MG11 
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Causality and superluminal behavior: general aspects, the case of k-essence and bimetric theory of gravity

Superluminal propagations are often thought to be a threat for causality. This is not always the case. We first discuss the notion of causality, and exhibit the links that exist between the notions of anteriority, causality and the Cauchy problem, closed cuves in space-time and constraints on initial data. We are then able to show, under some weak conditions, that k-essence scalar theories are causal even if the scalar waves can propagate superluminally, as well in flat spacetime as in a gravitational context. We also consider the case of some bimetric theories of gravity. These two models are of some interest in cosmology and as model building for MOND-like field theories. The arguments presented here are however quite general and apply to many other field theories. In particular, we argue that the superluminal behavior that arise from quantum effects in non trivial vacua do not threaten causality.

Causality and superluminal behavior: general aspects, the case of k-essence theories and bimetric theory of gravity

Superluminal propagations are often thought to be a threat for causality. This is not always the case. We first discuss the notion of causality, and exhibit the links that exists between the notion of anteriority causality and the Cauchy problem, the closed cuves in space-time and constraints on initial data. We are then able to show, under some conditions, that k-essence scalar theories are causal even if the scalar waves can propagate superluminally, as well in flat spacetime as in a gravitational context. We also consider the case of some bimetric theory of gravity. These two theories are of some interest in cosmology and as model building for MOND-like field theories. The arguments presented here are however quite general and apply to many other field theories. In particular, we argue that the superluminal behavior that arise from quantum effects in non trivial vacua do not threaten causality.

Causality and superluminal behavior: general aspects, the case of k-essences and bimetric theory of gravity

Superluminal propagations are often thought to be a threat for causality. This is not always the case. We first discuss the notion of causality, and exhibit the links that exists between the notion of anteriority causality and the Cauchy problem, the closed cuves in space-time and constraints on initial data. We are then able to show, under some conditions, that k-essence scalar theories are causal even if the scalar waves can propagate superluminally, as well in flat spacetime as in a gravitational context. We also consider the case of some bimetric theory of gravity. These two theories are of some interest in cosmology and as model building for MOND-like field theories. The arguments presented here are however quite general and apply to many other field theories. In particular, we argue that the superluminal behavior that arise from quantum effects in non trivial vacua do not threaten causality.