# The well-posedness of the Cauchy problem for self-interacting vector fields

@article{Barausse2022TheWO, title={The well-posedness of the Cauchy problem for self-interacting vector fields}, author={Enrico Barausse and Miguel Bezares and Marco Crisostomi and Guillermo Lara}, journal={Journal of Cosmology and Astroparticle Physics}, year={2022}, volume={2022} }

We point out that the initial-value (Cauchy) problem for self-interacting vector fields presents the same well-posedness issues as for first-order derivative self-interacting scalar fields (often referred to as k-essence). For the latter, suitable strategies have been employed in the last few years to successfully evolve the Cauchy problem at the level of the infrared theory, without the need for an explicit ultraviolet completion. We argue that the very same techniques can also be applied to…

## References

SHOWING 1-10 OF 25 REFERENCES

### K-dynamics: well-posed 1+1 evolutions in K-essence

- Mathematics, Physics
- 2020

We study the vacuum Cauchy problem for K-essence, i.e. cosmologically relevant scalar-tensor theories that involve first-order derivative self-interactions, and which pass all existing gravitational…

### Intrinsic Pathology of Self-Interacting Vector Fields.

- PhysicsPhysical review letters
- 2022

We show that self-interacting vector field theories exhibit unphysical behavior even when they are not coupled to any external field. This means any theory featuring such vectors is in danger of…

### The problem with Proca: ghost instabilities in self-interacting vector fields

- Physics
- 2022

Massive vector ﬁelds feature in several areas of particle physics, e.g., as carriers of weak interactions, dark matter candidates, or as an eﬀective description of photons in a plasma. Here we…

### UV completions, fixing the equations and nonlinearities in $k$-essence

- Physics
- 2021

Scalar-tensor theories with ﬁrst-derivative self interactions, known as k -essence, may provide in-teresting phenomenology on cosmological scales. On smaller scales, however, initial value evolutions…

### Nonlinear, noniterative treatment of EFT-motivated gravity

- Mathematics, Physics
- 2020

We study a higher derivative extension to General Relativity and present a fully nonlinear/non-perturbative treatment to construct initial data and study its dynamical behavior in spherical symmetry…

### Singularity Problem for Interacting Massive Vectors.

- PhysicsPhysical review letters
- 2022

Interacting massive spin-1 fields have been widely used in cosmology and particle physics. We obtain a new condition on the validity of the classical limit of these theories related to the nontrivial…

### Well-posed UV completion for simulating scalar Galileons

- PhysicsPhysical Review D
- 2022

The Galileon scalar ﬁeld theory is a prototypical example of an eﬀective ﬁeld theory that exhibits the Vainshtein screening mechanism, which is incorporated into many extensions to Einstein gravity.…

### Resolving pathology of self-interacting Proca ﬁeld: a case study of Proca star

- Physics
- 2022

It has been argued that a self-interacting massive vector ﬁeld is pathological due to a dynamical formation of a singular eﬀective metric of the vector ﬁeld, which is the onset of a gradient or ghost…

### Fixing the dynamical evolution in scalar-Gauss-Bonnet gravity

- PhysicsPhysical Review D
- 2022

One of the major obstacles to testing alternative theories of gravity with gravitational-wave data from merging binaries of compact objects is the formulation of their ﬁeld equations, which is often…

### Kinetic screening in nonlinear stellar oscillations and gravitational collapse

- PhysicsPhysical Review D
- 2021

We consider k-essence, a scalar-tensor theory with first-order derivative self-interactions that can screen local scales from scalar fifth forces, while allowing for sizeable deviations from General…