This is a follow up question based on a previous question I had asked a while ago (1 Light Year Diameter Planet). How many human civilizations could exist? How would society operate on a planet of this magnitude if we assume that the planet is habitable, has a gravity of 1g and the same land to water ratio as Earth?
What kind of methods of communication could exist and how would travel/transportation work?
Science
Since the dimensions are so huge, it is pretty much impossible that their society will realize they are actually sitting on a planet (instead of a huge, endless flat plane) until they have a comparable tech-level as today. Also see this question, about how a civilization would find out they are on a dyson sphere, the accepted answer about a 3AU dyson sphere. Your 1LY planet is still about 20000 times greater than the dyson sphere, but the similarities apply.
Compared to that, we on the other hand have already discovered that the earth is round in ancient Greek times -- we've known it for more than 2000 years. And we have known that we (earth) are not the center of the universe for more than 400 years. Meaning: your 1LY civilizations will have very... planet-centered religions, since they can't really imagine they are just one object amongst many in a huge cosmos (until they have reached at least 1950 technology and really great telescopes and really great scientists that can actually make sense of what the telescopes are telling them). Also, another hardship is that the physics (where the heck does a sun/moon come from on such a huge planet) must follow such complicated rules that we today can't even imagine them -- meaning their astronomy and exploration of the cosmos will be very, very delayed. Following from that will be, that a lot of technologies that have been developed for such cosmos explorations (first thing: space travel and sattelites) will get delayed a LOT.
Travel
Travel, on the other hand, should develop completely normally up to planes and other travel by air. However, space travel won't make a lot of sense until they are capable of bridging interstellar distances within a reasonable time.
The important step (where we currently are, trying to jump from orbit distances to interplanetary distances) will be pretty much useless to them, since they could just bridge the distance a lot easier in an airplane (at least you can land in the airplane, don't have to worry about exposure to cosmic radiation, no zero-G problems, etc.). If you compare the distance Earth-Mars (50-100 million kilometers when they are closest, let's say 1e8 km) to your 1LY planetary radius (ca. 1e13 km), you get that the radius is about 100,000 times greater than the measly Earth-Mars distance. That would be like traveling a couple hundred meters on earth. So, no, they really do not have any incentive of developing interplanetary-distance space flight for travel purposes -- they'd need to go for full interstellar right away.
You might see a need for interplanetary space travel though if you've got some strange objects orbiting your planet (like suns to make it light, for example?)
Communication
Planet-wide communication has the same problem as planet-wide travel: you need to be able to bridge interstellar distances within a reasonable amount of time. Because waiting for an answer for an entire (earth) year is not reasonable. So you need FTL technology -- and until you develop that, you've got isolated states/empires/... that can't really talk with each other, just like it was on earth before the invention of the telegraph. Travelers bringing news, hear-say of far-off countries, etc.
If you've got, for example, a desert on your 1LY planet that takes the same procentual space as the Sahara does on earth, it will be a completely insurmountable obstacle for hear-say communication spread with travel. Same with oceans if you just blow Earth geographics up to 1LY -- even a comparatively small ocean like the Caspian Sea will span distances from here to Pluto, not to mention the Atlantic or, worse, the Pacific. Oceans cannot be bridged in those dimensions. So, you would need two civilizations on both sides of the ocean who develop radio communication at approximately similar times, so that they can receive the radio waves from the other and realize: oh, there must be something beyond the Great Waters.
Ecology and Evolution
When considering such huge distances, you might get life evolving sentience in several places at once -- and in various different forms. Same for plant-life -- it might be a lot more diverse than we have on earth. Just travel a couple of AU (=distance earth-Sun), and you've got dinosaurs roaming the ground. Another couple AU later, you might have huge mammals like Mammoths and Sabertooth Tigers. Another couple AU later, insects might be the top of the food pyramid. And once you've gone another couple AUs, let's say, 60 AUs in total, you have still only covered a distance that would be around 12km on earth. Not even the stars will look different from there.
Planet-wide extinction events will be absolutely impossible, only local-sized.
