A path integral measure for gravity should also preserve the fundamental symmetry of general relativity, which is diffeomorphism symmetry. In previous work, we argued that a successful implementation of this symmetry into discrete quantum gravity models would imply discretization independence. We therefore consider the requirement of triangulation independence for the measure in (linearized) Regge calculus, which is a discrete model for quantum gravity, appearing in the semi–classical limit of spin foam models. To this end we develop a technique to evaluate the linearized Regge action associated to Pachner moves in 3D and 4D and show that it has a simple, factorized structure. We succeed in finding a local measure for 3D (linearized) Regge calculus that leads to triangulation independence. This measure factor coincides with the asymptotics of the Ponzano Regge Model, a 3D spin foam model for gravity. We furthermore discuss to which extent one can find a triangulation independent measure for 4D Regge calculus and how such a measure would be related to a quantum model for 4D flat space. To this end, we also determine the dependence of classical Regge calculus on the choice of triangulation in 3D and 4D.

Under certain conditions, sound waves in a fluid may be governed by a Klein-Gordon equation on an “effective spacetime” determined by the background flow properties. Here we consider the draining bathtub: a circulating, draining flow whose effective spacetime shares key features with the rotating black hole (Kerr) spacetime. We present a complete investigation of the role of quasinormal (QN) mode and Regge pole (RP) resonances of this system. First, we simulate a perturbation in the time domain by applying a finite-difference method, to demonstrate the ubiquity of “QN ringing.” Next, we solve the wave equation in the frequency domain with the continued-fraction method, to compute QN and RP spectra numerically. We then explore the geometric link between (prograde and retrograde) null geodesic orbits on the spacetime, and the properties of the QN/RP spectra. We develop a “geodesic-expansion” method which leads to asymptotic expressions (in inverse powers of mode number $m$) for the spectra, the radial functions, and the residues. Next, the role of the Regge poles in scattering and absorption processes is revealed through the application of the complex angular momentum method. We elucidate the link between the Regge poles and oscillations in the absorption cross section. Finally, we show that Regge poles provide a neat explanation for “orbiting” oscillations seen in the scattering cross section.

In the present paper, we focus on building simple nonperturbative analytical relativistic models of magnetars. With this purpose in mind, we first develop a method for generating exact interior solutions to the static and axisymmetric Einstein-Maxwell-hydrodynamic equations with anisotropic perfect fluid and with pure poloidal magnetic field. Then, using an explicit exact solution, we present a simple magnetar model and calculate some physically interesting quantities as the surface ellipticity and the total energy of the magnetized star.

The Newtonian or nonrelativistic decomposition of Einstein’s gravitational field is useful in the post-Newtonian approximation. We obtain the full nonquadratic Einstein-Hilbert action in terms of these fields as well as the harmonic gauge fixing term and find fairly simple expressions. We discuss alternatives to the harmonic gauge.

Vacuum solutions to the Einstein equations can be viewed as the interplay between the geometry and the gravitational wave energy content. The constraints on initial data reflect this interaction. We assume we are looking at cosmological solutions to the Einstein equations so we assume that the 3-space is compact, without boundary. In this article we investigate, using both analytic and numerical techniques, what happens when the extrinsic curvature is increased while the background geometry is held fixed. This is equivalent to trying to magnify the local gravitational wave kinetic energy on an unchanged background. We find that the physical intrinsic curvature does not blow up. Rather the local volume of space expands to accommodate this attempt to increase the kinetic energy.

