# de Sitter versus Minkowski QFT and cosmological constant

WMAP/Planck results confirm than we live in a de Sitter-like phase, i.e., a Universe with positive acceleration or positive cosmological constant! Therefore, I believe that a way to solve the cosmological constant problem could be to extend QFT from Minkowski to de Sitter space. I would not be surprised if our "mistake" to get the theoretical "wrong" value of the cosmological constant is associated to the fact of calculating the vacuum energy in a Minkowskian QFT setting.

My question is: what are the problems that a QFT on de Sitter space faces in order to explain the observed vacuum energy? Could it work?

PS: Does someone know good references about QFT in de Sitter space?

• Minor quibble: a de Sitter universe contains no matter. Our universe may be evolving towards being approximately de Sitter in the far future, but at the moment it is not a de Sitter universe. – John Rennie May 18 '13 at 15:09
• Thanks! I varied lightly the statement. I know what you mean, but with a non-zero cosmological constant, the Universe is more de Sitter like than Minkowskian! But yes, I was unprecise with "de Sitter Universe". I think I have improved the statement... I hope you will understand what I meant despite of that "bad language"... – riemannium May 18 '13 at 19:32

Rie. Like your question. I've been stewing on this for 5 yrs now, but have gotten nowhere. Suggestions. For moral support on the CC, see Carlo Rovelli's great paper:http://arxiv.org/abs/1002.3966. For physics(CC only, no dSS) see Beck: http://arxiv.org/abs/0810.0752

The electron & therefore QED must be involved. Dirac's 1935 paper was first to explore the relations of the electron in deSitter space. At first, it seems ridiculous: dS space is Defined tb devoid of particles & radiation ! However, there is a well defined area in GR w/its own metric, the Schwarzschild-deSitter metric. Combine that w/the infamous model of the Dirac electron as a Kerr-Newman BH & you see where this is going. If dS space can accommodate a BH, who cares if it's an electron ! So the idea is to do QED in dS space. The literature is Huge on QFT in dS space, but not much on QED/dS. Indeed, Planck's refined value of 3.3Gev/m^3 => a new target value for Lambda ~ 1.1E-52/m^2. Do let me know if you have any ideas how to attack this problem.

The 'absence' of radiation & particles in dS space is of course a classical concept & I agree that Unruh & Hawking change the rules. Dirac's 1935 paper was the first, vis a vis the electron & dS space. It transforms the momentum-Dirac eq. over to an angular momentum eq. So is this quon thing your idea ? I confess I've never heard of it. Refs? Anything beats SUSY, & I'm convinced she'll be history after the LHC 2015 run !

• Dear PsiStarPsi, thanks for the reference! Indeed, I must confess I do know the answer to this particular question, but I want to see the reaction to people to a non SUSY q-deformed relation between bosons and fermions due to quon interpolation. About your comments about Dirac, I had no knowledge about them! However, from a modern perspective, there is a reason why the argument that dS is devoid of particles and radiation: the Unruh and Hawking effect! – riemannium Aug 18 '13 at 9:53
• $T_{Unruh }(dS)=\sqrt{a+a_0}/2\pi$ for a dS spacetime "proves" that even in a "vacuum" spacetime like-de Sitter, the issue of being "radiation-less" is observer dependent! In general, any accelerated system and its observer will "see" radiation even in "vacuum" spacetimes like dS! – riemannium Aug 18 '13 at 10:41
• PsiStarPsi The quon idea is not mine! Unfortunately! Read Jack Ng papers and talks about infinite statistics and references therein. Even M-theory and branes have arrived to that crazy uncommon stuff. Even more, do you believe that there are generalized non-additive statistics that change the usual "naive" Boson-Fermion (even anyons) distinction a bit "fuzzy"...Indeed, C.Tsallis has proved recently that you can "recover" S~V for the BH idea through a nonextensive argument! I can not believe no one has realized that before. Holography can be "a disguise" of non-additive entropies! – riemannium Sep 3 '13 at 14:44