Hornblower, first problem is you need an Alcubierre drive

Possibly.  Is it clear what requires the least amount of energy, to create and sustain the warp, or to create the mass required to create the gravity the ordinary way?

A warp drive would take up the most energy by far. The conventional way is just spinning up a ring, and keep in mind, once you get it spinning, you don't have to add any more energy.

once you get it spinning, you don't have to add any more energy.

Since friction cannot be absolute zero, you still need a little energy to keep it rotating. Also consider that it makes orbital maneuvering and rotation a little more complex because of the sum of the various forces inside it, so eventually they would decide to stop it when they need to do precise maneuvers, I think, so more energy.
But except this, to have "artificial gravity" you need to have a force that applies to your whole body equally. Otherwise why not using a grid of small holes on the top that pushes you on the bottom? It would be a little uncomfortable, just like having a big spring attached to the bottom, and it wouldn't work as gravity, because the force would be applied to the surface of your body and not your body itself. And, with this said, what Watsisname says is correct because it doesn't apply an actual "force", so you need to compensate it with thrust. The problem here is to find a way that applies "conventional" force without requiring a very big ring (it's difficult to launch because of its mass), unfortunately we don't know any other...

As for comparing energy requirements, I think this could be an apples and oranges kind of thing.  Sure, we can speak of the total mass-energy for each method, but since the mass-energy to produce a warp bubble must be of an exotic form which probably can't exist, the most accurate description might be to say that the cost is infinite.

There's something to be said for the fact that using electrical energy or reaction mass to accelerate or spin up a ship for artificial gravity is conceptually simple and doable with current technology.  And it would be neat in a conceptual way if we could show that artificial gravity could be achieved by some modified form of warp, but sadly I don't think it does.

the most accurate description might be to say that the cost is infinite.

That is true normally but you can use rough estimations, like required energy for setting up conditions of weak energy and extrapolate energy costs from there.  I have done that a bit in the past and every time it is insanely high amounts of real tangible energy for minuscule amounts of "weak" or "negative" energy.

An 11 billion year old star with 5 rocky planets around it, found by transit method. That seems extremely odd since heavier elements were in shorter supply that long ago. That long ago there was only about 10% of the amount of heavier elements as when the Earth was formed. It seems strange to me that that many rocky worlds would develop rather than gas giants. Plus it was 1000 degrees warmer back then. Fourteen per cent of the intergalactic gas was helium 12 billion years ago, absorbing the intense radiation from active galaxies, losing electrons in the process until it was ionized completely, and since it had no more electrons to lose, the radiation simply passed through the gas without heating it. At this point the cooling effect of expansion took over.

Yeah, that's pretty old, and if you asked planetary scientists a decade or two ago most would have doubted terrestrial planets could have commonly formed that early.  But data are data, and we're seeing that this actually does happen at least some of the time.

We're also seeing that there doesn't seem to be a very strong dependence on terrestrial planet frequency with star metallicity, although there is a strong dependence for giants.  What this tells us is probably that the dominant mechanism for giant formation is core accretion, and in the early universe the core accretion was less likely to build embryos large enough (or quickly enough) to become giants.  So it might make some sense to see old terrestrial planets as "failed giants".

Plus it was 1000 degrees warmer back then.  Fourteen per cent of the intergalactic gas was helium 12 billion years ago, absorbing the intense radiation from active galaxies, losing electrons in the process until it was ionized completely, and since it had no more electrons to lose, the radiation simply passed through the gas without heating it. At this point the cooling effect of expansion took over.

Whoa, hold on.  We can't just say that it was hotter -- it depends on the context.  The temperature of the intergalactic medium is very different from the temperature of everything else, similar to how the temperature of the Sun's corona is orders of magnitude hotter than the temperature of the surface.  The density matters, and the mechanism by which heating (and cooling) occurs.

In the context of planet formation, we should look at the ISM temperatures.  While it's easy to heat diffuse gas by photoionization, it's not so easy to heat a dusty interstellar medium or molecular cloud.  11 billion years ago corresponds to a cosmic redshift of z~2.5, and we see that the ISM back then was typically quite cool -- tens of Kelvins.  Plenty cool enough for star and planet formation.

I imagine too that if I was in the middle of a million degree cloud of gas I wouldn't even feel the heat since so few atoms actually hit me, while a planet might warm up only a smidgen

Pretty much.  It's kind of like how the temperature in Earth's atmosphere hundreds of km up (like where the ISS orbits) can be around 1000K, yet it doesn't cause any problem to the station or an astronaut in orbit.  And the intergalactic medium is even more diffuse than that.


On an unrelated note, I've had quantum tunneling on my brain again, and I would like to pose a question for everyone, for fun:

As mentioned earlier, particles can quantum mechanically "teleport" across gaps that, classically, they should not be able to cross.  Like a ball which is rolled towards a hill much too tall for it to possibly get over, and yet the ball makes it to the other side anyway, as if the hill wasn't even there.

Suppose you want to visit Saturn (and who wouldn't?).  Unfortunately, you do not have a rocket, or a space ship, or a mythical wormhole.  But you don't let that get you down.  You do have a spacesuit, and a lunchbox packed and ready to go.  And you can jump!  You're in excellent physical shape and can vertically jump with an impressive max speed of about 4 m/s!  

What is the probability that you can quantum jump to Saturn? 

(Internet cookie to whoever gets closest).

1x10^-70? 

What is the probability that you can quantum jump to Saturn? 

Slightly larger than the probability that Saturn can quantum jump to you?

1x10^-70? 

More like 10^-10^10

midtskogen, lol, wouldn't that be absurd?

The probability is small, no doubt about it.  But what number is so small as to match the absurdity of it?  Is 1 in 10⁷⁰ enough?  That's thirty powers of 10 from a googol, and ten powers of 10 from the number of protons in the universe!

Edit:  Ninja'd by FFT, who raised the ante a lot!

Probability you will pop out of existence here on Earth with your suit and lunch pail and appear somewhere in orbit around Saturn:
Possible equations to use:

[tex]P_T(E)=\frac{1}{{1}\ +\frac{V_0^2}{4E\left(V_0-E\right)}\sinh^2(2\kappa a)}[/tex]
or
[tex]T=[1+\frac{V_{0}^{2}}{4E(V_{0}-E)}sinh^{2}(\frac{2a}{\hbar}\sqrt{2m(V_{0}-E)}]^{-1}[/tex]

T being the transmission probability for tunneling. We need to know the potential energy of the distance between us and Saturn in Joules. You will need all the electrons in your mass to line up just right, so the wave number of all your electrons must be calculated using Schrodinger equation which is the square root portion of the equation above. Velocity is included because if you measure a particle's momentum, there is a larger spread of possible positions it could have, so you must have kinetic energy. Your mass (m) must be known, as well as the distance (a) you wish to travel. h is Plank's Constant divided by 2*pi (approximately 1.06x10-34 J*s). Fourier series and Fourier transforms might be needed too, because of the uncertainty principle.

Simplified for a 50kg person, traveling a distance that is a 30 joule potential barrier and with 25 joules of kinetic energy.
[tex]P= e(-2((sqrt(100(30-25)))/1.06x10-34)(1))[/tex]

Chances are better you will win every lottery played anywhere on Earth every single time for the rest of your life. Still not zero, but hey, it happened to Ford Perfect when he appeared aboard the Heart of Gold, so it might happen to you!