In this paper we explore the effect of decaying dark matter (DDM) on large-scale structure and possible constraints from galaxy imaging surveys. DDM models have been studied, in part, as a way to address apparent discrepancies between the predictions of standard cold dark matter models and observations of galactic structure. Our study is aimed at developing independent constraints on these models. In such models, DDM decays into a less massive, stable dark matter (SDM) particle and a significantly lighter particle. The small mass splitting between the parent DDM and the daughter SDM provides the SDM with a recoil or “kick” velocity $v_k$, inducing a free-streaming suppression of matter fluctuations. This suppression can be probed via weak lensing power spectra measured by a number of forthcoming imaging surveys that aim primarily to constrain dark energy. Using scales on which linear perturbation theory alone is valid (multipoles $\ell <300$), surveys like Euclid or the Large Synoptic Survey Telescope can be sensitive to $v_k\gtrsim 90\mathrm{km}/\mathrm{s}$ for lifetimes $\tau \sim 1–5\mathrm{Gyr}$. To estimate more aggressive constraints, we model nonlinear corrections to lensing power using a simple halo evolution model that is in good agreement with numerical simulations. In our most ambitious forecasts, using multipoles $\ell <3000$, we find that imaging surveys can be sensitive to $v_k\sim 10\mathrm{km}/\mathrm{s}$ for lifetimes $\tau \lesssim 10\mathrm{Gyr}$. Lensing will provide a particularly interesting complement to existing constraints in that they will probe the long lifetime regime ($\tau \gg H_0^{-1}$) far better than contemporary techniques. A caveat to these ambitious forecasts is that the evolution of perturbations on nonlinear scales will need to be well calibrated by numerical simulations before they can be realized. This work motivates the pursuit of such a numerical simulation campaign to constrain dark matter with cosmological weak lensing.

Gravitational lensing by large scale structure introduces non-Gaussianity into the cosmic microwave background and imprints a new observable, which can be used as a cosmological probe. We apply a four-point estimator to the Wilkinson Microwave Anisotropy Probe (WMAP) 7-year coadded temperature maps alone to reconstruct the gravitational lensing signal. The Gaussian bias is simulated and subtracted, and the higher-order bias is investigated. We measure a gravitational lensing signal with a statistical amplitude of $\mathcal{C}=1.27\pm 0.98$ using all the correlations of the W- and V-band differencing assemblies . We therefore conclude that WMAP 7-year data alone cannot detect lensing.

In this paper we study in detail the effect of our recently proposed model of parity and charge-parity (PCP) violating varying alpha on the Cosmic Microwave Background (CMB) photon passing through the intragalaxy-cluster medium (ICM). The ICM is well known to be composed of magnetized plasma. According to our model, the polarization and intensity of the CMB would be affected when traversing through the ICM due to nontrivial scalar photon interactions. We have calculated the evolution of such polarization and intensity collectively, known as the Stokes parameters of the CMB photon during its journey through the ICM and tested our results against the Sunyaev-Zel’dovich (SZ) measurement on the Coma galaxy cluster. Our model contains a PCP-violating parameter, $\beta$, and a scale of alpha variation $\omega$. Using the derived constrained on the photon-to-scalar conversion probability, ${\overline{P}}_{\gamma \to \varphi }$, for the Coma cluster in [34,35]we found a contour plot in the ($\omega ,\beta$) parameter plane. The $\beta =0$ line in this parameter space corresponds to well-studied Maxwell-dilaton type models which has lower bound on $\omega ⪆6.4\times {10}^9\mathrm{GeV}$. In general, as the absolute value of $\beta$ increases, the lower bound on $\omega$ also increases. Our model in general predicts the modification of the CMB polarization with a nontrivial dependence on the parity-violating coupling parameter $\beta$. However, it is unconstrained in this particular study. We show that this effect can in principle be detected in the future measurements on CMB polarization such that $\beta$ can also be constrained.

In the curvaton scenario, residual isocurvature perturbations can be imprinted in the cosmic neutrino component after the decay of the curvaton field, implying in turn a nonzero chemical potential in the neutrino distribution. We study the constraints that future experiments like Planck, SPIDER or CMBPol will be able to put on the amplitude of isocurvature perturbations in the neutrino component. We express our results in terms of the square root $\gamma$ of the nonadiabaticity parameter $\alpha$ and of the extra relativistic degrees of freedom $\Delta N_{\mathrm{eff}}$. Assuming a fiducial model with purely adiabatic fluctuations, we find that Planck (SPIDER) will be able to put the following upper limits at the $1\sigma$ level: $\gamma \le 5.3\times {10}^{-3}(1.2\times {10}^{-2})$ and $\Delta N_{\mathrm{eff}}\le 0.16(0.40)$. CMBPol will further improve these constraints to $\gamma \le 1.5\times {10}^{-3}$ and $\Delta N_{\mathrm{eff}}\le 0.043$. Finally, we recast these bounds in terms of the background neutrino degeneracy parameter $\overline{\xi }$ and the corresponding perturbation amplitude ${\sigma }_{\xi }$, and compare with the bounds on $\overline{\xi }$ that can be derived from big bang nucleosynthesis (BBN).

