The effect of an expanding universe on massive objects

Abstract

We present some astrophysical consequences of the metric for a point mass in an expanding universe derived in Nandra, Lasenby & Hobson, and of the associated invariant expression for the force required to keep a test particle at rest relative to the central mass. We focus on the effect of an expanding universe on massive objects on the scale of galaxies and clusters. Using Newtonian and general-relativistic approaches, we identify two important time-dependent physical radii for such objects when the cosmological expansion is accelerating. The first radius, $r_F$, is that at which the total radial force on a test particle is zero, which is also the radius of the largest possible circular orbit about the central mass $m$ and where the gas pressure and its gradient vanish. The second radius, $r_S$, which is \approx r_F/1.6$, is that of the largest possible stable circular orbit, which we interpret as the theoretical maximum size for an object of mass $m$. In contrast, for a decelerating cosmological expansion, no such finite radii exist. Assuming a cosmological expansion consistent with a $\Lambda$CDM concordance model, at the present epoch we find that these radii put a sensible constraint on the typical sizes of both galaxies and clusters at low redshift. For galaxies, we also find that these radii agree closely with zeroes in the radial velocity field in the neighbourhood of nearby galaxies, as inferred by Peirani & Pacheco from recent observations of stellar velocities. We then consider the future effect on massive objects of an accelerating cosmological expansion driven by phantom energy, for which the universe is predicted to end in a `Big Rip' at a finite time in the future at which the scale factor becomes singular. In particular, we present a novel calculation of the time prior to the Big Rip that an object of a given mass and size will become gravitationally unbound.Comment: 16 pages, 5 tables, 6 figures; new version, to match the version published in MNRA

Constraining condensate dark matter in galaxy clusters

“…On the other hand, v BHΛ (r) is notably different for larger values of the radius r. This is in accordance with the findings of [15]. Nevertheless, we point out that the approximation used in (24) does not include an expansion in the mass distribution itself.…”

“…As in [15], we can also keep the BH profile unmodified and add an expansion term such that the velocity takes the form In that plot, the point in which the velocity reaches zero value corresponds to null centripetal force, i.e., the particle ceases to be gravitationally influenced by the cluster and is carried away by the cosmological expansion. The vertical lines mark the radii obtained by the BH density profile, for the specific parameters chosen to draw the figure.…”

“…Following the assumptions made in [14,15], we can consider the cluster to be embedded in an expanding spacetime background, with the expansion rate given by the Hubble parameter H = Λ/3 and Λ being a small cosmological constant.…”

“…In the case of a cluster that is expanding due to a cosmological constant Λ, the centripetal force on the orbiting body is written as [15] …”

“…We use a data set of 114 clusters radii and perform a statistical analysis to obtain the most representative scattering length value for a specific particle mass. Moreover, since cluster sizes may be in a scale which can be affected by the cosmological expansion, we repeat this procedure including a small valued cosmological constant in a Newtonian approximation [14,15], in the attempt to obtain noticeably distinct results from the non-expanding case (for a relativistic version of BEC dark matter, see, e.g, [16]). This paper is organized as follows: section II presents a brief review of the theoretical background on Bose-Einstein condensate dark matter.…”