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UV completions, fixing the equations, and nonlinearities in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>k</mml:mi></mml:math> -essence
Scalar-tensor theories with first-derivative self-interactions, known as $k$-essence, may provide interesting phenomenology on cosmological scales. On smaller scales, however, initial value evolutions (which are crucial for predicting the behavior of astrophysical systems, such as binaries of compact objects) may run into instabilities related to the Cauchy problem becoming potentially ill-posed. …