We discuss the diffuse flux of electron neutrinos and antineutrinos from cosmological failed supernovae, stars that collapse directly into a black hole with no explosion. This flux has a hotter energy spectrum compared to the flux from regular, neutron star-forming collapses and therefore it dominates the total diffuse flux from core collapses above 20–45 MeV of neutrino energy. Reflecting the features of the originally emitted neutrinos, the flux of ${\nu }_e$ and ${\overline{\nu }}_e$ at Earth is larger when the survival probability of these species is larger, and also when the equations of state of nuclear matter are stiffer. In the 19–29 MeV energy window, the flux from failed supernovae is substantial, ranging from $\sim 7\%$ to a dominant fraction of the total flux from all core collapses. It can be as large as ${\varphi }_{\overline{e}}^{\mathrm{BH}}=0.38{\mathrm{s}}^{-1}{\mathrm{cm}}^{-2}$ for ${\overline{\nu }}_e$ and as large as ${\varphi }_e^{\mathrm{BH}}=0.28{\mathrm{s}}^{-1}{\mathrm{cm}}^{-2}$ for ${\nu }_e$, normalized to a local rate of core collapses of $R_{cc}(0)={10}^{-4}{\mathrm{yr}}^{-1}{\mathrm{Mpc}}^{-3}$. In 5 years, a 0.45 Mt water Cherenkov detector should see $\sim 5–65$ events from failed supernovae, while up to $\sim 160$ events are expected for the same mass with Gadolinium added. A 0.1 Mt liquid argon experiment should record $\sim 1–11$ events. Signatures of neutrinos from failed supernovae are the enhancement of the total rates of events from core collapses (up to a factor of $\sim 2$) and the appearance of high energy tails in the event spectra.

It is found by Cai and Su that the interaction between dark energy and cold dark matter is likely to change the sign during the cosmological evolution. Motivated by this, we suggest a new form of interaction between dark energy and dark matter, which changes from negative to positive as the expansion of or universe changes from decelerated to accelerated. We find that the interacting model is consistent with the second law of thermodynamics and the observational constraints. And, we also discuss the unified adiabatic-squared sound speed of the model.

It is often stated that the cosmological vector mode has only a decaying mode and gives negligible effects on cosmological observations. The vector mode, however, has a growing mode if there exists anisotropic stress in energy distributions in the universe. In this paper, we consider a primordial vector mode sustained by free-streaming neutrinos and its associated magnetic field generation. First, we put an observational constraint on the amount of the vector mode from the 7-year WMAP data. The constraint is found as $r_v\lesssim -\frac{r}{40}+0.012$, where $r_v$ and $r$ are the amounts of vector and tensor perturbation amplitudes with respect to the scalar one, respectively. Second, we calculate the spectrum of magnetic fields inevitably created from the primordial vector mode, given the constraint on $r_v$. It is found that the maximum amount of magnetic fields generated from the vector mode is given by $B\lesssim {10}^{-22}\mathrm{G}(\frac{r_v}{0.012}{)}^{1/2}(\frac{k}{0.002}{)}^{(n_v+1)/2}$, with $n_v$ being a spectral index of the vector mode. We find a nontrivial cancellation of the magnetic field generation in the radiation-dominated era, which creates a characteristic cutoff in the magnetic field spectrum around $k\approx 1.0{\mathrm{Mpc}}^{-1}$.

We study the flavor structure of the three-site Higgsless model and evaluate the constraints on the model arising from flavor physics. We find that current data constrain the model to exhibit only minimal flavor violation at tree level. Moreover, at the one-loop level, by studying the leading chiral-logarithmic corrections to chirality-preserving $\Delta F=1$ and $\Delta F=2$ processes from new physics in the model, we show that the combination of minimal flavor violation and ideal delocalization ensures that these flavor-changing effects are sufficiently small that the model remains phenomenologically viable.

In R-parity violating supersymmetric models both leptogenesis and the correct neutrino masses are hard to achieve together. The presence of certain soft nonholomorphic R-parity violating terms helps to resolve this problem. We consider a scenario where the lightest and the second-lightest neutralino are nearly degenerate in mass and enough $CP$-asymmetry can be produced through resonant leptogenesis. In this model, the lighter chargino and the lightest neutralino are highly degenerate. We have relatively lighter gauginos which can be produced at the LHC (with $\sqrt{s}=14\mathrm{TeV}$) leading to heavily ionizing charged tracks. At the same time this model can also generate the correct neutrino mass scale. Thus our scenario is phenomenologically rich and testable at colliders.

