A general analytic procedure is developed to deal with the Newtonian limit of $f(R)$ gravity. A discussion comparing the Newtonian and the post-Newtonian limit of these models is proposed in order to point out the differences between the two approaches. We calculate the post-Newtonian parameters of such theories without any redefinition of the degrees of freedom, in particular, without adopting some scalar fields and without any change from Jordan to Einstein frame. Considering the Taylor expansion of a generic $f(R)$ theory, it is possible to obtain general solutions in terms of the metric coefficients up to the third order of approximation. In particular, the solution relative to the $g_{tt}$ component gives a gravitational potential always corrected with respect to the Newtonian one of the linear theory $f(R)=R$. Furthermore, we show that the Birkhoff theorem is not a general result for $f(R)$ gravity since time-dependent evolution for spherically symmetric solutions can be achieved depending on the order of perturbations. Finally, we discuss the post-Minkowskian limit and the emergence of massive gravitational wave solutions.

We give a rigorous and mathematically well defined presentation of the covariant and gauge invariant theory of scalar perturbations of a Friedmann-Lemaître-Robertson-Walker universe for fourth order gravity, where the matter is described by a perfect fluid with a barotropic equation of state. The general perturbations equations are applied to a simple background solution of $R^n$ gravity. We obtain exact solutions of the perturbations equations for scales much bigger than the Hubble radius. These solutions have a number of interesting features. In particular, we find that for all values of $n$ there is always a growing mode for the density contrast, even if the universe undergoes an accelerated expansion. Such behavior does not occur in standard general relativity, where as soon as dark energy dominates, the density contrast experiences an unrelenting decay. This peculiarity is sufficiently novel to warrant further investigation of fourth order gravity models.

The direct effect of an axion field on Josephson junctions is analyzed through the consequences on the effective potential barrier that prevents the junction from switching from the superconducting to the finite-voltage state. We describe a method to reliably compute the quasipotential with stochastic simulations, which allows for the spanning of the coupling parameter from weakly interacting axion to tight interactions. As a result, we obtain an axion field that induces a change in the potential barrier, therefore determining a significant detectable effect for such a kind of elusive particle.

We study 5D Brans–Dicke theory in the framework of (gravitational) baryogenesis and primordial light element formation. Such a model is able to explain the present cosmic accelerated expansion without recurring to matter fields in 5D or dark energy in 4D. In fact, the 5D to 4D reduction arises a space-matter tensor of geometrical origin that plays the role of a new ingredient on-shell. For an isotropic and homogeneous Universe, the cosmological equations admit a power-law solution of the scale factor, $$a(t)\sim t^\alpha$$a ( t ) ∼ t α , we constrain the exponential factor $$\alpha$$α by using the present bounds on the matter–antimatter asymmetry in the Universe and Big Bang Nucleosynthesis. A possible connection with dark matter relic abundance is also discussed.

We explore the gravitational baryogenesis paradigm in the homogeneous and isotropic cosmology of generalized coupling gravity and, in particular, of the so-called Minimal Exponential Measure Model (MEMe). We show that, also in this theory, the time derivative of the Ricci scalar couples with matter currents and can preserve an unbalance in the baryon-antibaryon number beyond thermal equilibrium. Using the current bounds on the ratio of baryon number to entropy density, we can considerably improve the known constraints on the parameter q that characterizes the MEMe model. This estimate also allows us to draw stringent constraints on the spatial curvature of the cosmological model.