The discussion centers on the effects of the expanding universe on our solar system, specifically addressing why gravitationally bound systems, such as solar systems and galaxies, do not experience noticeable expansion. Participants concluded that while the Hubble constant is approximately 10^-17 s^-1, the expansion's effect is negligible compared to the forces binding celestial objects. Dark energy does exert a minimal influence, but it is insufficient to overcome gravitational forces within these systems. Estimates suggest that the distance between Earth and the Sun has increased by about 0.1 mm over billions of years due to cosmic expansion.
PREREQUISITESAstronomers, astrophysicists, and students of cosmology seeking to understand the dynamics of cosmic expansion and its negligible effects on gravitationally bound systems.
Mark M said:It needs to be extremely weak, and there needs to be a sufficiently large distance in between the objects. Unfortunately, it's a grey line. It's like asking 'When do we start using global coordinates instead of local coordinates?'. There isn't a well defined answer.
Well, normal expansion has absolutely no effect inside of galaxies. See the website I posted above by John Baez.
Neither Brooklyn, nor its atoms, nor the solar system, nor even the galaxy, is expanding.
...You can see that the cosmological constant reduces the attractive force of gravity by some small amount. For atoms, this would have the effect of making atoms ever so slightly larger than they otherwise would be (the difference really is utterly negligible, however).
The FRW spacetime simply doesn't apply at the local scale.
...regular expansion does not affect gravitationally bound objects. Dark energy does.
So how does one reconcile the two different spacetimes from the article? If the universe as a whole is expanding, but locally it has zero effect, where's the middle ground? How weak does gravity need to be between two objects for expansion to occur?
It needs to be extremely weak, and there needs to be a sufficiently large distance in between the objects. Unfortunately, it's a grey line. It's like asking 'When do we start using global coordinates instead of local coordinates?'. There isn't a well defined answer.
a negative pressure dark energy is the same thing as a cosmological constant.
The difference is that the curvature from the cosmological constant is intrinsic, it's just there. With a dark energy case, the negative pressure creates the curvature.
Do you agree that regular metric expansion (as in FRW) does not have an effect within gravitationally bound systems?
Well, you could think of a cosmological constant as being a geometric feature of the particular space-time. For example, a space with a cosmological constant and no matter is a de Sitter space. A de Sitter space just comes with this constant force (the cosmological constant). Nothing present in the space causes this, it's 'built in' to it's equations.Naty1 said:Was not aware of such a distinction...but it makes no sense to me...'intrinsic' usually means we have no good ideas! In this case, assigning such a 'constant' factor of integration and ascribing a specific physical meaning amid the mess of GR is byond my paygrade!
It comes from the normal Einstein Field equations. Take a look: R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu} Now, say no matter is present, so we can ignore the the Ricci tensor and scalar. (Those are the two 'R's, the tensor has a subscript). Now the equation becomes g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu} Using a little algebra, you can solve for the stress-energy tensor (the 'T'), and get this T_{\mu \nu} = - \frac {\Lambda c^{4}} {8 \pi G} g_{ \mu \nu} From which you could derive the expression I posted above.the exact mathematical relationship between vacuum energy and the cosmological constant is interesting...have not seen it...
They most definitely don't apply for non-homogenous distributions of matter, such as galaxies. So, as John Baez explained on that page, we say that no expansion is occurring in the galaxies (dark energy is a different matter).Do you think the assumptions that go into the FLRW metric solution
to the EFE apply within gravitationally bound systems?
If anything there is a vanishingly small FRW element to the metric of bound structures. If the FRW metric 'prevail(ed) on all scales and everywhere, even inside gravitationally bound structures or within atoms' then why do galaxies maintain a constant size as the distance between them expands? Commonly we are told that the local mass concentration 'overcomes' the expansion preventing this from occurring. This is one of the worst and most fallacious explanations you could possibly give someone! What really happens then?
The FRW metric is the inevitable result of the cosmological principle, CP. which is that the universe is homogeneous and isotropic. The metric is only valid if these principles hold. Consider now a galaxy, solar system or planet. Does the CP hold? No. Is it a remotely useful approximation? Not at all! Unsurprisingly then the dynamics of bodies in these systems and on these scales bears no resemblance to the dynamics of galaxies. So for instance, there is no redshift of light due to a(t) when we observe light from the other side of our galaxy, or from say Andromeda. The FRW metric simply is not valid on these scales.
….. The better way to look at it is that the presence of the mass in the galaxy gives the metric of space-time around this mass a form that would look much more like a Schwarzschild metric than FRW (though we cannot fully solve GR for a galaxy.). The point is though that there is not expansion to 'overcome' since the 'expansion' is merely the result of the metric [variable over time] formed by a homogeneous and isotropic mass distribution. If the mass doesn't obey these principles we shouldn't be surprised that we don't see any 'expansion'.
If you don't believe me hold an object in each hand with outstretched arms. When you let them go what happens? I think you will find that they both plummet towards the local centre of mass (the centre of the Earth) rather than drift off into the Hubble flow! The local mass concentration can hardly be described as a mere perturbation to the FRW metric!
….the 'expansion' (which we both definitely agree is a bad term for it!) is a result of the FRW metric, in particular a(t). The metric in the region of bound structure looks nothing like the FRW metric, in particular it has no global time dependence (though will of course evolve). For this reason I stand by the statement that the FRW metric is not valid on scales which are significantly inhomogeneous, since the metric has no component that reflects the global a(t), and hence the FRW picture does not relate to the dynamics of the system.
Well, you could think of a cosmological constant as being a geometric feature of the particular space-time. For example, a space with a cosmological constant and no matter is a de Sitter space. A de Sitter space just comes with this constant force (the cosmological constant). Nothing present in the space causes this, it's 'built in' to it's equations.