Here some quotes I found interesting to think about before going to sleep.
"How far can one travel from the Earth?
Since one might not travel faster than light, one might conclude that a human can never travel further from the earth than 40 light years, if the traveler is active between the age of 20 and 60. So a traveler would never be able to reach more than the very few star systems which exist within the limit of 20-40 light years from the earth. But that would be a mistaken conclusion. Because of time dilation, the traveller can travel thousands of light years during their 40 active years. If the spaceship accelerates at a constant 1G, they will, after 354 days, reach speeds a little under the speed of light, and time dilation will increase their lifespan to thousands of years, seen from the reference system of the Solar System, but the traveller's subjective lifespan will not thereby change. If the traveller returns to the earth they will land thousands of years into the future. Their speed will not be seen as higher than the speed of light by observers on earth, and the traveller will not measure their speed as being higher than the speed of light, but will see a length contraction of the universe in their direction of travel. And as the traveller turns around to return, the Earth will seem to experience much more time than the traveller does.
The expansion of the universe causes distant galaxies to recede from us faster than the speed of light, if comoving distance and cosmological time are used to calculate the speeds of these galaxies. However, in general relativity, velocity is a local notion, so velocity calculated using comoving coordinates does not have any simple relation to velocity calculated locally (see comoving distance for a discussion of different notions of 'velocity' in cosmology). Rules that apply to relative velocities in special relativity, such as the rule that relative velocities cannot increase past the speed of light, do not apply to relative velocities in comoving coordinates, which are often described in terms of the "expansion of space" between galaxies. This expansion rate is thought to have been at its peak during the inflationary epoch thought to have occurred in a tiny fraction of the second after the Big Bang (models suggest the period would have been from around 10−36 seconds after the Big Bang to around 10−33 seconds), when the universe may have rapidly expanded by a factor of around 1020to 1030.
There are many galaxies visible in telescopes with red shift numbers of 1.4 or higher. All of these are currently traveling away from us at speeds greater than the speed of light. Because the Hubble parameter is decreasing with time, there can actually be cases where a galaxy that is receding from us faster than light does manage to emit a signal which reaches us eventually. However, because the expansion of the universe is accelerating, it is projected that most galaxies will eventually cross a type of cosmological event horizon where any light they emit past that point will never be able to reach us at any time in the infinite future, because the light never reaches a point where its "peculiar velocity" towards us exceeds the expansion velocity away from us (these two notions of velocity are also discussed in Comoving distance#Uses of the proper distance). The current distance to this cosmological event horizon is about 16 billion light years, meaning that a signal from an event happening at present would eventually be able to reach us in the future if the event was less than 16 billion light years away, but the signal would never reach us if the event was more than 16 billion light years away."