino mixing angle ${\theta }_{13}$ at reactor experiments, which have confirmed previous indications in favor of ${\theta }_{13}>0$. Recent data presented at the Neutrino 2012 conference are also included. We focus on the correlations between ${\theta }_{13}$ and the mixing angle ${\theta }_{23}$, as well as between ${\theta }_{13}$ and the neutrino $CP$-violation phase $\delta$. We find interesting indications for ${\theta }_{23}<\pi /4$ and possible hints for $\delta \sim \pi$, with no significant difference between normal and inverted mass hierarchy.

We analyze the impact of LHC and Tevatron Higgs data on the viability of the standard model with a sequential fourth generation, assuming Dirac neutrinos and a Higgs mass of 125 GeV. To this end we perform a combined fit to the signal cross sections of $pp\to H\to \gamma \gamma$, $Z{Z}^{*}$, $W{W}^{*}$ at the LHC, to $p\overline{p}\to VH\to Vb\overline{b}$ ($V=W$, $Z$) at the Tevatron and to the electroweak precision observables. Fixing the mass of the fourth-generation down-type quark $b^{\prime }$ to 600 GeV we find best-fit values of $m_{t^{\prime }}=632\mathrm{GeV}$, $m_{l_4}=113.6\mathrm{GeV}$ and $m_{{\nu }_4}=58.0\mathrm{GeV}$ for the other fourth-generation fermion masses. We compare the ${\chi }^2$ values and pulls of the different observables in the three- and four-generation case and show that the data is better described by the three-generation standard model. We also investigate the effects of mixing between the third- and fourth-generation quarks and of a future increased lower bound on the fourth-generation charged lepton mass of 250 GeV.

A search is presented for heavy-quark pair production ($Q\overline{Q}$) under the decay hypothesis $Q\overline{Q}\to W^{+}q{W}^{-}\overline{q}$ with $q=d$, $s$, $b$ for up-type $Q$ or $q=u$, $c$ for down-type $Q$. The search is performed with $1.04{\mathrm{fb}}^{-1}$ of integrated luminosity from $pp$ collisions at $\sqrt{s}=7\mathrm{TeV}$ collected by the ATLAS detector at the CERN LHC. Dilepton final states are selected, requiring large missing transverse momentum and at least two jets. Mass reconstruction of heavy-quark candidates is performed by assuming that the $W$ boson decay products are nearly collinear. The data are in agreement with standard model expectations; a heavy quark with mass less than 350 GeV is excluded at 95% confidence level.

We have searched for proton decay via $p\to {\mu }^{+}{K}^0$ using data from a $91.7\mathrm{kiloton}·\mathrm{year}$ exposure of Super-Kamiokande- I, a $49.2\mathrm{kiloton}·\mathrm{year}$ exposure of Super-Kamiokande II, and a $31.9\mathrm{kiloton}·\mathrm{year}$ exposure of Super-Kamiokande III. The number of candidate events in the data was consistent with the atmospheric neutrino background expectation and no evidence for proton decay in this mode was found. We set a partial lifetime lower limit of $1.6\times {10}^{33}\mathrm{years}$ at the 90% confidence level.

From an extended relativistic dynamics for a particle moving in a cosmic background field with temperature $T$, we aim to obtain the speed of light with an explicit dependence on the background temperature of the universe. Although finding the speed of light in the early universe much larger than its current value, our approach does not violate the postulate of special relativity. Moreover, it is shown that the high value of the speed of light in the early universe was drastically decreased before the beginning of the inflationary period. So we are led to conclude that the theory of varying speed of light should be questioned as a possible solution of the horizon problem.

We examine cyclic phantom models for the Universe, in which the universe is dominated sequentially by radiation, matter, and a phantom dark energy field, followed by a standard inflationary phase. Since this cycle repeats endlessly, the universe spends a substantial portion of its lifetime in a state for which the matter and dark energy densities have comparable magnitudes, thus ameliorating the coincidence problem. We calculate the fraction of time that the universe spends in such a coincidental state and find that it is nearly the same as in the case of a phantom model with a future big rip. In the limit where the dark energy equation of state parameter, $w$, is close to $-1$, we show that the fraction of time, $f$, for which the ratio of the dark energy density to the matter density lies between $r_1$ and $r_2$, is $f=-(1+w)\ln [(\sqrt{r_2}+\sqrt{1+r_2})/(\sqrt{r_1}+\sqrt{1+r_1})]$.

Unified field theories try to merge the internal symmetries of the standard model into a single group. Here we lay out something different. We give evidence that a theory may be ultraunified; that is, beyond aiming to unify the internal symmetries into a single group, those groups may be unified together with the quarks and leptons that they act on. Furthermore, the ($3+1$) Lorentz transformations may likewise be unified with the scalars, spinors, four-vectors, and field strength tensors that they act on. These simplifications occur because the representations can be found in the form of an algebra acting on itself. The approach described in this paper is meant to tie everything into the Dixon algebra: $\mathbb{R}\otimes \mathbb{C}\otimes \mathbb{H}\otimes \mathbb{O}$, the tensor product of the division algebras, whose connection to the standard model was earlier advocated for in Dixon [Division Algebras: Octonions, Quaternions, Complex Numbers and the Algebraic Design of Physics (Kluwer Academic Publishers, Dordrecht, 1994).]. Here we propose a principle of ideals, which states that particle sectors of the standard model are given by generalized ideals of the algebra. As we show, this method very quickly uncovers all of the Lorentz representations of the standard model and one full generation of quarks and leptons.