The research ideas and program

Two years ago, being excited about BICEPT2 results, which unfortunately turned out to be wrong, I have initiated an action plan in Cosmology.
The action plan
I have been very busy in the last year with Research and Development in Computer Science, Projects and Administration at ITI-VNU. During the time I have organized a small group of young physicists and we started discussions on a regular weekly basis. We have four people right now and used to work Saturday afternoon or a late afternoon during the work days. We have streamlined the topic very much. The research seems feasible with promising results. However, the program still encompasses a very large field ranging from the symbolic computation, non-commutative geometry, general relativity, cosmology and elementary particle physics. That why we need more helps from others as well.

For the interested physicists, I would like to call their attentions and invite them to participate, even if they are just interested in one aspect of the topic. Let me summarize the recent discussion:

   1. Our cosmology is expanding with an observed acceleration. This needs an explanation.

   2. The acceleration can be explained by the existence dark matter or a modification of general relativity (or both).

   3. Adding a mass to gravity is an old and traditional idea from Pauli-Fierz. However, this theory suffers two issue:
          a) Van Dame- Veltman-Zakharov discontinuity: Massive gravity has five degree of freedom and massless gravity has only two. So, the transition between the two theories has a gap, that might be problematic, since GR is verified with a high accuracy. The additional three degrees of freedom will have quite different consequences.
          b)  Deser-Boulware ghost: In the nonlinear theory, massive gravity has ghost degrees of freedom with negative kinetic energy and might move with a speed larger than the one of light.
 
   4. Recently, these problems has been cured by adding higher interactions (de Rham-Garbadge-Tolley, 2010) or by using bigravity (Hassan-Rosen, 2011).

   5. Actually, a theory of bigravity based on noncommutative geometry was constructed by Nguyen Ai Viet and K.C.Wali in the period of 1995-2000. In this theory, one massive and one massless gravity have emerged naturally from noncommutative space-time on the geometric foundation like Einstein theory, while Hassan-Rosen bigravity lacks theoretical foundations derived from first principle.

   6. Since Viet-Wali model contains more contents, our group is working on a special case, trying to compare the mass terms with Hassan-Rosen and DeRham et al.

   7.  Secondly, we must identify two types of matter fields which are coupled to the two gravity fields. In two works of Nguyen Ai Viet in 1995,1996, I have naively used Alain Connes's noncommutative space-time of M4 X Z2, where each copy of spacetime contained one type of chiral matter field.  From this unified I have derived some relations between fundamental parameters. Among other relations, the Higgs and top quark masses could be calculated.

   8. In a more generic sense, the space-time for bigravity does not necessarily coincide with Connes'. Connes' space-time is good to describe the unified Higgs-Electromagnetic-Weak interactions ( or full model of SM).  This theory can emerge from gravity in another noncommutative space-time. So, we can have a minimal finite content theory of all the interations. This model can explain why gluons do not have related Higgs fields as well. We are to recalculate the Higgs and top quark mass in this model before going further to explore the cosmological consequences.

    9. Looks like a lot of good ideas have streamlined in this model. It is promising but needs a lot of work in next couple years. We hope to have some ground to attack the new field with success.