Turnaround radius in an accelerated universe with quasi-local mass

Abstract

Abstract. We apply the Hawking-Hayward quasi-local energy construct to obtain in a rigorous way the turnaround radius of cosmic structures in General Relativity. A splitting of this quasi-local mass into local and cosmological parts describes the interplay between local attraction and cosmological expansion.

Photon motion in Kerr–de Sitter spacetimes

“…The conditions (24) and (27), ensuring the allowance of the latitudinal motion, must be complemented by the case that the functions X θ ± are not defined. Their definition range is given by Eqs.…”

“…Both high-frequency quasiperiodic oscillations and jets originating at the accretion discs can be reflected by current carrying string loops in SdS and KdS spacetimes [28,33,77,78,93]. In the spherically symmetric spacetimes, the Keplerian and toroidal disc structures can be precisely described by a pseudo-Newtonian potential of Paczynski type [79,88], which appears to be useful also in studies of the motion of interacting galaxies [56,81,82] demonstrating relation of the gravitationally bound galactic systems to the so-called static radius of the SdS or KdS spacetimes [4,5,23,24,66,67]. This idea has been confirmed by the recent study of general relativistic static polytropic spheres in spacetimes with the repulsive cosmological constant [75,85].…”

The turnaround radius as a probe of dark energy and modified gravity

“…This new approach is based on the Hawking quasilocal energy of General Relativity (GR) and is part of a broader program aiming at applying this formal concept to cosmology. Thus far, the quasilocal energy has been applied to Newtonian N-body simulations of large scale structure formation [1], and to the decade-old problem of lensing by the cosmological constant [2].…”

Cosmic structure sizes in generic dark energy models

“…Since its proposal, the maximum turn around radius as a useful cosmological observable has received considerable attention in the context of modified or alternative gravity/dark energy models [31][32][33][34][35][36][37]. The goal is of course to constrain the additional parameters of such theories.…”

“…The goal is of course to constrain the additional parameters of such theories. For example, for a McVittie space-time [38][39][40] a derivation of the turn around radius can be found in [31][32][33], by analyzing geodesics and also using the quasilocal mass function of [41,42]. In [34] a constraint on the matter-galileon coupling parameter was obtained for a cubic galileon model [43].…”