crazunggoy47 OP t1_jajwm2d wrote on March 1, 2023 at 11:22 PM

Reply to comment by Any-Broccoli-3911 in Why do cosmologists say that gravity should "slow down" the expansion of the universe? by crazunggoy47

>The expansion of the universe is kinetic energy. [...] Also, the observed speed is always less than the speed of light, so everything has a finite energy.

Is that true? I thought that for distant galaxies, the recessional speed was often greater than c, since c is only a local speed limit, and does not apply to space time inflation.

Consider the rapid inflation of the universe, which went from electron-sized to golf-ball sized in 10–35 seconds; applying a naïve speed calculation would yield speed = distance / time = 43 mm / 10^(–35) seconds >>>>>> 3 x 10^(–8) m/s.

This is all to say, I'm mostly questioning whether the perceived recessional velocity can really correspond to kinetic energy.

Aseyhe t1_jakbf7x wrote on March 2, 2023 at 1:10 AM

Relative velocities of distant objects aren't well defined in curved spacetimes. It's often said that distant objects are receding faster than light, and there are standard ways of writing down their distance such that the distance grows faster than the speed of light. However, there is no relativistically meaningful sense in which these objects are moving faster than light in relation to us. Also, the distance isn't uniquely defined either.

In intuitive terms, the relative velocity is the angle between two vectors in spacetime. Imagine drawing two arrows on a sheet. If those arrows are in the same place, you can measure the angle between them. If they are in different places, but the sheet is flat, you can also define the angle between them uniquely. However, if they are in different places and the sheet is not flat, the angle between the arrows is not uniquely defined.

Any-Broccoli-3911 t1_jajx0tj wrote on March 1, 2023 at 11:24 PM

The observed speed is always less than c.

The comoving speed is not limited. If you consider ont special relativity, it's equal to gamma*v so as v goes towards c, the comoving speed goes to infinity. Even with general relativity, it's still true that the comoving speed goes to infinity as the observed speed goes to c.

gamma is the Lorentz factor 1/sqrt(1-v2/c2)

crazunggoy47 OP t1_jajyba4 wrote on March 1, 2023 at 11:34 PM

Hmm. So if I understand you correctly, you're saying that an object that's moving away from us due to cosmic expansion has a finite kinetic energy (relative to us). So, from our perspective we should "expect" that kinetic energy to be falling, as our own gravity pulls them back in.

And then that galaxy, will also see the exact same thing. From its perspective every other galaxy is fleeing *it*. And if every galaxy sees this, and it just so happens that every trajectory has too little KE, then every galaxy would see the other galaxies crashing down on them.

Is that right?

Any-Broccoli-3911 t1_jajymds wrote on March 1, 2023 at 11:36 PM

Yes, though the galaxies that are outside the local group have enough energy not to crash into us even if we don't consider dark energy which will push them away even faster. Without dark energy, they would decelerate relative to us, but still always going away.