>Why? They're building ships larger than Earth and space is huge and full of resources, the only possible reason for them to give our planet a second glance is for us and maybe to study life in general

Could be our planet is so small they're not even giving it a first glance... Like forestry machinery driving over an anthill to get to the area they are going to log. Using our sun for fuel before continuing on their merry way etc...

Earth is puny. But... Our Sun might be useful.

There are unique things about our Sun. It's an energy dense mid-sequence star, in a galaxy mostly comprised of red giants. Also, it's in the center of a fairly empty region of space: https://www.google.com/amp/s/www.sciencealert.com/the-solar-system-floats-in-a-void-now-we-know-how-that-void-triggered-the-formation-of-stars/amp

If some aliens decided that our star is good for refueling or for settling a colony (or both) we'd be toast.

To achieve any fraction of the speed of light, you'll need a ton of energy. And, due to time-dilation, it's a one-way trip. If aliens decide to swing by us, it can only mean so many things...

They’ll probably destroy earth to make room for a new space highway.

Maybe they have a policy of eliminating sentient life before it can become a threat.

Maybe they just like hunting undeveloped species in exotic locations.

Maybe the humanoid form is considered blasphemy against their deity?

If we do encounter an alien civilisation, I really hope they have good bioethics, or at least trivially care about us. But yeah, it’s scary a single individual can react so much differently. I sometimes rescue worms from footpaths, but the next person might step on them for fun. I’m a bit worried aliens could be like this, though I’m a bit optimistic in that I think they’ll engineer their own niceness into them.

Fast forward 8 billion years. Earth heroically united to survive humanities existential crisis. Technology progressed until humans are cyborg gods. We are a many planet, post scarcity civilization.

A few million light years from earth, there is a galactic zoo planet called “Burf.” Burf was formed by humanity a couple billion years ago, as a sort of nature retreat. It was set to a nice temperature, seeded with some basic life, and left to sprout.

Burf is a wonderful planet. Life forms like to warp in, and work remote from its many beautiful vantage points. They watch waterfalls, and arctic storms. Float above the primitive ape cities, and casually follow their emerging stories.

Of course, we keep an eye on the apes to see if they will pass the great filter. After all, we don’t want to rescue a malevolent dying race and start an intergalactic war. Again.

If the primitive apes can realize that they are all stuck on the same lifeboat and come together for future generations, we will happily accept them into the galactic fold. If they succumb to violence and greed, we will let nature take its course, and perhaps help Burf recover from whatever stain they leave behind.

Sometimes our kind interacts with the apes. Frequently, it’s by accident, by getting too close. Sometimes, it is avid fans of the Ape Story, deliberately interjecting themselves to warn the apes that they’ll go extinct if they aren’t careful, or floating above their nuclear weapons, shining a bright red light on them to say “this is a bad idea.”

We’ve even had a few accidents out around Not Vegas involving intoxicants and bright neon lights. But we are not supposed to interfere, and to let the great filter do it’s work on Burf.

Masking a mothership might be an issue, especially on the scale discussed here.

The equations for reaching a fraction of the speed of light are fairly simple (specifically, without considering warp-drive techniques). Building a working system is undoubtedly complex, but it's chiefly a game of attaining the required energy.

Cloaking a large stellar object so that it's invisible is a much more difficult task. There still might be ways, but spacetime should see clear warping at the given masses and velocities.

Well, if LIGO is detecting it, I’m not sure how they could hide. That would imply their warp drive created gravitational waves / ripples in the fabric of spacetime

That's very similar to what I say, why would they have to mutilate cattle and anally probe people? If they can get here they can probably tell everything they need to from orbit. The don't need to stick something up our ass or mutilate some helpless animals.