Thanks for the suggestion. I am however afraid that the answer is "probably not".

The reason is that I focus on particle physics whereas the model of Petit focuses on cosmology. The goals of the two are different (microscopic world versus our universe). In the context of the standard model of cosmology, there is dark matter, so that there is a way to relate particle physics and cosmology by introducing the concept of a dark matter particle. In the model of Petit, there is no dark matter, so that the two stay disconnected. In this sense, the model of Petit won't help us to go beyond the Standard Model of particle physics.

As a side note, I have noticed that the model of Petit (which I didn't know) has not been well received by cosmologists. The reason seems that since its proposal in the end of the 1970s, there are still no predictions that are unique to his model, and no evidence supporting it. I however have not studied this more, but this thread is interesting, on that topic.