We study the mechanisms of the gravitational collapse of the Bose-Einstein condensate dark matter halos, described by the zero temperature time-dependent nonlinear Schrödinger equation (the Gross-Pitaevskii equation), with repulsive interparticle interactions. By using a variational approach, and by choosing an appropriate trial wave function, we reformulate the Gross-Pitaevskii equation with spherical symmetry as Newton’s equation of motion for a particle in an effective potential, which is determined by the zero-point kinetic energy, the gravitational energy, and the particles interaction energy, respectively. The velocity of the condensate is proportional to the radial distance, with a time-dependent proportionality function. The equation of motion of the collapsing dark matter condensate is studied by using both analytical and numerical methods. The collapse of the condensate ends with the formation of a stable configuration, corresponding to the minimum of the effective potential. The radius and the mass of the resulting dark matter object are obtained, as well as the collapse time of the condensate. The numerical values of these global astrophysical quantities, characterizing condensed dark matter systems, strongly depend on the two parameters describing the condensate, the mass of the dark matter particle, and of the scattering length, respectively. The stability of the condensate under small perturbations is also studied, and the oscillations frequency of the halo is obtained. Hence these results show that the gravitational collapse of the condensed dark matter halos can lead to the formation of stable astrophysical systems with both galactic and stellar sizes.

We present a perturbative treatment of gravitational wave memory. The coordinate invariance of Einstein’s equations leads to a type of gauge invariance in perturbation theory. As with any gauge invariant theory, results are more clear when expressed in terms of manifestly gauge invariant quantities. Therefore we derive all our results from the perturbed Weyl tensor rather than the perturbed metric. We derive gravitational wave memory for the Einstein equations coupled to a general energy-momentum tensor that reaches null infinity.

Asymptotically locally anti–de Sitter and asymptotically flat black hole solutions are found for a particular case of the Horndeski action. The action contains the Einstein-Hilbert term with a cosmological constant, a real scalar field with a nonminimal kinetic coupling given by the Einstein tensor, the minimal kinetic coupling, and the Maxwell term. There is no scalar potential. The solution has two integration constants related with the mass and the electric charge. The solution is given for all dimensions. A new class of asymptotically locally flat spherically symmetric black holes is found when the minimal kinetic coupling vanishes and the cosmological constant is present. In this case, we get a solution which represents an electric universe. The electric field at infinity is only supported by $\mathrm{\Lambda }$. When the cosmological constant vanishes, the black hole is asymptotically flat.

We investigate the compatibility of minimally coupled scalar, fermion and gauge fields with asymptotically safe quantum gravity, using nonperturbative functional renormalization group methods. We study $d=4,5$ and 6 dimensions and within certain approximations find that for a given number of gauge fields there is a maximal number of scalar and fermion degrees of freedom compatible with an interacting fixed point at positive Newton coupling. The bounds impose severe constraints on grand unification with fundamental Higgs scalars. Supersymmetry and universal extra dimensions are also generally disfavored. The standard model and its extensions accommodating right-handed neutrinos, the axion and dark-matter models with a single scalar are compatible with a fixed point.

We carry out a general study on the collapse of axially (and reflection-)symmetric sources in the context of general relativity. All basic equations and concepts required to perform such a general study are deployed. These equations are written down for a general anisotropic dissipative fluid. The proposed approach allows for analytical studies as well as for numerical applications. A causal transport equation derived from the Israel-Stewart theory is applied, to discuss some thermodynamic aspects of the problem. A set of scalar functions (the structure scalars) derived from the orthogonal splitting of the Riemann tensor are calculated and their role in the dynamics of the source is clearly exhibited. The characterization of the gravitational radiation emitted by the source is discussed.

We investigate the possibility of sustained orbital resonances in extreme mass ratio inspirals. Using a near-identity averaging transformation, we reduce the equations of motion for a particle moving in Kerr spacetime with self-force corrections in the neighborhood of a resonant geodesic to a one-dimensional equation for a particle moving in an effective potential. From this effective equation we obtain the necessary and sufficient conditions that the self-force needs to satisfy to allow inspiralling orbits to be captured in sustained resonance. Along the way we also obtain the full nonlinear expression for the jump in the adiabatic constants of motion incurred as an inspiral transiently evolves through a strong resonance to first-order in the mass ratio. Finally, we find that if the resonance is strong enough to allow capture in sustained resonance, only a small fraction (order of the square root of mass-ratio) of all inspirals will indeed be captured. This makes observation of sustained resonances in extreme mass ratio inspirals—if they exist—very unlikely for space-based observatories like eLisa.

