Spectral interaction between universes

Abstract

We derive a perturbative formula for the direct interaction between two four-dimensional geometries. Based on the spectral action principle we give an explicit potential up to the third order perturbation around the flat vacua. We present the leading terms of the interaction as polynomials of the invariants of the two metrics and compare the expansion to the models of bimetric gravity.

Towards modified bimetric theories within non-product spectral geometry

“…We make here some comments on the analysis of doubled geometry models in the case when the tensors A μν do not differ sufficiently from the diagonal ones. This is not identical to the situation where the metrics are a small perturbation of the Euclidean ones-for the discussion of the latter we refer to [12].…”

“…are polynomial integrals over higher spheres which can be evaluated by generalizing the methods from [17]-see also [12] for further discussion.…”

“…In particular, the interaction potential for bimetric model is a polynomial one, while for the two-sheeted model it is a rational function. Further similarities and differences for generic metrics were recently analysed in [12], where yet another interpretation of this model in terms of interacting branes was proposed.…”

Modave lectures on Noncommutative Geometry and its applications to physics

“…This suggests that spectral methods can be potentially used to describe Hassan-Rosen bimetric gravity models [42]. This idea was discussed in detail in [43] and it turns out that the effective potential has a different form but it shares a lot of features with the bimetric models. One can now try different modifications of the classical triples and try to derive other modified gravity models.…”