# cosmological constant problem

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Posted (edited)

hello

what do you think of this interpretation please ?

It is sufficient to calculate the dark energy density parameter ΩΛ at Planck time, origin of our universe :

ΩΛ= Λ c2 / ( 3 H2 ). Source : Page 4

ΩΛ,tp = 1/3 Λ c2 tp2

with tH = 1/H,

where tH is Hubble time and H is Hubble constant

The vacuum catastrophe = Λ / lp-2 = Λ lp2

as

lp = c tp

lp2 = c2 tp2

The vacuum catastrophe = Λ c2 tp2

The vacuum catastrophe = 3 ΩΛ,tp

Conclusion

The vacuum catastrophe would be the energy density parameter of cosmological constant at Planck time in the ΛCDM model with a factor of 3 (and with a divisor of 8 pi if we express the problem in J/m³ instead of m-2) , and it would no longer be a problem.

For the value lp-2 = 3,83 * 1069 m-2 from the QFT
Lucas Lombriser, université de Genève, communiqué de presse ,
https://www.unige.ch/communication/communiques/2019/cosmologie-une-solution-a-la-pire-prediction-en-physique

Edited by stephaneww
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The Lambda-CDM model is a model based on classical General Relativity, so it only describes the evolution of spacetime after the inflationary epoch. You cannot extend it further back than that.

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Posted (edited)

um, cosmic inflation is more than speculative

I have a very simple cosmological model that allows to calculate the total mass of the universe since Planck's time until today, and that is consistent with the Lambda-CDM model. It does without the inflation theory even if it knows a close phenomenon in its young age.

M (total,universe)= 1/2 mp/tp * tH * ( Observational universe radius / Hubble radius)3

tH = Hubble time

mp : Planck mass

tp : Planck time

edit : to have an exact value, I use Λ = 1.10241 10-52 m-2

 edit 2 : we don't need Λ
Edited by stephaneww
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Posted (edited)
1 hour ago, stephaneww said:

um, cosmic inflation is more than speculative

True, it is, at least in some sense. But even if you disregard inflation completely, you can only extend the Lambda-CDM model as far back as ~10^(-32)s or so - and you’d struggle to explain the large-structure of the universe without inflation. But under no circumstances can you extend it to the Planck epoch, that’s outside its domain of applicability, since GR is a purely classical model.

Edited by Markus Hanke
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Posted (edited)

I don't take inflation as completely useless. It solves a lot of problems

My extension of the Lambda-CDM model, going back to Planck time, would be just virtual to provide an interpretation to the cosmological constant problem. (I hear your argument: the theory says it doesn't work, we can't go back that far in time in GR)

Note: One needs to set a value to Lambda (but you don't need to take mine) to have the radius of the observable universe for my toy cosmological model. A thousand apologies.

Edited by stephaneww
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It’s quite alright to ponder these issues. That’s how understanding is made.

But here’s another thing - in the GR field equations, Lambda is not directly identified with any kind of energy. Regardless of which side of the equation you choose to put it, what happens is that, in vacuum, it stops the Einstein tensor from being zero. The physical meaning of this tensor is that, once a future time direction is chosen, it gives the average of scalar curvature in the spatial directions. This means that, taken at face value, Lambda is best understood as a background curvature that is always present, even in the absence of all gravitational sources. It’s purely a geometric entity that modifies the global geometry of the manifold.

Identifying this background curvature with Dark Energy is one possible hypothesis - but there’s no principle that requires us to posit this. There are other options.

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Posted (edited)
6 hours ago, Markus Hanke said:

But here’s another thing - in the GR field equations, Lambda is not directly identified with any kind of energy. Regardless of which side of the equation you choose to put it, what happens is that, in vacuum, it stops the Einstein tensor from being zero. The physical meaning of this tensor is that, once a future time direction is chosen, it gives the average of scalar curvature in the spatial directions. This means that, taken at face value, Lambda is best understood as a background curvature that is always present, even in the absence of all gravitational sources. It’s purely a geometric entity that modifies the global geometry of the manifold.

um, I don't understand theses arguments. The problem cames from me.

On 10/8/2021 at 2:45 AM, Markus Hanke said:

... But under no circumstances can you extend it to the Planck epoch, that’s outside its domain of applicability, since GR is a purely classical model.

My toy cosmological model may also explain the large-structure of the universe and other problems solved by inflation (I am not sure) and has the advantage of being compatible (I think) with the Lamda-CDM model up to Planck time.

Edited by stephaneww
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hello

I add a more complete pdf on this question of Planck mass flow following the arxiv article: https://arxiv.org/pdf/2109.11953.pdf
"Essay written for the Gravity Research Foundation 2021 Awards for Essays on Gravitation

by Bruno Valeixo Bento and Stav Zalel

for the role of time in the evolution of universes

reminder you must be logged in to read the PDF

Edited by stephaneww

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