Why the dark energy density is inversely proportional to the surface area of the volume studied?

Sabine Hossenfelder commented in her posting "Surprise Comeback: Dark Energy Could Be Holographic After All" (see this) the idea that the mysterious dark energy might not be real but an outcome of holography and assignable to the 3-D surface which in holography contains the information determining the dynamic in the interior of the space-time. The comments were inspired the the article "Evolution of perturbations in the model of Tallis holographic dark energy" (see this) by Artyom et al.

The starting point observation is that the dark energy density is in a good approximation found to be proportional to 1/S, where S is the surface area of a large sphere surrounding the region studied. By the way, Sabine makes a little mistake here: she talks about dark energy rather than dark energy density. The reader can check this from the article of Artyom et al. The model of Tallis has been given up long ago but the authors represent an argument that since dark energy is not ordinary cosmic fluid, ordinary perturbation theoretic analysis does not apply.

TGD suggests however a much simpler explanation of the finding. In TGD, dark energy is identifiable as a galactic dark matter and consists of magnetic and volume energy assignable to very long monopole flux tubes with a huge string tension. No galactic dark matter halo nor exotic dark matter particles are needed. The galactic velocity spectrum is correctly predicted from the string tension which is also predicted.

To see whether TGD can explain the finding that dark energy density is proportional to 1/S, one must estimate the average density of dark energy in a large cylindrical volume around a long cosmic string. The dark energy is proportional to the length L of the string. The volume is roughly V=SL, where S, is the surface area of the cross section of the cylinder. Therefore one has that dark energy density satisfied E/V= E/SL= 1/S. Just as has been found.

For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.