Recent work in the literature has found a suppression or, instead, an enhancement of the cosmic microwave background power spectrum in quantum gravity, although the effect is too small to be observed in both cases. The present paper studies in detail the equations recently proposed for a Born-Oppenheimer–type analysis of the problem. By using a perturbative approach to the analysis of the nonlinear ordinary differential equation obeyed by the two-point function for scalar fluctuations, we find various explicit forms of such a two-point function, with the associated power spectrum. In particular, a new family of power spectra is obtained and studied. The theoretical prediction of power enhancement at large scales is hence confirmed.

The regularized vacuum fluctuation related to a conformally coupled massless scalar field defined on a space-time with dynamical horizon is computed with respect a radially moving observer in a generic flat Friedmann-Lemaître-Robertson-Walker space-time. Two simple measurement prescriptions are given in order to remove the ambiguity associated with the short distance singularity of the correlation function. In some cases, it turns out that one is dealing with a quantum thermometer, recovering a proposal due to Buchholz et al. in order to determine local temperature in the framework of quantum field theory. In general, by arranging the detector so that it does not register for inertial motion in flat space, the regularized quantum fluctuation may be used as a probe of space-time geometry and, in particular, may provide information on the Hubble parameter. As an aside, it is not possible in general to fully decouple the effect of the detector’s motion from the Universe expansion, a fact that could be interpreted as a kind of Machian effect, which can be traced back to the global nature of the vacuum.

One of the outstanding problems of classical celestial mechanics was the restricted three-body problem, in which a planetoid of small mass is subject to the Newtonian attraction of two celestial bodies of large mass, as it occurs, for example, in the Sun-Earth-Moon system. On the other hand, over the last decades, a systematic investigation of quantum corrections to the Newtonian potential has been carried out in the literature on quantum gravity. The present paper studies the effect of these tiny quantum corrections on the evaluation of equilibrium points. It is shown that, despite the extreme smallness of the corrections, there exists no choice of sign of these corrections for which all qualitative features of the restricted three-body problem in Newtonian theory remain unaffected. Moreover, first-order stability of equilibrium points is characterized by solving a pair of algebraic equations of fifth degree, where some coefficients depend on the Planck length. The coordinates of stable equilibrium points are slightly changed with respect to Newtonian theory, because the planetoid is no longer at equal distance from the two bodies of large mass. The effect is conceptually interesting but too small to be observed, at least for the restricted three-body problems available in the solar system.

We examine the possibility of dealing with gravitational singularities on a quantum level through the use of coherent state or wavelet quantization instead of canonical quantization. We consider the Robertson-Walker metric coupled to a perfect fluid. It is the simplest model of a gravitational collapse, and the results obtained here may serve as a useful starting point for more complex investigations in the future. We follow a quantization procedure based on affine coherent states or wavelets built from the unitary irreducible representation of the affine group of the real line with positive dilation. The main issue of our approach is the appearance of a quantum centrifugal potential allowing for regularization of the singularity, essential self-adjointness of the Hamiltonian, and unambiguous quantum dynamical evolution.

The background dynamical evolution of a universe filled with matter and a cosmological scalar field is analyzed employing dynamical system techniques. After the phenomenology of a canonical scalar field with exponential potential is revised, square and square root kinetic corrections to the scalar field canonical Lagrangian are considered and the resulting dynamics at cosmological distances is obtained and studied. These noncanonical cosmological models imply new interesting phenomenology including early time matter dominated solutions, cosmological scaling solutions and late time phantom dominated solutions with dynamical crossing of the phantom barrier. Stability and viability issues for these scalar fields are presented and discussed.

Alterations of the gravity Lagrangian introduced in modified torsion gravity theories—also referred to as $f(T)$ gravity—allows for an accelerated expansion in a matter-dominated Universe. In this framework, the cosmic speed-up is driven by an effective “torsion fluid.” Besides the background evolution of the Universe, structure formation is also modified because of a time-dependent effective gravitational constant. Here, we investigate the imprints of $f(T)$ gravity on galaxy clustering and weak gravitational lensing to the aim of understanding whether future galaxy surveys could constrain torsion gravity and discriminate between it and standard general relativity. Specifically, we compute Fisher matrix forecasts for two viable $f(T)$ models to both infer the accuracy on the measurement of the model parameters and evaluate the power that a combined clustering and shear analysis will have as a tool for model selection. We find that with such a combination of probes it will indeed be possible to tightly constrain $f(T)$ model parameters. Moreover, the Occam’s razor provided by the Bayes factor will allow us to confirm an $f(T)$ power-law extension of the concordance $\mathrm{\Lambda }\mathrm{CDM}$ model, if a value larger than 0.02 of its power-law slope were measured, whereas in $\mathrm{\Lambda }\mathrm{CDM}$ it is exactly 0.

