We consider models of Extended Gravity and in particular, generic models containing scalartensor and higher-order curvature terms, as well as a model derived from noncommutative spectral geometry. Studying, in the weak-field approximation, the geodesic and Lense-Thirring processions, we impose constraints on the free parameters of such models by using the recent experimental results of the Gravity Probe B and LARES satellites.
A physical interpretation of the two-sheeted space, the most fundamental ingredient of noncommutative spectral geometry proposed by Connes as an approach to unification, is presented. It is shown that the doubling of the algebra is related to dissipation and to the gauge structure of the theory, the gauge field acting as a reservoir for the matter field. In a regime of completely deterministic dynamics, dissipation appears to play a key role in the quantization of the theory, according to the 't Hooft's conjecture. It is thus argued that the noncommutative spectral geometry classical construction carries the seeds of quantization, implicit in its feature of the doubling of the algebra.
We study the Casimir effect in the framework of Standard Model Extension (SME). Employing the weak field approximation, the vacuum energy density ε and the pressure for a massless scalar field confined between two nearby parallel plates in a static spacetime background are calculated. In particular, through the analysis of ε, we speculate a constraint on the Lorentz-violating terms 00 which is lower than the bounds currently available for this quantity. After that, the correction to the pressure given by the gravitational sector of SME is presented. Finally, we remark that our outcome has an intrinsic validity that goes beyond the treated case of a point-like source of gravity.
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