A concept similar to this was done in L. Ron Hubbard’s classic science fiction novel, Battlefield Earth. It does, however, require some sort of instantaneous FTL transport.

The theory behind this is that the image of an event travels outward in an ever-expanding sphere at the speed of light. If you were to position a lens at the appropriate distance (e.g., one light-year to see one year into the past), you would be able to view details of what happened in the past. The lens would need to have a significant amount of reduction, because the surface area of the expanding sphere is huge.

In Battlefield Earth, to discover what happened to the Psychlo homeworld, Johnny and his friends teleport a probe into space at an appropriate distance from the Psychlo world and create a huge gravitational lens to reduce the images. This allows them to see that the planet blew up.

Since we do not have the ability to travel faster than light, however, I don’t see how we on earth could view our own past unless the light was somehow bounced back to us. Even then, we do not currently have the ability to pick up details, because our lenses are too small.

Note that the novel Battlefield Earth is much, much better than the movie by the same name.

Regarding point 2, and I’m talking off the cuff here, it seems that in a truly infinite universe (assuming infinite mass as well), the probability of light being deflected back to us through a complex set of gravitational interactions would approach 1 (to such an extent as to be indistinguishable from 1). Naturally, we most likely would not recognize such a reflection as it would be both much older and quite distored. Also, it could take an arbitrarily large amount of time before this happened, so this ignores the possibility of a big crunch or a cold death, so this is purely hypothetical.

After writing this, I suddenly remembered Olber’s paradox, and although there are proposed solutions for it in the electromagnetic spectrum (without eliminating the infinite mass proposition), I have not seen one that could handle gravitons or even neutrinos. (An infinite barrage of neutrinos, even though they interact very weakly, would be a problem.)

Assuming that the earth was created about, what, 6 billion years ago, we could only see an image of our own region of space if the universe were only 6 billion light years in diameter. So, all this talk of wrapping universes only works in a universe smaller than ours or on a planet older than ours.

The whole bending light thing would be a little more possible but again, the light can only have travelled 6 billion lyrs putting a huge contraint on the given system.

So, it may not be possible to see an image of solar system, planet or otherwise, in a 6 billion year old universe.

The current state of our galaxy never existed before so you cannot see our galaxy repeated. Even if by space-loops or the curvature of light you would be able to see our galaxy by some enormous telescope, you would most likely not recognize it because it would look completely different.

It would look like it did when the light from it started to travel, millions to billions of years ago.

We would not recognize it.