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" ... At some point, of course, this becomes wildly impractical. When the wavelength of a leftover photon from the Big Bang becomes larger than a planet, or the spatial density of photons becomes lower than 1-per-solar system, it seems implausible that we’d ever build a detector capable of measuring it. On long enough cosmic timescales, the number density of particles — both matter particles and photons — as well as the energy per photon we’d observe, both asymptote towards zero. ... "
" ... It’s true that, for all of time since (at least) the hot Big Bang, the Universe has been expanding. It’s also true that while time is linear, passing at that constant perceived rate of one second per second, the rate at which the Universe expands is not. The Universe expanded much more quickly in the past, is expanding more slowly today, and will asymptote to a finite, positive value. This, as far as we understand it, means that distant galaxies that aren’t gravitationally bound to us will continue to recede from our perspective, faster and faster, until what remains of our Local Group is the only remaining thing we can access. ... "
" ... The blue "shading" represent the possible uncertainties in how the dark energy density was/will be... [+] different in the past and future. The data points to a true cosmological "constant," but other possibilities are still allowed. As matter becomes less and less important, dark energy becomes the only term that matters. The expansion rate has dropped over time, but will now asymptote to around 55 km/s/Mpc. ... "
" ... With the same, constant force applied, your speed would begin to asymptote: approaching, but never quite reaching, the speed of light. But the closer to that unreachable limit you get, with every extra percentage point as you go from 99% to 99.9% to 99.999% and so on, lengths contract and time dilates even more severely. ... "