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Ok so this is my thought process... please bear with me

I understand that as the universe expands, there is supposed formation of matter due to dark energy,and with an increase in mass comes and increase in overall gravitational potential energy in the universe as a whole.

That being said isn't the rate of gravitational potential increase equal to the rate of universal expansion where this energy might be converted to the kinetic energy for this expansion? With these two cancelling each other out, what would remain is the distance between universal bodies of great mass increasing, which should reduce the gravitational potential energies between them, reducing the total GPE of the universe as it expands.

Is this confusion due to the input of energy into the closed system that is our universe or am i just thinking about it the wrong way?

Jack Jones
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    Dark energy does not create matter. – G. Smith Jun 30 '19 at 17:20
  • Potential energy between to gravitational objects means that it is possible to convert it to kinetic energy: Water in a high reservoir in the mountains moves turbines as it looses potential energy. An expanding universe of gravitational objects transforms kinetic energy into potential energy: one all kinetic energy is tranformed, it will start back attracted by each other's gravity to transform potential energy to kinetic energy ( one possible cosmological model) – anna v Jun 30 '19 at 17:44
  • @G.Smith "Dark energy does not create matter" - Are you sure? Dark energy is repulsive thus increasing velocities and therefore increasing kinetic energy that can be used to create particle pairs. Also, according to Einstein (in natural units): $E=m$ meaning energy is matter. E.g. are photons "matter" or "energy"? How about massless gluons, which account for 99% of the baryonic mass? Thus, if "dark energy does not create matter", then dark energy is not energy. – safesphere Jun 30 '19 at 18:39
  • Energy is a product of force and distance. In General Relativity, gravity is not a force. Therefore there is no potential energy. When things fall down where time moves slower, their kinetic energy increases, because, according to the Noether theorem, energy is not conserved in non-uniform time. However, the fact that this process is reversible allows us to introduce a concept of "potential energy" that makes calculations easier at the expense of violating the Noether theorem. – safesphere Jun 30 '19 at 18:52
  • @annav Thanks for this, i was trying to see if the question could be approached irrespective of General Relativity, while only using the logic of the PE, KE relation at the cosmological scale. The attraction you speak of would indeed cause acceleration due to gravity between bodies as they move in new orbits – Jack Jones Jul 01 '19 at 08:08

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I am not particularly familiar with Cosmology. I'm sure others can answer your questions much better, but here are a few of my thoughts that don't take into account dark matter and dark energy.

I understand that as the universe expands, there is supposed formation of matter due to dark energy,and with an increase in mass comes and increase in overall gravitational potential energy in the universe as a whole.

Gravitational potential energy becomes more negative with increasing mass, and more positive (increases) with increasing separation. So to the extent that the separation of normal mass (I think they call it baryonic mass) appears to be increasing due to expansion of the universe, that alone will cause an increase in gravitational potential energy.

That being said isn't the rate of gravitational potential increase equal to the rate of universal expansion where this energy might be converted to the kinetic energy for this expansion?

For an isolated system one normally associates a decrease in potential energy with an increase in kinetic energy, not the other way around. Maybe its different in cosmology.

With these two cancelling each other out, what would remain is the distance between universal bodies of great mass increasing, which should reduce the gravitational potential energies between them, reducing the total GPE of the universe as it expands.

Like I said, we normally associate an decrease in potential energy cancelling out an increase in kinetic energy, for conservation of energy.

Is this confusion due to the input of energy into the closed system that is our universe or am i just thinking about it the wrong way?

Can't say. But maybe the confusion stems from thinking gravitational potential energy decreases with increasing separation of mass.

Hope this helps.

