Given an arbitrary Wilson action of a real scalar field, we discuss how to construct the energy-momentum tensor of the theory. Using the exact renormalization group, we can determine the energy-momentum tensor implicitly, but we are short of obtaining an explicit formula in terms of the Wilson action.

By using $\mathrm{AdS}/\mathrm{CFT}$, we study the critical electric field, the Schwinger pair creation rate and the potential phase diagram for the quark and antiquark in four confining supergravity backgrounds which are the Witten QCD (WQCD), the Maldacena-Nunez (MN), the Klebanov-Tseytlin (KT) and the Klebanov-Strassler (KS) models. We compare the rate of phase transition in these models and compare it also with the conformal case. We then present the phase diagrams of the entanglement entropy of a strip in these geometries and find the predicted butterfly shape in the diagrams. We found that the phase transitions have a higher rate in WQCD and KT relative to MN and KS. Finally we show the effect of turning on an additional magnetic field on the rate of pair creation by using the imaginary part of the Euler-Heisenberg effective Lagrangian. The result is increasing the parallel magnetic field would increase the pair creation rate and increasing the perpendicular magnetic field would decrease the rate.

A pointlike object moving in a background black hole spacetime experiences a gravitational self-force which can be expressed as a local function of the object’s instantaneous position and velocity, to linear order in the mass ratio. We consider the worldline dynamics defined by the conservative part of the local self-force, turning off the dissipative part, and we ask: Is that dynamical system a Hamiltonian system, and if so, is it integrable? In the Schwarzschild spacetime, we show that the system is Hamiltonian and integrable, to linear order in the mass ratio, for generic (but not necessarily all) stable bound orbits. There exist an energy and an angular momentum, being perturbed versions of their counterparts for geodesic motion, which are conserved under the forced motion. We also discuss difficulties associated with establishing analogous results in the Kerr spacetime. This result may be useful for future computational schemes, based on a local Hamiltonian description, for calculating the conservative self-force and its observable effects. It is also relevant to the assumption of the existence of a Hamiltonian for the conservative dynamics for generic orbits in the effective-one-body formalism, to linear order in the mass ratio, but to all orders in the post-Newtonian expansion.

We argue that the anomalous power asymmetry observed in the cosmic microwave background (CMB) may have originated in a cosmic bounce preceding inflation. In loop quantum cosmology (LQC), the big bang singularity is generically replaced by a bounce due to quantum gravitational effects. We compute the spectrum of inflationary non-Gaussianity and show that strong correlation between observable scales and modes with longer (superhorizon) wavelength arise as a consequence of the evolution of perturbations across the LQC bounce. These correlations are strongly scale dependent and induce a dipole-dominated modulation on large angular scales in the CMB, in agreement with observations.

It has been argued that Hořava gravity needs to be extended to include terms that mix spatial and time derivatives in order to avoid unacceptable violations of Lorentz invariance in the matter sector. In an earlier paper we have shown that including such mixed derivative terms generically leads to 4th instead of 6th order dispersion relations and this could be (naïvely) interpreted as a threat to renormalizability. We have also argued that power counting renormalizability is not actually compromised, but instead the simplest power counting renormalizable model is not unitary. In this paper we consider the Lifshitz scalar as a toy theory and we generalize our analysis to include higher order operators. We show that models which are power counting renormalizable and unitary do exist. Our results suggest the existence of a new class of theories that can be thought of as Hořava gravity with mixed derivative terms.

We formulate certain inequalities for the geometric quantities characterizing causal diamonds in curved and Minkowski spacetimes. These inequalities involve the redshift factor which, as we show explicitly in the spherically symmetric case, is monotonic in the radial direction, and it takes its maximal value at the center. As a by-product of our discussion we rederive Bishop’s inequality without assuming the positivity of the spatial Ricci tensor. We then generalize our considerations to arbitrary, static and not necessarily spherically symmetric, asymptotically flat spacetimes. In the case of spacetimes with a horizon our generalization involves the so-called domain of dependence. The respective volume, expressed in terms of the duration measured by a distant observer compared with the volume of the domain in Minkowski spacetime, exhibits behaviors which differ if $d=4$ or $d>4$. This peculiarity of four dimensions is due to the logarithmic subleading term in the asymptotic expansion of the metric near infinity. In terms of the invariant duration measured by a comoving observer associated with the diamond we establish an inequality which is universal for all $d$. We suggest some possible applications of our results including comparison theorems for entanglement entropy, causal set theory, and fundamental limits on computation.

