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.

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.

In this paper, we study the Casimir effect in a curved spacetime described by gravitational actions quadratic in the curvature. In particular, we consider the dynamics of a massless scalar field confined between two nearby plates and compute the corresponding mean vacuum energy density and pressure in the framework of quadratic theories of gravity. Since we are interested in the weak-field limit, as far as the gravitational sector is concerned we work in the linear regime. Remarkably, corrections to the flat spacetime result due to extended models of gravity (although very small) may appear at the first-order of our perturbative analysis, whereas general relativity contributions start appearing at the second order. Future experiments on the Casimir effect might represent a useful tool to test and constrain extended theories of gravity.

The weak field limit of scalar tensor theories of gravity is discussed in view of conformal transformations. Specifically, we consider how physical quantities, like gravitational potentials derived in the Newtonian approximation for the same scalar-tensor theory, behave in the Jordan and in the Einstein frame. The approach allows to discriminate features that are invariant under conformal transformations and gives contributions in the debate of selecting the true physical frame. As a particular example, the case of f (R) gravity is considered.

We analyze axion-photon mixing in the framework of quantum field theory. The condensate structure of the vacuum for mixed fields induces corrections to the oscillation formulae and leads to non-zero energy of the vacuum for the component of the photon mixed with the axion. This energy generates a new effect of the vacuum polarization and it has the state equation of the cosmological constant, w = −1. This result holds for any homogeneous and isotropic curved space-time, as well as for diagonal metrics. Numerical estimates of the corrections to the oscillation formulae are presented by considering the intensity of the magnetic field available in the laboratory. Moreover, we estimate the vacuum energy density induced by axion-photon mixing in the Minkowski space-time. A value compatible with that of the energy density of the universe can be obtained for axions with a mass of (10 −3 − 10 −2 )eV in the presence of the strong magnetic fields that characterize astrophysical objects such as pulsars or neutron stars. In addition, a value of the energy density less than that of the Casimir effect is obtained for magnetic fields used in experiments such as PVLAS. The vacuum polarization induced by this energy could be detected in next experiments and it might provide an indirect proof of the existence of the axion-photon mixing.The quantum field theory effects presented in this work may lead to new methods for studying axion-like particles.

The role of Mach's principle in physics is discussed in relation to the equivalence principle. The difhculties encountered in attempting to incorporate Mach's principle into general relativity are discussed. A modified relativistic theory of gravitation, apparently compatible with Mach s principle, is developed.