Recent Developments in Degenerate Higher Order Scalar Tensor Theories

Degenerate Higher Order Scalar Tensor (DHOST) theories are the most general scalar-tensor theories whose Lagrangian depends on the metric tensor and a single scalar field and its derivatives up to second order. They propagate only one scalar degree of freedom, without being plagued by Ostrogradsky instabilities. This is achieved through certain degeneracies of the functions forming their Lagrangian. They generalize the Horndeski and beyond-Horndeski theories. Originally proposed to describe the late-time acceleration of the expansion of the universe, generalizing the cosmological constant, they can also be used to build models of the early universe, to describe inflation or alternatives to standard inflation. In the late universe, they modify the standard Vainstein screening mechanism from Horndeski theories (which can have observable consequences) and are suited to build black hole models, featuring non-stealth Kerr black hole solutions. In this work, their phenomenology is reviewed, looking at their basic properties, their parameterizations and classifications, focusing on solutions in the early and the late universe and at cosmological and astrophysical constraints.