The so-called $f(X)$ hybrid metric-Palatini gravity, where $X=R+T$, with $T$ the stress-energy trace and $R$ the Ricci scalar, presents a unique viable generalization of the $f(R)$ theories within the metric-affine formalism. In this paper, the cosmology of the $f(X)$ theories is studied using the dynamical system approach. The method consists of formulating the propagation equation in terms of suitable (expansion-normalized) variables as an autonomous system. The fixed points of the system then represent exact cosmological solutions described by power law or de Sitter expansion. The formalism is applied to two classes of $f(X)$ models, revealing both standard cosmological fixed points and new accelerating solutions that can be attractors in the phase space. In addition, the fixed point with vanishing expansion rate is considered with special care in order to characterize the stability of Einstein static spaces and bouncing solutions.

We report results of a high resolution numerical-relativity simulation for the merger of black hole-magnetized neutron star binaries on Japanese supercomputer “K.” We focus on a binary that is subject to tidal disruption and subsequent formation of a massive accretion torus. We find the launch of thermally driven torus wind, subsequent formation of a funnel wall above the torus and a magnetosphere with collimated poloidal magnetic field, and high Blandford-Znajek luminosity. We show for the first time this picture in a self-consistent simulation. The turbulencelike motion induced by the nonaxisymmetric magnetorotational instability as well as the Kelvin-Helmholtz instability inside the accretion torus works as an agent to drive the mass accretion and converts the accretion energy to thermal energy, which results in the generation of a strong wind. By an in-depth resolution study, we reveal that high resolution is essential to draw such a picture. We also discuss the implication for the r-process nucleosynthesis, the radioactively powered transient emission, and short gamma ray bursts.

The renormalization group running of the gravitational constant has a universal form and represents a possible extension of general relativity. These renormalization group effects on general relativity will cause the running of the gravitational constant, and there exists a scale of renormalization $\alpha \nu$, which depends on the mass of an astronomical system and needs to be determined by observations. We test renormalization group effects on general relativity and obtain the upper bounds of $\alpha \nu$ in the low-mass scales: the Solar System and five systems of binary pulsars. Using the supplementary advances of the perihelia provided by INPOP10a (IMCCE, France) and EPM2011 (IAA RAS, Russia) ephemerides, we obtain new upper bounds on $\alpha \nu$ in the Solar System when the Lense–Thirring effect due to the Sun’s angular momentum and the uncertainty of the Sun’s quadrupole moment are properly taken into account. These two factors were absent in the previous work. We find that INPOP10a yields the upper bound as $\alpha \nu =(0.3\pm 2.8)\times {10}^{-20}$ while EPM2011 gives $\alpha \nu =(-2.5\pm 8.3)\times {10}^{-21}$. Both of them are tighter than the previous result by 4 orders of magnitude. Furthermore, based on the observational data sets of five systems of binary pulsars: PSR $\mathrm{J}0737-3039$, PSR $\mathrm{B}1534+12$, PSR $\mathrm{J}1756-2251$, PSR $\mathrm{B}1913+16$, and PSR $\mathrm{B}2127+11\mathrm{C}$, the upper bound is found as $\alpha \nu =(-2.6\pm 5.1)\times {10}^{-17}$. From the bounds of this work at a low-mass scale and the ones at the mass scale of galaxies, we might catch an updated glimpse of the mass dependence of $\alpha \nu$, and it is found that our improvement of the upper bounds in the Solar System can significantly change the possible pattern of the relation between $\log |\alpha \nu |$ and $\log m$ from a linear one to a power law, where $m$ is the mass of an astronomical system. This suggests that $|\alpha \nu |$ needs to be suppressed more rapidly with the decrease of the mass of low-mass systems. It also predicts that $|\alpha \nu |$ might have an upper limit in high-mass astrophysical systems, which can be tested in the future.

