Λ effect in the cosmological expansion of void

Abstract

We investigate the dynamical effect of the cosmological constant Λ on a single spherical vacuum void evolving in the universe within a global solution of Newton-Friedmann models. As a result, the main characteristic is that the void expands with a huge initial burst up to match asymptotically the Hubble flow. The size of voids increases with Ω • and with Λ, which is interpreted as respectively by the gravitational attraction of borders from outside regions and by the gravitational repulsion of vacuum from the inner region. The Λ-effect on the kinematics intervenes significantly by amplifying the expansion rate at redshift z ∼ 1.7 for a background density parameter Ω • ∼ 0.3. For a class of parameters values, which corresponds in GR to spatially closed Friedmann models, it is interesting to note that a test particle in the inner region moves toward the border. Such a peculiar feature shows that the empty regions are swept out ; which stands as a stability criterion. -Marseille II et du Sud Toulon-Var. Laboratoire affiliéà la FRUMAM (FR 2291).

Dynamics of Void and its Shape in Redshift Space

“…7. It is remarkable that the present GR approach for the sub-horizon void confirms the previous result found in the Newtonian dynamics [13]. Even for a relativistic spherical void with a horizon size radius R i = H −1 i , the relativistic effect turns out to be weak.…”

“…Our analysis on the expansion of the void is given in §. 3, by which we confirm the previous result based on a covariant formulation of Newtonian dynamics [13]. In §.4, we analyze the shape of a void in the redshift space by which we show that such a distortion effect could be observable, similarly to "Fingers of God" or to the Kaiser effect.…”

“…There may be a loitering period during which a spherical void can grow much faster compared to the cosmological expansion. It clearly appears as a bump in the curve for λ 0 = 1.4 in Fig 1 . Such a feature could be used to evaluate the value of λ 0 by a statistical analysis of cosmological parameters from observational data [13]. Here we will show one simple example, by which the peculiar velocity of a void shell creates an observable deformation of a void shape in the redshift space.…”

“…which is used to classify the FL cosmological models. It stands for the dimensionless expression of the scalar curvature of the comoving space, which is identified to an integration constant in the Newtonian dynamics [13].…”

“…Hence, with the aim to understand the mechanism of the large scale structure formation, we have to improve the Newtonian N -body simulation. For this purpose, the Newton-Friedmann model [13], which is based on the covariant formulation of Euler-Poisson equations [22], appears to be more adapted for being implemented in the numerical codes, although we may need further study in its practical formulation.…”