We consider the early time cosmology of $f(R)$ theories in Palatini formalism and study the conditions that guarantee the existence of homogeneous and isotropic models that avoid the big bang singularity. We show that for such models the big bang singularity can be replaced by a cosmic bounce without violating any energy condition. In fact, the bounce is possible even for pressureless dust. We give a characterization of such models and discuss their dynamics in the region near the bounce. We also find that power-law Lagrangians with a finite number of terms may lead to nonsingular universes, which contrasts with the infinite-series Palatini $f(R)$ Lagrangian that one needs to fully capture the effective dynamics of loop quantum cosmology. We argue that these models could also avoid the formation of singularities during stellar gravitational collapse.

We show that electrically charged solutions within the Eddington-inspired Born–Infeld theory of gravity replace the central singularity by a wormhole

We demonstrate the existence of Bloch oscillations of acoustic fields in sound propagation through a superlattice of water cavities and layers of methyl methacrylate. To obtain the acoustic equivalent of a Wannier-Stark ladder, we employ a set of cavities with different thicknesses. Bloch oscillations are observed as time-resolved oscillations of transmission in a direct analogy to electronic Bloch oscillations in biased semiconductor superlattices. Moreover, for a particular gradient of cavity thicknesses, an overlap of two acoustic minibands occurs, which results in resonant Zener-like transmission enhancement.

We study ground states and excitations of light octet and decuplet baryons within the framework of Dyson-Schwinger and Faddeev equations. We improve upon similar approaches by explicitly taking into account the momentum-dependent dynamics of the quark-gluon interaction that leads to dynamical chiral symmetry breaking. We perform calculations in both the three-body Faddeev framework and the quark-diquark approximation in order to assess the impact of the latter on the spectrum. Our results indicate that both approaches agree well with each other. The resulting spectra furthermore agree one-to-one with experiment, provided well-known deficiencies of the rainbow-ladder approximation are compensated for. We also discuss the mass evolution of the Roper and the excited $\mathrm{\Delta }$ with varying pion mass and analyze the internal structure in terms of their partial wave decompositions.

We study the field equations of modified theories of gravity in which the Lagrangian is a general function of the Ricci scalar and Ricci-squared terms in Palatini formalism. We show that the independent connection can be expressed as the Levi-Cività connection of an auxiliary metric which, in particular cases of interest, is related with the physical metric by means of a disformal transformation. This relation between physical and auxiliary metric boils down to a conformal transformation in the case of $f(R)$ theories. We also show with explicit models that the inclusion of Ricci-squared terms in the action can impose upper bounds on the accessible values of pressure and density, which might have important consequences for the early time cosmology and black hole formation scenarios. Our results indicate that the phenomenology of $f(R,R_{\mu \nu }{R}^{\mu \nu })$ theories is much richer than that of $f(R)$ and $f(R_{\mu \nu }{R}^{\mu \nu })$ theories and that they also share some similarities with Bekenstein’s relativistic theory of MOND.