We consider the motion of spinning test particles with nonzero rest mass in the “pole-dipole” approximation, as described by the Mathisson-Papapetrou-Dixon (MPD) equations, and examine its properties in dependence on the spin supplementary condition added to close the system. In order to better understand the spin-curvature interaction, the MPD equation of motion is decomposed in the orthonormal tetrad whose time vector is given by the four-velocity $V^{\mu }$ chosen to fix the spin condition (the “reference observer”) and the first spatial vector by the corresponding spin $s^{\mu }$; such projections do not contain the Weyl scalars ${\mathrm{\Psi }}_0$ and ${\mathrm{\Psi }}_4$ obtained in the associated Newman-Penrose (NP) null tetrad. One natural option of how to choose the remaining two spatial basis vectors is shown to follow “intrinsically” whenever $V^{\mu }$ has been chosen; it is realizable if the particle’s four-velocity and four-momentum are not parallel. In order to see how the problem depends on the algebraic type of curvature, one first identifies the first vector of the NP tetrad $k^{\mu }$ with the highest-multiplicity principal null direction of the Weyl tensor, and then sets $V^{\mu }$ so that $k^{\mu }$ belong to the spin-bivector eigenplane. In spacetimes of any algebraic type but III, it is known to be possible to rotate the tetrads so as to become “transverse,” namely so that ${\mathrm{\Psi }}_1$ and ${\mathrm{\Psi }}_3$ vanish. If the spin-bivector eigenplane could be made to coincide with the real-vector plane of any of such transverse frames, the spinning particle motion would consequently be fully determined by ${\mathrm{\Psi }}_2$ and the cosmological constant; however, this can be managed in exceptional cases only. Besides focusing on specific Petrov types, we derive several sets of useful relations that are valid generally and check whether/how the exercise simplifies for some specific types of motion. The particular option of having four-velocity parallel to four-momentum is advocated, and a natural resolution of nonuniqueness of the corresponding reference observer $V^{\mu }$ is suggested.

Using a scalar field as an intrinsic “clock” while investigating the dynamics of gravitational systems has been successfully pursued in various researches on the border between classical and quantum gravity. The objective of our research was to check explicitly whether the scalar field can serve as a time variable during dynamical evolution of the matter-geometry system, especially in regions of high curvature, which are essential from the perspective of quantum gravity. For this purpose, we analyzed a gravitational collapse of a self-interacting scalar field within the framework of general relativity. The obtained results indicated that the hypersurfaces of constant scalar field are spacelike in dynamical regions nearby the singularities formed during the investigated process. The scalar field values change monotonically in the areas, in which the constancy hypersurfaces are spacelike.

We give an analytical formula for the vacuum polarization of a massless minimally coupled scalar field at the horizon of a rotating black hole with subtracted geometry. This is the first example of an exact, analytical result for a four-dimensional rotating black hole.

The time evolution of cosmological parameters in the early Universe at the deconfinement transition is studied by an equation of state (EoS) which takes into account the finite baryon density and the background magnetic field. The nonperturbative dynamics is described by the field correlator method which gives, with a small number of free parameters, a good fit of lattice data. The entire system has two components, i.e., the quark-gluon plasma and the electroweak sector, and the solutions of the Friedmann equation show that the scale factors $a(t)$ and $H(t)=(1/a)da/dt$ are weakly dependent on the EoS, but the deceleration parameter $q(t)$ and the jerk $j(t)$ are strongly modified above the critical temperature $T_c$, corresponding to a critical time $t_c\simeq 20–25\mu \mathrm{s}$. The time evolution of the cosmological parameters suggests that above and around $T_c$, there is a transient state of acceleration typical of a matter-dominated universe; this is entailed by the QCD strong interaction. The effect of the hadronic matter below $T_c$ does not qualitatively change the previous behavior and one can consistently follow the cosmological evolution up to $100\mu \mathrm{s}$.

This paper examines the properties of “lattice universes” wherein point masses are arranged in a regular lattice on spacelike hypersurfaces; open, flat, and closed universes are considered. The universes are modeled using the Lindquist-Wheeler (LW) approximation scheme, which approximates the space-time in each lattice cell by Schwarzschild geometry. Extending Lindquist and Wheeler’s work, we derive cosmological scale factors describing the evolution of all three types of universes, and we use these scale factors to show that the universes’ dynamics strongly resemble those of Friedmann-Lemaître-Robertson-Walker (FLRW) universes. In particular, we use the scale factors to make more salient the resemblance between Clifton and Ferreira’s Friedmann-like equations for the LW models and the actual Friedmann equations of FLRW space-times. Cosmological redshifts for such universes are then determined numerically, using a modification of Clifton and Ferreira’s approach; the redshifts are found to closely resemble their FLRW counterparts, though with certain differences attributable to the “lumpiness” in the underlying matter content. Most notably, the LW redshifts can differ from their FLRW counterparts by as much as 30%, even though they increase linearly with FLRW redshifts, and they exhibit a nonzero integrated Sachs-Wolfe effect, something which would not be possible in matter-dominated FLRW universes without a cosmological constant.

We analyze the shapes of cosmic string loops found in large-scale simulations of an expanding-universe string network. The simulation does not include gravitational backreaction, but we model that process by smoothing the loop using Lorentzian convolution. We find that loops at formation consist of generally straight segments separated by kinks. We do not see cusps or any cusplike structure at the scale of the entire loop, although we do see very small regions of string that move with large Lorentz boosts. However, smoothing of the string almost always introduces two cusps on each loop. The smoothing process does not lead to any significant fragmentation of loops that were in non-self-intersecting trajectories before smoothing.