Societies
Despite a technology level that might surpass us, they will be isolated societies comparable to countries in Midieval times. Yes, there will be trade amongst neighboring empires/states, and there will be ones who trade with countries even further away. But knowledge of all civilizations that exist around the globe (heck, even a rough map of the globe) will be pretty much impossible until technology for interstellar travel has been found.
The escape velocity of this world is 10% of lightspeed.
Space will be limited to sounding rockets until they develop technologies way beyond anything we can envision. Furthermore, putting something in orbit gains you very little because the craft rapidly departs, not to be seen again for many decades.
Astronomy will be pretty much limited to locating objects until the development of general relativity--until you know how (and that you even need to) to correct for the gravity well you're in no observations of the sky will match observations on the surface.
Beyond this, the inhabitants won't be very ecologically minded. Pollution that blows away from you due to the prevailing winds never comes back.
Number of Human Civilizations : Many, many orders of magnitude more than on Earth. Emigration from existing civilizations would be quite common as there is, almost literally, limitless free space to spread out.
I will assume stockpiles of metals and other resources are available because technology would regress to stone-age level at locations not receiving imports from off-planet.
Given modern tech, you could have large countries, but these will be limited to relatively near-by land. Civilizations located at different points on this planet will likely not have any interaction.
How would society operate? By splitting into many, many, many different societies. The distance is too great for a single society to maintain any coherency.
Communication Communication will largely be by existing methods. Civilizations far enough apart will not have much communication. Unless there are radio stations set up inside the planet to facilitate communication, direct communication will be impossible for those over the horizon from each other. Even with communication, the time-delay would be horrible.
Travel Largely the same. Sub-orbital flights might become a thing, given a large enough incentive to need to travel far enough for the expense to be worth it. If internal "spacedocks" or "airports" are available, traveling through the interior will be a more direct line for far off locations. This travel will be quite lengthy however.
Additionally Most of these assumptions depend on the humans on the planet being seeded by the civilization that built the planet, rather than being the civilization that built the planet. If they are that civilization, or have access to its toys (FTL travel or communication, endless energy, etc) then basically the answers become "Whatever you want".
Quite honestly it all depends on the speed of travel.
If they have only cars and planes then @Michael has the right answer. However it is only possible to expand great empires if you have great transportation. Take an example from history. "All roads lead to Rome" Rome literally built myriads of roads and pathways. This enabled them to travel safely and efficiently across their gigantic empire.
The Romans made transportation fast, and available to everyone. Do this and you will conquer the world.
The culture of the world conquering super country will be one that values roads and values conquest.
First of all. Let me make some basic assumptions. I will assume your world will consist of mostly ocean. I will also assume that there are many continents roughly the same size that we have on earth. That will mean an awefull lot of continents. Furthermore I will assume that your humans evolved on this world.
Evolution One light year means that on with a speed of 1km/h one would need 1 billion years to cross the planet. With this speed a species that reaches the other side of the world would have evolved into something completelly different by that time. This speed would also mean that even if we assume life starts at one place by one billion years life would be everywhere.
Probably live would move to each continent separately, but nearby continent would influence one another.
Intelligence Intelligent life could evolve on many of these continent. But it would still be unlikely for two species to evolve to intelligence at exactly the same time on neighbouring continents.
Looking at human evolution it appears that we could not cross any oceans until quite late in our evolution. The americas where only settled 40000 years ago. That means that for most of its evolution sentient life will be bound to only a few continents.
Only after devoloping ships will people discover the other islands. Note that by that time the people will propably already have developed an advanced culture.
From there a culture can spread across the rest of the world at a relative slow speed. In our society it took only a few centuries from there to developing modern communication technology.
Effects This would mean that each civilization has a mother continent from where it originates. Politically people further away will become independent from their mother continent. However it would be unlikelly for them to lose all communication with their mother continent.
Some information of general interest (scientific for instance) could well spread very wide, but a lot of information will probably be only of local interest and people on other continent would not be interested in them.
