Dark effects in $$\tilde{f}(R,P)$$ gravity

In the present paper a new cosmological model is proposed by extending the Einstein–Hilbert Lagrangian with a generic functional $$\tilde{f}(R,P)$$ f ~ ( R , P ) , which depends on the scalar curvature R and a term P which encodes a possible influence from specific cubic contractions of the Riemann tensor. After proposing the corresponding action, the associated modified Friedmann relations are deduced, in the case where the generic functional has the following decomposition, $$\tilde{f}(R,P)=f(R)+g(P)$$ f ~ ( R , P ) = f ( R ) + g ( P ) . The present study takes into account the power-law and the exponential decomposition for the specific form of the corresponding generic functional. For the analytical approach the specific method of dynamical system analysis is employed, revealing the fundamental properties of the phase space structure, discussing the dynamical consequences for the cosmological solutions obtained. It is revealed that the cosmological solutions associated to the critical points can explain various dynamical eras, with a high sensitivity to the values of the corresponding parameters, encoding different effects due to the geometrical nature of the specific couplings.

Applying explicit symplectic integrator to study chaos of charged particles around magnetized Kerr black hole

In a recent work of Wu, Wang, Sun and Liu, a second-order explicit symplectic integrator was proposed for the integrable Kerr spacetime geometry. It is still suited for simulating the nonintegrable dynamics of charged particles moving around the Kerr black hole embedded in an external magnetic field. Its successful construction is due to the contribution of a time transformation. The algorithm exhibits a good long-term numerical performance in stable Hamiltonian errors and computational efficiency. As its application, the dynamics of order and chaos of charged particles is surveyed. In some circumstances, an increase of the dragging effects of the spacetime seems to weaken the extent of chaos from the global phase-space structure on Poincaré sections. However, an increase of the magnetic parameter strengthens the chaotic properties. On the other hand, fast Lyapunov indicators show that there is no universal rule for the dependence of the transition between different dynamical regimes on the black hole spin. The dragging effects of the spacetime do not always weaken the extent of chaos from a local point of view.

Phase transition at high supersymmetry breaking scale in heterotic string theory

When supersymmetry is spontaneously broken at the tree level, the spectrum of the heterotic string compactified on orbifolds of tori contains an infinite number of potentially tachyonic modes. We show that this implies instabilities of Minkowski space–time, when the scale of supersymmetry breaking is of the order of the string scale. We derive the phase space structure of vacua in the case where the tachyonic spectrum contains a mode with trivial momenta and winding numbers along the internal directions not involved in the supersymmetry breaking.

The Phase Space Structure of Dark Matter Halos

The phase space structure of dark matter halos can be used to measure the mass of the halo, infer mass accretion rates, and probe the effects of modified gravity. Previous studies showed that the splashback radius can be measured in position space using a sharp drop in the density profile. Using N-body simulations, we model the distribution of the kinematically distinct infalling and orbiting populations of subhalos and halos. We show that the two are mixed spatially all the way to redge, which extends past the splashback radius defined by the drop in the spherically averaged density profile. This edge radius can be interpreted as a radius which contains a fixed fraction of the apocenters of dark matter particles. Our results highlight the possibility of measuring the outer boundary of a dark matter halo using its phase space structure and provide a firm theoretical foundation to the satellite galaxy model adopted in the companion paper (Tomooka et al. 2020), where we analyzed the phase space distribution of SDSS redMaPPer clusters.

Explicit symplectic-like integration with corrected map for inseparable Hamiltonian

ABSTRACT Symplectic algorithms are widely used for long-term integration of astrophysical problems. However, this technique can only be easily constructed for separable Hamiltonian, as preserving the phase-space structure. Recently, for inseparable Hamiltonian, the fourth-order extended phase-space explicit symplectic-like methods have been developed by using the Yoshida’s triple product with a mid-point map, where the algorithm is more effective, stable and also more accurate, compared with the sequent permutations of momenta and position coordinates, especially for some chaotic case. However, it has been found that, for the cases such as with chaotic orbits of spinning compact binary or circular restricted three-body system, it may cause secular drift in energy error and even more the computation break down. To solve this problem, we have made further improvement on the mid-point map with a momentum-scaling correction, which turns out to behave more stably in long-term evolution and have smaller energy error than previous methods. In particular, it could obtain a comparable phase-space distance as computing from the eighth-order Runge–Kutta method with the same time-step.

