There are many places over the internet, like for example this one, that says about current "limit" of what is reachable being about 18 billion lightyears away.
However, does it account for acceleration of the expansion? Or it treats it as something almost constant?
What I really ask about it: for now, the boundary is about 18 billion lightyears, but if expansion speeds up, then what will be the limit in a million years? 10 million years? What about a 1 billion years? 10 billion years? 1 trillion years?
Do we have some estimates or simplified formulas that one could use for mental exercises during commuting to his work? :-)
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Cosmological horizons is the term you're looking for. Specifically the particle horizon is what you're looking for, I think.
It's the event horizon. The particle horizon is the greatest distance something that started travelling in the past can have reached you from, so it corresponds to the size of the present-day observable universe.
Yeah, it wasn't clear from OPs post which one they're thinking of and the linked article is blocked where I'm right now, so I had to guess.
Yes, the Cosmic Event Horizon is based on the Hubble Parameter, not the Hubble Constant. If the universe continued to expand only at the current Hubble Constant rate (~67 kps/Mpc) that’s called the Hubble Sphere and is about 14B ly out. But expansion will, over time, converge closer to 45-54 kps/Mpc. So the Cosmic Event Horizon where light will eventually catch up to a future observer is ~18B ly out. So it accounts for a changing Hubble Constant.
And it’s easy to estimate without integrating over time: just take the lightspeed (300,000 kps) and divide by the future convergence (50 kps/Mpc) and you get ~6,000 Mpc. Multiply that by 3.26 light years per parsec and you get ~19.5B ly. That’s within the margin of error of the expected future Hubble Parameter.
(Note: expansion between observable objects is accelerating because the observable sphere is further out over time. By all current measurements the universe will always accelerate. But the rate of acceleration is converging lower, to ~45-54 kps/Mpc. It’s converging at a lower rate per megaparsec because the mass-energy density is approaching zero, so only dark energy will be driving expansion in a bout 10B yrs)
(Note: these cosmic horizons assume a flat space, which is a reasonable assumption consistent with current measurements)
(Note: these cosmic horizons assume a constant dark energy which some propose may not be constant. There is ongoing research, but should dark energy disappear, then expansion would halt and there would no longer be horizons. It’s difficult to extrapolate 10106 yrs out based on observing only the first 1.38x1010 yrs)
What is the universe expanding into? What is this cosmic spillover and growth filling?