Undergrad Why Is the Planck Scale a Limit in Cosmological Constant Calculations?

[exponent137]

For instance, in introduction in https://www.sciencedirect.com/science/article/pii/S0550321314001400 we can find that vacuum energy is proportional to $k_{max}^4$ where it is written that "If we believe the general relativity up to the Planck scale $k_{max}=10^{19}GeV$"

And so the cosmological constant is calculated. The question here is why Planck scale is limitation in this calculation. (It is not my question here why such disagreement $10^{120}$ between measurement and calculation exists.)

 

[mfb]

We know new physics has to happen the latest at this point - this new physics could introduce additional contributions, but they should in general be at least of the same order of magnitude as the contribution up to this point, unless some unknown feature makes the overall contribution very small.

 

[exponent137]

Yes, this would be a new theory, but I am interested, why it is chosen in this calculation that $k_{max}=$ Planck energy? It is written in some links that this is a simple calculation.

 

[PeterDonis]

why it is chosen in this calculation that $k_{max}=$ Planck energy?

Because that is our current best guess as to the energy scale at which GR breaks down, and therefore the energy scale at which we would expect such a calculation to be cut off.

 

[exponent137]

1. Can the Lamb shift be a parallel pedagogical example: https://en.wikipedia.org/wiki/Lamb_shift?
The integral of excitations of vacuum is calculated between Bohr length and Compton wavelength. (Compton wavelength is in connection with the mass of the electron.)

2. In your example minimal possible black hole mass is one cut off, as said with different words? Another cut off is zero energy?

3. Can your sentence (best guess as to the energy scale at which GR breaks down) be written more precisely:
"best guess as to the energy scale at which quantum mechanics breaks down, because of an existence of quantum gravity, because the energy scale at which GR breaks down"? If I understand you correctly?

 

[mfb]

1. Can the Lamb shift be a parallel pedagogical example: https://en.wikipedia.org/wiki/Lamb_shift?

I don't think so.

2. In your example minimal possible black hole mass is one cut off, as said with different words? Another cut off is zero energy?

It is expected that the smallest possible black hole has a mass of the order of a Planck mass. This is not the cut-off discussed before.

"best guess as to the energy scale at which quantum mechanics breaks down, because of an existence of quantum gravity, because the energy scale at which GR breaks down"

No. What you wrote doesn't make sense.

 

[haushofer]

What this calculation basically says, is that you expect a UV (ultraviolet)-divergence if you introduce the cosmological constant. Which is a bit weird, because the cosmological constant is a term which only plays a role at very large distances, hence in the IR (infrared). I guess that is the important message to take home from this calculation: usually in QFT's we can separate the IR from the UV, such that we can "integrate out" phenomena appearing at higher energy scales and we obtain effective field theories. The cosmological constant seems to contradict this paradigm.

 

[George Jones]

For instance, in introduction in https://www.sciencedirect.com/science/article/pii/S0550321314001400 we can find that vacuum energy is proportional to $k_{max}^4$ where it is written that "If we believe the general relativity up to the Planck scale $k_{max}=10^{19}GeV$"

And so the cosmological constant is calculated. The question here is why Planck scale is limitation in this calculation. (It is not my question here why such disagreement $10^{120}$ between measurement and calculation exists.)

See this blog post by Sabine Hossenfelder,

http://backreaction.blogspot.ca/2017/12/the-cosmological-constant-is-not-worst.html

Point 4. in the above post references the interesting technical review "Everything You Always Wanted To Know About The Cosmological Constant Problem (But Were Afraid To Ask)" by Jerome Martin,

http://arxiv.org/abs/1205.3365

See also the interesting exchange between Hossenfelder and Don Lincoln in the comments section of the blog post.

 

[exponent137]

George
I will read your links, this is what I need. But I will need some time because they are long. Can you please focus me, where it is written about the problem mentioned, ie, why the calculation uses $k_{max}=$Planck energy, ie, why calculation is cut off at Planck energy.

Thanks also to others.

 

[Vanadium 50]

If George types in all the information in those links, why do you think it will be any less long?

 

[exponent137]

I read your arXiv paper and also https://arxiv.org/pdf/1105.6296.pdf.
In page 3 above eq. (12) in https://arxiv.org/pdf/1105.6296.pdf, it is written how they estimated renormalisation scale $\mu$. I do not understand their logic.
For instance:
1. "these photons couple to the metric", why, how, why this is important, etc?
2. Why gravitons energy is used?
3. Why it is connected to the Hubble parameter?
etc.

p.s. But I understand mainly why $M_{pl}^4$ is not appropriate, thus they introduce formula (12) or (11).