We propose optimal estimators for bispectra from excited states. Two common properties of such bispectra are the enhancement in the collinear limit and the prediction of oscillating features. We review the physics behind excited states and some of the choices made in the literature. We show that the enfolded template is a good template in the collinear limit but does poorly elsewhere, establishing a strong case for an improved estimator. Although the detailed scale dependence of the bispectra differs depending on various assumptions, generally the predicted bispectra are either effectively one- or two-dimensional, and a simple Fourier basis suffices for accurate reconstruction. For an optimal CMB data analysis, combining all $n$-point functions, the choice for the excited state needs to be the same when computing power spectrum, bispectrum and higher-order correlation functions. This has not always been the case, which could lead to wrong conclusions. We calculate the bispectrum for different choices previously discussed for the power spectrum, setting up a consistent framework to search for evidence of excited states in the CMB data.

We study the possibility of asymmetric dark matter with self-interactions forming compact stable objects. We solve the Tolman-Oppenheimer-Volkoff equation and find the mass-radius relation of such “dark stars,” their density profile and their Chandrasekhar mass limit. We consider fermionic asymmetric dark matter with Yukawa-type self-interactions appropriate for solving the well-known problems of the collisionless dark matter paradigm. We find that in several cases the relativistic effects are significant.

Multiple tracers of the cosmic density field, with different bias, number and luminosity evolution, can be used to measure the large-scale properties of the Universe. We show how an optimal combination of tracers can be used to detect general-relativistic effects in the observed density of sources. We forecast for the detectability of these effects, as well as measurements of primordial non-Gaussianity and large-scale lensing magnification with current and upcoming large-scale structure experiments. In particular we quantify the significance of these detections in the short term with experiments such as the Dark Energy Survey (DES), and in the long term with the Large Synoptic Survey Telescope (LSST) and the Square Kilometre Array (SKA). We review the main observational challenges that must be overcome to carry out these measurements.

Ekpyrotic bouncing cosmologies have been proposed as alternatives to inflation. In these scenarios, the Universe is smoothed and flattened during a period of slow contraction preceding the bounce while quantum fluctuations generate nearly scale-invariant superhorizon perturbations that seed structure in the post-bounce Universe. An analysis by Tolley and Wesley (2007) showed that, for a wide range of ekpyrotic models, generating a scale-invariant spectrum of adiabatic or entropic fluctuations is only possible if the cosmological background is unstable, in which case the scenario is highly sensitive to initial conditions. In this paper, we analyze an important counterexample: a simple action that generates a Gaussian, scale-invariant spectrum of entropic perturbations during ekpyrotic contraction without requiring fine-tuned initial conditions. Based on this example, we discuss some generalizations.

We propose a new and robust method to test the consistency of the cosmic evolution given by a cosmological model. It is realized by comparing the combined quantity $r_{\mathrm{d}}^{\mathrm{CMB}}/D_{\mathrm{V}}^{\mathrm{SN}}$, which is derived from the comoving sound horizon $r_{\mathrm{d}}$ from cosmic microwave background (CMB) measurements and the effective distance $D_{\mathrm{V}}$ derived from low-redshift type-Ia supernovae (SNe Ia) data, with direct and independent $r_{\mathrm{d}}/D_{\mathrm{V}}$ obtained by baryon acoustic oscillation (BAO) measurements at median redshifts. We apply this test method for the $\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) and $w\mathrm{CDM}$ models, and investigate the consistency of the derived value of $r_{\mathrm{d}}/D_{\mathrm{V}}$ from Planck 2015 and the SN Ia data sets of Union2.1 and joint light-curve analysis (JLA) ($z<1.5$), and the $r_{\mathrm{d}}/D_{\mathrm{V}}$ directly given by BAO data from six-degree-field galaxy survey (6dFGS), Sloan Digital Sky Survey Data Release 7 Main Galaxy Survey (SDSS-DR7 MGS), DR11 of SDSS-III, WiggleZ and $\mathrm{Ly}\alpha$ forecast surveys from baryon oscillation spectroscopic data (BOSS) DR-11 over $0.1<z<2.36$. We find that $r_{\mathrm{d}}^{\mathrm{CMB}}/D_{\mathrm{V}}^{\mathrm{SN}}$ for both nonflat $\mathrm{\Lambda }\mathrm{CDM}$ and flat $w\mathrm{CDM}$ models with Union2.1 and JLA data are well consistent with the BAO and CMB measurements within $1\sigma$ C.L. Future surveys will further tighten up the constraints significantly, and provide a stronger test on the consistency.