Just to clarify, I am not asking about the fate of the universe or about the big rip at all. What I am asking about is the timing of the effects of expansion, and at the current acceleration rate of expansion when will the expansion start affecting matter and objects made of it considerably (when will expansion start stretching matter and objects). This concerns smaller (like us), and larger (like the Milky Way) objects too. And the balance between the forces, that is, when the expansion will start dominating over the other forces.
There are other questions about this, but none of them actually answer my timing question.
I have read this question:
Nowadays, the value of the Hubble constant is H0≈70 km s−1 Mpc−1≈0.07 Gyr−1, meaning it takes roughly a billion years for some structure to be expanded by 0.07=7% (values and this last bit quoted from Wikipedia's page on the Hubble Law). Hence, for small structures such as crystals, the effect is essentially negligible. Nevertheless, if the constant was sufficiently large, the expansion would be able to tear the crystals apart. In fact, for a constant of H∼1018 s−1 it should be able to rip the electron from a hydrogen atom (I'm estimating the number by converting the typical size of a hydrogen atom to a time scale using the speed of light as a conversion factor).
For example, the solar system does expand due to cosmological expansion, but the effect is undetectably small. See Cooperstock, Faraoni, and Vollick, "The influence of the cosmological expansion on local systems," The strain on a bound system is proportional to (d/dt)(a¨/a), where a(t) is the cosmological scale factor. This quantity is not constant in realistic models, and can be nonzero even if the cosmological constant is zero. Also, it vanishes identically in a cosmology that consists only of dark energy (=cosmological constant).
Now all of these answers agree on these:
space expands everywhere, yes "inside" us and the matter we are made up of, even inside the Milky Way, it is just that the other forces (EM and strong, gravity) are dominating (over expansion) at this rate of expansion, and holding structures together
expansion is accelerating
expansion (even at the current rate) does affect matter and objects made up of it, it is just that at the current rate, it would take billions of years for a considerable effect
hence, there is a rate of expansion, where the expansion's effect on matter will be non-negligible, and this is calculatable
Now based on these, and the fact that expansion is accelerating (and according to our currently accepted theories, it will keep accelerating), we are heading towards a universe, where matter will be stretched (because expansion will start dominating over the other forces) and objects made up of matter will be too (us, and our galaxy too).
I am just asking about the timing of this, when will this effect be considerable? So there must be a rate of expansion, at which these effects become dominant. I am asking for this rate, or when (assuming continued acceleration) we will reach this rate.
- When will space expansion stretch the Milky Way considerably?