On the phase-space structure of galaxy clusters from cosmological simulations

ABSTRACT Cosmological N-body simulations represent an excellent tool to study the formation and evolution of dark matter (DM) haloes and the mechanisms that have originated the universal profile at the largest mass scales in the Universe. In particular, the combination of the velocity dispersion σv with the density ρ can be used to define the pseudo-entropy $S(r)=\sigma _\mathrm{v}^2/\rho ^{\, 2/3}$, whose profile is well described by a simple power law $S\propto \, r^{\, \alpha }$. We analyse a set of cosmological hydrodynamical re-simulations of massive galaxy clusters and study the pseudo-entropy profiles as traced by different collisionless components in simulated galaxy clusters: DM, stars, and substructures. We analyse four sets of simulations, exploring different resolution and physics (N-body and full hydrodynamical simulations) to investigate convergence and the impact of baryons. We find that baryons significantly affect the inner region of pseudo-entropy profiles as traced by substructures, while DM particles profiles are characterized by an almost universal behaviour, thus suggesting that the level of pseudo-entropy could represent a potential low-scatter mass-proxy. We compare observed and simulated pseudo-entropy profiles and find good agreement in both normalization and slope. We demonstrate, however, that the method used to derive observed pseudo-entropy profiles could introduce biases and underestimate the impact of mergers. Finally, we investigate the pseudo-entropy traced by the stars focusing our interest in the dynamical distinction between intracluster light and the stars bound to the brightest cluster galaxy: the combination of these two pseudo-entropy profiles is well described by a single power law out to almost the entire cluster virial radius.

The messy merger of a large satellite and a Milky Way-like galaxy

Aims. About 10 billion years ago the Milky Way merged with a massive satellite, Gaia-Enceladus. To gain insight into the properties of its debris we analyse in detail a suite of simulations that includes an experiment that produces a good match to the kinematics of nearby halo stars inferred from Gaia data. Methods. We compare the kinematic distributions of stellar particles in the simulations and study the distribution of debris in orbital angular momentum, eccentricity, and energy, and its relation to the mass loss history of the simulated satellite. Results. We confirm that Gaia-Enceladus probably fell in on a retrograde, 30° inclination orbit. We find that while 75% of the debris in our preferred simulation has high eccentricity (> 0.8), roughly 9% has eccentricity lower than 0.6. Star particles lost early have large retrograde motions, and a subset of these have low eccentricity. Such stars would be expected to have lower metallicities as they stem from the outskirts of the satellite, and hence naively they could be confused with debris associated with a separate system. These considerations seem to apply to some of the stars from the postulated Sequoia galaxy. Conclusions. When a massive disc galaxy undergoes a merger event, it leaves behind debris with a complex phase-space structure, a wide range of orbital properties, and a range of chemical abundances. Observationally, this results in substructures with very different properties, which can be misinterpreted as implying independent progeny. Detailed chemical abundances of large samples of stars and tailored hydrodynamical simulations are critical to resolving such conundrums.

Dynamical description of a quintom cosmological model nonminimally coupled with gravity

In this work we have studied a cosmological model based on a quintom dark energy model non-minimally coupled with gravity, endowed with a specific potential energy of the exponential squared type. For this specific type of potential energy and non-minimal coupling, the dynamical properties are analyzed and the corresponding cosmological effects are discussed. Considering the linear stability method, we have investigated the dynamical properties of the phase space structure, determining the physically acceptable solutions. The analysis showed that in this model we can have various cosmological epochs, corresponding to radiation, matter domination, and de Sitter eras. Each solution is investigated from a physical and cosmological point of view, obtaining possible constraints of the model’s parameters. In principle the present cosmological setup represent a possible viable scalar tensor theory which can explain various transitional effects related to the behavior of the dark energy equation of state and the evolution of the Universe at large scales.