Using separate universe simulations, we accurately quantify super-sample covariance (SSC), the typically dominant sampling error for matter power spectrum estimators in a finite volume, which arises from the presence of super survey modes. By quantifying the power spectrum response to a background mode, this approach automatically captures the separate effects of beat coupling in the quasilinear regime, halo sample variance in the nonlinear regime and a new dilation effect which changes scales in the power spectrum coherently across the survey volume, including the baryon acoustic oscillation scale. It models these effects at typically the few percent level or better with a handful of small volume simulations for any survey geometry compared with directly using many thousands of survey volumes in a suite of large-volume simulations. The stochasticity of the response is sufficiently small that in the quasilinear regime, SSC can be alternately included by fitting the mean density in the volume with these fixed templates in parameter estimation. We also test the halo model prescription and find agreement typically at better than the 10% level for the response.

In this paper we investigate the case of nonminimal coupling in the (extended) nonlinear massive gravity theories. We first consider massive gravity in the Brans-Dicke background such that the graviton mass is replaced by $A^2(\sigma )m$ where $\sigma$ is the Brans-Dicke field and $A(\sigma )$ is the conformal coupling and show that there is no viable thermal history of the Universe in this case. We then invoke a cubic Galileon term as the nonlinear completion of the $\sigma$ Lagrangian and show that there is a stable de Sitter solution in this case. However, the de Sitter is blocked by the matter phase, which is also a simultaneous attractor of the dynamics. The de Sitter phase can, however, be realized by invoking unnatural fine-tunings. We next investigate the cosmology of quasidilaton nonlinear massive gravity with nonminimal coupling. As a generic feature of the nonminimal coupling, we show that the model exhibits a transient phantom phase that is otherwise impossible. While performing the observational data analysis on the models, we find that a small value of the coupling constant is allowed for quasidilaton nonlinear massive gravity. For both of the cases under consideration, it is observed that we have an effective pressure of matter that comes from the constraint equation. For mass-varying nonlinear massive gravity in the Brans-Dicke background, the effective pressure of matter is nonzero, which affects the evolution of the Hubble parameter, thereby spoiling the consistency of the model with data. As for the quasidilaton nonlinear massive gravity, the effective pressure of matter can be kept around zero by controlling the coupling constant, and the model is shown to be fit well with observations.

The interacting dark energy model could propose a effective way to avoid the coincidence problem. In this paper, dark energy is taken as a fluid with a constant equation-of-state parameter $w_x$. In a general gauge, we could obtain two sets of different perturbation equations when the momentum transfer potential is vanished in the rest frame of dark matter or dark energy. There are many kinds of interacting forms from the phenomenological considerations; here, we choose $Q=3H{\xi }_x{\rho }_x$, which owns the stable perturbations in most cases. Then, according to the Markov chain Monte Carlo method, we constrain the model by currently available cosmic observations, which include cosmic microwave background radiation, baryon acoustic oscillation, type Ia supernovae, and $f{\sigma }_8(z)$ data points from redshift-space distortion. Jointing the geometry tests with the large scale structure information, the results show a tighter constraint on the interacting model than the case without $f{\sigma }_8(z)$ data. We find the interaction rate in $3\sigma$ regions: ${\xi }_x={0.00372}_{-0.00372-0.00372-0.00372}^{+0.000768+0.00655+0.0102}$. It means that the recently cosmic observations favor a small interaction rate between the dark sectors, snf at the same time, the measurement of redshift-space distortion could rule out a large interaction rate in the $1\sigma$ region.

One possible description for the current accelerated expansion of the Universe is quintessence dynamics. The basic idea of quintessence consists of analyzing cosmological scenarios driven by scalar fields. In this work we present some interesting features on the cosmological scenario obtained from the solutions of an effective two scalar field model in a flat space-time. This effective model was constructed by coupling two single scalar field systems in a nontrivial way via an extension method. The solutions related to the fields allowed us to compute analytical cosmological parameters. The behavior of these parameters are highlighted, as well as the different epochs obtained from them.

