f(R) theories

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.Comment: 156 pages, 14 figures, Invited review article in Living Reviews in Relativity, Published version, Comments are welcom

Mechanochemical Synthesis, Characterization and Reactivity of a Room Temperature Stable Calcium Electride

\ua9 2024 The Authors. Published by American Chemical Society.A new calcium-based Room temperature Stable Electride (RoSE), K[{Ca[N(Mes)(SiMe3)]3(e-)}2K3] (2), is successfully synthesized from the reaction of a calcium tris-amide, [Ca{N(Mes)(SiMe3)}3K] (1) (Mes = 2,4,6-trimethylphenyl), with potassium under mechanochemical treatment. The dimeric structure of K[{Ca[N(Mes)(SiMe3)]3(e-)}2K3] is calculated using ab initio random structure searching (AIRSS) methods. This shows the existence of highly localized anionic electrons (e-) and suggests poor electrical conductance, as confirmed via electroconductivity measurements. The two anionic electrons in 2 are strongly antiferromagnetically coupled, thus in agreement with the largely diamagnetic response from magnetometry. Reaction of 2 with pyridine affords 4,4′-bipyridine, while reaction with benzene gives C-H activation and formation of a calcium hydride complex, [K(η6-C6H6)4][{Ca[N(Mes)(SiMe3)](H)}2K3] (3). Computational DFT analysis reveals the crucial role played by the ligand framework in the stabilization of this new Ca-hydride complex