Observational signatures of Jordan-Brans-Dicke theories of gravity

We analyze the Jordan-Brans-Dicke model (JBD) of gravity, where deviations from General Relativity (GR) are described by a scalar field non-minimally coupled to gravity. The theory is characterized by a constant coupling parameter, $\omega_{\rm JBD}$; GR is recovered in the limit $\omega_{\rm JBD} \to \infty$. In such theories, gravity modifications manifest at early times, so that one cannot rely on the usual approach of looking for inconsistencies in the expansion history and perturbations growth in order to discriminate between JBD and GR. However, we show that a similar technique can be successfully applied to early and late times observables instead. Cosmological parameters inferred extrapolating early-time observations to the present will match those recovered from direct late-time observations only if the correct gravity theory is used. We use the primary CMB, as will be seen by the Planck satellite, as the early-time observable; and forthcoming and planned Supernov{\ae}, Baryonic Acoustic Oscillations and Weak Lensing experiments as late-time observables. We find that detection of values of $\omega_{\rm JBD}$ as large as 500 and 1000 is within reach of the upcoming (2010) and next-generation (2020) experiments, respectively.Comment: minor revision, references added, matching version published in JCA

A Duality Relative To A Limit Doctrine

We give a unified proof of Gabriel-Ulmer duality for locally finitely presentable categories, Adamek-Lawvere-Rosicky duality for varieties and Morita duality for presheaf categories. As an application, we compare presheaf categories and varieties

A duality relative to a limit doctrine

ABSTRACT. We give a unified proof of Gabriel-Ulmer duality for locally finitely presentable categories, Adámek-Lawvere-Rosick´y duality for varieties and Morita duality for presheaf categories. As an application, we compare presheaf categories and varieties. 1