Lagrangian displacement field $\mathbf{\Psi }$ is the central object in Lagrangian perturbation theory (LPT). LPT is very successful at high redshifts, but it performs poorly at low redshifts due to severe shell crossing. To understand and quantify the effects of shell crossing, we extract $\mathbf{\Psi }$ from $N$-body simulation and decompose it into scalar and vector parts. We find that at late time the power spectrum of the scalar part agrees with 1-loop results from LPT at large scales, while the power in small scales is much suppressed due to shell crossing. At $z=0$, the power spectrum of $\mathbf{\Psi }$ is 10% lower than the 1-loop results at $k=0.1{\mathrm{Mpc}}^{-1}h$. Shell crossing also generates the vector contribution in $\mathrm{\Psi }$, although its effect is subdominant in comparison with the power suppression in the scalar part. At $z=0$, the vector part contributes 10% to the total power spectrum of $\mathbf{\Psi }$ at $k=1{\mathrm{Mpc}}^{-1}h$, while only 1% is expected from the vector contribution in LPT. We also examine the standard LPT recipes and some of its variants. In one of the variants, we include a power suppression factor in the displacement potential to take into account the power suppression in small scales after shell crossing. However, these simple phenomenological approaches are found to yield limited improvement compared to the standard LPT after the onset of shell crossing.

In the frame of a moving observer, the cosmic microwave background (CMB) fluctuation exhibits violation of statistical isotropy (SI). The SI violation effect from our local motion on CMB temperature fluctuation has been measured in the recent Planck results P. A. R. Ade et al., arXiv:1303.5083 [Astron. Astrophys. (to be published)]; N. Aghanim et al., arXiv:1303.5087. We calculate the effect of our local motion with velocity $(\beta \equiv |\mathit{v}|/c=1.23\times {10}^{-3})$ on the CMB polarization field. The Lorentz transformation of the polarization field leads to aberration in the direction of incoming photons and also modulation of the Stokes parameters, which results in mixing of power between different CMB multipoles. We show that for small values of $\beta$, the effect on the angular power spectra that correspond to the diagonal terms in the spherical harmonic space is at $O({\beta }^2)$. But nonzero off-diagonal terms at the linear order in $\beta$ could provide a measurable signature of SI violation in the bipolar spherical harmonic (BipoSH) representation. We also calculate the measurability of $\beta$ from polarization maps from experiments like Planck and PRISM. It is possible to measure $\beta$ from the ideal, cosmic variance limited BipoSH spectra of $EE$, $TE$, $BB$, but not in $EB$ and $TB$. With the instrumental noise and angular resolution of Planck, it is not possible to measure $\beta$ with high statistical significance from BipoSH spectra of polarization. PRISM can measure $\beta$ with high significance in both $EE$ and $TE$ BipoSH spectra, but not in $BB$, $EB$ and $TB$ BipoSH spectra.

We argue that the excess of sub-PeV/PeV neutrinos recently reported by IceCube could plausibly originate through pion-production processes in the same sources responsible for cosmic rays (CRs) with energy above the second knee around $10^{18}\mathrm{eV}$. The pion-production efficiency for escaping CRs that produce PeV neutrinos is required to be $\gtrsim 0.1$ in such sources. On the basis of current data, we identify semirelativistic hypernova remnants as possible sources that satisfy the requirements. By virtue of their fast ejecta, such objects can accelerate protons to EeV energies, which, in turn, can interact with the dense surrounding medium during propagation in their host galaxies to produce sufficient high-energy neutrinos via proton-proton ($pp$) collisions. Their accompanying gamma-ray flux can remain below the diffuse isotropic gamma-ray background observed by the Fermi Large Area Telescope. In order to test this scenario and discriminate from alternatives, the density of target protons/nuclei and the residence time of CRs in the interacting region are crucial uncertainties that need to be clarified. As long as the neutrinos and EeV CRs originate from the same source class, detection of $\gtrsim 10\mathrm{PeV}$ neutrinos may be expected within 5–10 years’ operation of IceCube. Together with further observations in the PeV range, the neutrinos can help in revealing the currently unknown sources of EeV CRs.

We probe the gravitational interaction of two black holes in the strong-field regime by computing the scattering angle $\chi$ of hyperboliclike, close binary-black-hole encounters as a function of the impact parameter. The fully general-relativistic result from numerical relativity is compared to two analytic approximations: post-Newtonian theory and the effective-one-body formalism. As the impact parameter decreases, so that black holes pass within a few times their Schwarzschild radii, we find that the post-Newtonian prediction becomes quite inaccurate, while the effective-one-body one keeps showing a good agreement with numerical results. Because we have explored a regime which is very different from the one considered so far with binaries in quasicircular orbits, our results open a new avenue to improve analytic representations of the general-relativistic two-body Hamiltonian.