You have observed that objects tend conserve energy.

Objects inside the cosmological horizon are the ones I observe tend to conserve energy.

Yes, exactly.

You have also observed that the cosmological horizon isn't absolute, but is in fact centered on you.

I think you said this backwards, or else I don't know what you mean by saying the horizon is centered on me.

The cosmological horizon is defined in terms of a distance from a given observer. It is the distance beyond which you cannot observe anything, due to the expansion of the universe.

You have also observed that time is symmetric (charge and parity flipped).

I don't know what you mean by this.

If you run the universe backwards, flipping all charges (positive to negative and vice versa) and parity (like a mirror image of the universe, I think) then the laws of physics, as we know them, remain unchanged at the atomic level. (Don't ask about all those eggs suddenly unscrambling in this reversed universe).

You have observed that a model of the universe without any absolute coordinates is more likely.

Your terminology is unfamiliar to me.

This is one of the foundational assumptions of relativity - that there is no absolute rest frame. That a set of coordinates using any one non-accelerating object as the origin is just as useful as the set of coordinates using any other non-accelerating object as the origin; you can use the same equations to describe the universe, regardless of the velocity of the origin. (Note that the acceleration of the origin still has an effect). For argument in support of this point, I recommend "On The Electrodynamics of Moving Bodies" by A. Einstein (it's more readable than most people think).

Thus we induce that were you put on a spaceship, you would never cross the cosmological horizon, from your own point of view.

I'm uncertain how we induce this from the previous statements.

• Accelerate the spaceship to near-lightspeed, then shut off the engines and coast along
• Define a reference frame using the (now non-accelerating) spaceship as the origin. The spaceship thus remains at the origin - it does not move. (Note that in this reference frame, the Earth is moving backwards at pretty close to the speed of light).
• Recall that the cosmological horizon is defined in terms of a distance from yourself. In this newly defined reference frame, it is not moving. Nor is your spaceship.
• Hence, the spaceship will never cross your cosmological horizon (though it will eventually cross Earth's cosmological horizon)

Similarly it is very likely that some other person would have the same experiences.

I can't agree to this statement until I understand the ones previous to it.

Quite. I hope this helps.