special relativity - Constant $g$ acceleration from astronaut's frame of reference

When a spaceship is experiencing a constant acceleration of $10m/s^2$, the astronauts will be moving at nearly the speed of light after about a year in the earth's reference frame. This means the spaceship's energy will start to diverge as a function of the speed $v$ so there will be a huge amount of energy necessary to increase the speed of the ship any further. This way, the speed of light can never be crossed.

All of this is clear to me, but all of this is also formulated in earth's reference frame. But from the astronaut's reference frame: the spaceship is simply accelerating at $10m/s^2$ and so the force on the spaceship is constant. Then why would we need huge amounts of energy to accelerate the spaceship?

For example, I read somewhere that the amount of energy that would be needed to accelerate a large spaceship to half the speed of light is more than 2000 times the current world annual energy consumption. How does this make sense in the astronaut's (non-inertial) frame?

Answer

In the rocket, it seems that the amount of energy per unit time stays constant. When the astronauts look outside they see al the other objects in the universe move faster and faster (it seems these objects are in free fall in a homogeneous gravitational field). This means that the astronauts see the time on these objects move slower and slower.

So say, for example, that when one second has passed in the ship, half a second has passed on all the other objects. The astronauts conclude that for all these objects the spaceship uses in this case twice as much energy per unit time.

The spaceship speeds up. Then there comes a moment that the astronauts see that the time on all the other objects goes at a pace that's 1/3 of the time in the ship. So the astronauts (who still use the same amount of energy per unit time) that for all these objects the spaceship uses three times as much energy because in one unit of time on these objects three units of time are used in the spaceship.

The spaceship approaches lightspeed. The astronauts (for whom the amount of energy used per unit time still is the same) see that the pace of time on all the other objects approaches zero. This means that the astronauts conclude that for all these objects the amount of energy per unit time used in the ship approaches infinity.

Of course, it's only the spaceship that accelerates and who's (relativistic) kinetic energy is increased. Here the twin paradox springs to mind. It's the spaceship that's first accelerating. After it has stopped accelerating, the universe and the spaceship are in relative motion to each other. If we let the spaceship return to Earth then the astronauts will be much younger as the people on Earth. This is an asymmetric situation. If the whole universe accelerates towards the spaceship then the people on Earth (on arriving near the spaceship) will have the same age as the astronauts in the ship. This is a symmetric situation. But that aside.