The possibility of a significant effect of exotic particles on the $Z^{\prime }\to \gamma \gamma \gamma$ and $Z\to \gamma \gamma \gamma$ decays is investigated in the context of the minimal 331 model. This model, which is based in the $S{U}_C(3)\times S{U}_L(3)\times U_X(1)$ gauge group, predicts the existence of many exotic charged particles that can significantly enhance the decay widths. It is found that the standard model prediction for the $Z\to \gamma \gamma \gamma$ decay remains essentially unchanged, as the new physics effects quickly decouple. On the other hand, it is found that the contributions of the new exotic quarks and gauge bosons predicted by this model lead to a branching fraction for the $Z^{\prime }\to \gamma \gamma \gamma$ decay of about ${10}^{-6}$, which is about 3 orders of magnitude larger than that of the $Z\to \gamma \gamma \gamma$ decay.

One of the distinctive features of the QCD phase diagram is the possible emergence of a critical endpoint. The critical region around the critical point and the path dependency of the critical exponents are investigated within effective chiral ($2+1$)-flavor models with and without Polyakov loops. Results obtained in no-sea mean-field approximations where a divergent vacuum part in the fermion-loop contribution is neglected are compared to the renormalized ones. Furthermore, the modifications caused by the backreaction of the matter fluctuations on the pure Yang-Mills system are discussed. Higher-order, non-Gaussian moments of event-by-event distributions of various particle multiplicities are enhanced near the critical point and could serve as a probe to determine its location in the phase diagram. By means of a novel derivative technique higher-order generalized quark-number susceptibilities are calculated and their sign structure in the phase diagram is analyzed.

The phase structure of the Polyakov loop-extended chiral quark-meson model is explored in a nonperturbative approach, beyond a mean-field approximation, in the presence of a magnetic field. We show that by including meson fluctuations one cannot resolve the qualitative discrepancy on the dependence of the crossover transition temperature in a nonzero magnetic field between effective model predictions and recent lattice results [1]. We compute the curvature of the crossover line in the $T-{\mu }_B$ plane at a nonzero magnetic field and show that the curvature increases with increasing magnetic field. On the basis of QCD inequalities, we also argue that, at least in the large $N_c$ limit, a chiral critical end point and, consequently, a change from crossover to a first-order chiral phase transition are excluded at zero baryon chemical potential and nonzero magnetic field.

We use the known soft and collinear limits of tree- and one-loop scattering amplitudes—computed over a decade ago—to explicitly construct a subtraction scheme for next-to-next-to-leading order (NNLO) computations. Our approach combines partitioning of the final-state phase-space together with the technique of sector decomposition, following recent suggestions in Ref. [34]. We apply this scheme to a toy example: the NNLO QED corrections to the decay of the $Z$ boson to a pair of massless leptons. We argue that the main features of this subtraction scheme remain valid for computations of processes of arbitrary complexity with NNLO accuracy.

A mixing of near-threshold quarkoniumlike resonances with heavy meson-antimeson pairs results in an enhancement of heavy quark spin symmetry breaking, since the meson pairs are not eigenstates of the heavy quark spin. The decomposition of $P$-wave states of meson pairs in terms of the heavy quark pair spin states is considered in the channel with $J^{\mathrm{PC}}=1^{--}$, which is directly produced in $e^{+}{e}^{-}$ annihilation. Specific processes are suggested for experimental study of the effects of the mixing with heavy meson pairs and of the internal spin structure of bottomonium and charmonium resonances.

We study the unpolarized fragmentation functions and the parton distribution functions of the pion employing the nonlocal chiral quark model. This model manifests the nonlocal interactions between the quarks and pseudoscalar mesons in the light-cone coordinate. We find that the nonlocal interactions result in substantial differences in comparison to the result of typical models with only local couplings. We also perform the high $Q^2$-evolution for our results which is calculated at a relatively low-renormalization scale $Q^2\approx 0.36{\mathrm{GeV}}^2$ and compare them with the experimental data. It has shown that our results after evolution are in qualitatively good agreement with those experimental data.