Constraints on noncommutative spectral action from Gravity Probe B and torsion balance experiments

Abstract

Abstract. Noncommutative spectral geometry offers a purely geometric explanation for the standard model of strong and electroweak interactions, including a geometric explanation for the origin of the Higgs field. Within this framework, the gravitational, the electroweak and the strong forces are all described as purely gravitational forces on a unified noncommutative space-time. In this study, we infer a constraint on one of the three free parameters of the model, namely the one characterising the coupling constants at unification, by linearising the field equations in the limit of weak gravitational fields generated by a rotating gravitational source, and by making use of recent experimental data. In particular, using data obtained by Gravity Probe B, we set a lower bound on the Weyl term appearing in the noncommutative spectral action, namely β 10 −6 m −1 . This constraint becomes stronger once we use results from torsion balance experiments, leading to β 10 4 m −1 . The latter is much stronger than any constraint imposed so far to curvature squared terms.

Constraining models of extended gravity using Gravity Probe B and LARES experiments

“…a bound similar to the one obtained earlier on using binary pulsars [54], or the Gravity Probe B data [52]. It is important to note that a much stronger limit, m Y > 10 4 m −1 , has been obtained using the torsion balance experiments [52].…”

“…It is important to note that a much stronger limit, m Y > 10 4 m −1 , has been obtained using the torsion balance experiments [52]. In conclusion, using data form Gravity Probe B and LARES missions, we obtain similar constraints on m Y ; a result that one could have anticipated since both these experiments are designed to test the same type of physical phenomenon.…”

“…The values of the geodesic precession and the Lense-Thirring precession, measured by the Gravity Probe B satellite and those predicted by GR, are given in Table II. Imposing the constraint |Ω LT | δΩ LT , [52], with r * = R ⊕ + h where R ⊕ is the radius of the Earth and h = 650 km is the altitude of the satellite, we get …”

Spectral dimensions from the spectral action

“…These models may also be extended to include physics beyond the standard model [13][14][15][16] or supersymmetry [17][18][19][20]. Their renormalization has been studied in [21][22][23][24][25] and the phenomenological implications of the resulting effective actions have been carried out, e.g., in [26][27][28]. A more detailed discussion of the cutoff Λ may be found in [29], and the generalization to non-commutative spaces built from non-associative algebras has been pursued in [30].…”

Casimir effect in extended theories of gravity

“…These corrections to the gravitational Lagrangian were already considered by several authors [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]). From a conceptual viewpoint, there is no reason a priori to restrict the gravitational Lagrangian to a linear function of the Ricci scalar minimally coupled to matter [38].…”