Bob D
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  • “Certainly gravitational potential energy increases with mass.” It’s negative, so it decreases with mass. Its magnitude increases, but you didn't mention magnitude. $U=-Gm_1m_2/r_{12}$ – G. Smith Jun 30 '19 at 17:44
  • @G.Smith I did mean with the magnitude of mass. Thanks for pointing that out. – Bob D Jun 30 '19 at 17:49
  • Mass is always positive, so I’m not talking about the sign of mass. I’m talking about the sign of gravitational potential energy. – G. Smith Jun 30 '19 at 17:51
  • @G.Smith Gravitational potential energy becomes more negative with increasing mass and becomes more positive (increases) with increasing separation. Correct? – Bob D Jun 30 '19 at 18:04
  • That’s correct. – G. Smith Jun 30 '19 at 18:05
  • @G.Smith You may not believe it but I do understand gravitational potential energy. I sometimes have difficulty with increasing and decreasing vs becoming more or less positive or negative. Maybe a form of dyslexia. Thanks for you help. – Bob D Jun 30 '19 at 18:11
  • @safesphere Like I said cosmology, nor relativity for that matter, is my forte. Anyway, thanks for the lesson. – Bob D Jun 30 '19 at 18:28
  • Thanks for the insight, that was a grand typo on my part...should've been more clear about the relationship of PE and KE, However this was quite helpful. – Jack Jones Jul 01 '19 at 07:42
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The Hamiltonian constraint of ADM general relativity is $N{\cal H} = 0$, for $N$ a lapse function and $\cal H$ the Hamitlonian. This equation tells us that in general spacetime manifold do not have any way of defining a Gaussian surface from which one can compute mass-energy. I wrote a physics stack exchange

How did the universe shift from "dark matter dominated" to "dark energy dominated"?

how to derive in a purely Newtonian fashion this Hamiltonian, without the $k/a^2$ term for $a$ the scale factor. This Hamiltonian is \begin{equation} {\cal H} = \left(\frac{\mathrm da}{\mathrm dt}\right)^2 - \frac{8\pi G\rho a^2}{3}= 0. \end{equation} This defines the Hubble parameter $H = (\dot a/a)$ that depends on the density of mass-energy $$ \left(\frac{\dot a}{a}\right)^2 = H^2 = \frac{8\pi G\rho}{3}. $$ This is a quick and easy way of deriving the Friedman-Lemaitre-Robertson-Walker equation. The constant vacuum density $\rho$ leads to the conclusion that things in a funny way gravitationally repel, or “fall up.” This is one way to think of the accelerated expansion of the universe. There is then a constant and positive vacuum energy $\rho$ which defines the cosmological constant $\Lambda = 8\pi G\rho/c^2$, where the $c^2$ comes when we consider $\rho$ energy density instead of mass density.

We first see that $\left(\frac{\dot a}{a}\right)~=~\frac{d~ln(a)}{dt}$ which easily leads to the the fact \begin{equation} a(t)~=~a_0~exp\left(t~\sqrt{\frac{8\pi G\rho}{3c^2}}\right). \end{equation} Now consider this with equation 1. This means the potential energy for a mass accelerating away from some coordinate position is decreasing and becoming more negative. However, the potential energy for any two masses separated by the same distance is the same. Two masses connected by a rod that keeps them from comoving with the expansion of space will then have the same gravitational potential. This is of course made up for by the equal amount of kinetic energy that is generated.

Lawrence B. Crowell
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  • A great answer +1. Completely accessible for the OP starting with the first sentence. from "dark matter dominated" to "dark energy dominated" (neither have been observed) plus the vacuum density $\rho$ (with no physical meaning) - a remarkable cosmological model, a triumph of modern science. – safesphere Jul 01 '19 at 03:53
  • This was extremely helpful. Correct me if i'm wrong but you came to this conclusion by changing your reference frame in the manner of general relativity. Could the same conclusion arise form The fact that KE= - PE , and so for a mass accelerating away from some coordinate position, KE is increasing so PE is becoming more negative. Since there's an equivalence, mass can be cancelled so that the potential energy for any two masses separated by the same distance is the same. And if there's no motion, the two masses connected by a rod will then have the same gravitational potential. – Jack Jones Jul 01 '19 at 09:18
  • All of this holds on the Hubble frame, which is a spatial region that has a symmetry condition. That Newton's laws works this way to me suggests the observable universe is some sort of holographic projection from a horizon in 4-space plus time region. It is amazing that plain vanilla Newtonian physics works this well. – Lawrence B. Crowell Jul 01 '19 at 21:40