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

Barausse, Enrico; Bezares, Miguel; Crisostomi, Marco; Lara, Guillermo

doi:10.1088/1475-7516/2022/11/050

Cited by 18 publications

(5 citation statements)

References 25 publications

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“…However, in some cases it is possible to view it as an effective field theory where the more complete theory can be pathology-free. In this perspective, the problematic theory can still be useful as long as its limitations are recognized [38,39]. Investigating this approach will be one of the main topics of interest in the coming years.…”

Section: Discussionmentioning

confidence: 99%

Pervasiveness of the breakdown of self-interacting vector field theories

Coates¹,

Ramazanoğlu²

2023

Preprint

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Various groups recently argued that self-interacting vector field theories lack a well-defined time evolution when the field grows to large amplitudes, which has drastic consequences for models in gravity and high energy theory. Such field amplitudes can be a result of an external driving mechanism, or occur intrinsically, due to large values of the field and its derivatives in the initial data. This brings a natural question: is small amplitude initial data guaranteed to evolve indefinitely in these theories in the absence of an outside driving term? We answer this question in the negative, demonstrating that arbitrarily low amplitude initial data can still lead to the breakdown of the theory. Namely, ingoing spherically symmetric wave packets in more than one spatial dimensions grow as an inverse power of the radius, and their amplitudes can generically reach high enough values where time evolution ceases to exist. This simple example further establishes the pervasiveness of the pathology of self-interacting vector field theories.

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Section: Discussionmentioning

confidence: 99%

Pervasiveness of the breakdown of self-interacting vector field theories

Coates¹,

Ramazanoğlu²

2023

Preprint

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“…An example is a field theory with non-linear kinetic terms, used for k-essance [96]. A similar construction to this case has been suggested, in fact, for self-interacting Proca models [97,98].…”

Section: Introductionmentioning

confidence: 90%

Proca-Higgs balls and stars in a UV completion for Proca self-interactions

Herdeiro

Radu

Filho

2023

J. Cosmol. Astropart. Phys.

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We consider a Proca-Higgs model wherein a complex vector field gains mass via spontaneous symmetry breaking, by coupling to a real scalar field with a Higgs-type potential. This vector version of the scalar Friedberg-Lee-Sirlin model, can be considered as a UV completion of a complex Proca model with self-interactions. We study the flat spacetime and self-gravitating solitons of the model, that we dub Proca-Higgs balls and stars respectively, exploring the domain of solutions and describing some of their mathematical and physical properties. The stars reduce to the well-known (mini-)Proca stars in some limits. The full model evades the hyperbolicity problems of the self-interacting Proca models, offering novel possibilities for dynamical studies beyond mini-Proca stars.

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“…if the latter is occurring at very low energies), it is still possible that the instability is simply due to a breakdown of the Cauchy (initial-data) problem. In fact, the instability of [61] manifests itself as the effective metric on which the scalar waves travels becoming singular, which is reminiscent of the Tricomi/Keldysh breakdown of the Cauchy problem in K-essence [44-46, 62, 63] and non-linear Proca [64] theory. The latter has been shown to be fixable by suitable choices of gauge and self-interactions [45,63], and/or by a UV completion [46,65].…”

Section: Jcap03(2023)044mentioning

confidence: 99%

Testing gravitational wave propagation with multiband detections

Baker

Barausse

Anson

et al. 2023

J. Cosmol. Astropart. Phys.

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Effective field theories (EFT) of dark energy (DE) — built to parameterise the properties of DE in an agnostic manner — are severely constrained by measurements of the propagation speed of gravitational waves (GW). However, GW frequencies probed by ground-based interferometers lie around the typical strong coupling scale of the EFT, and it is likely that the effective description breaks down before even reaching that scale. We discuss how this leaves the possibility that an appropriate ultraviolet completion of DE scenarios, valid at scales beyond an EFT description, can avoid present constraints on the GW speed. Instead, additional constraints in the lower frequency LISA band would be harder to escape, since the energies involved are orders of magnitude lower. By implementing a method based on GW multiband detections, we show indeed that a single joint observation of a GW150914-like event by LISA and a terrestrial interferometer would allow one to constrain the speed of light and gravitons to match to within 10-15. Multiband GW observations can therefore firmly constrain scenarios based on the EFT of DE, in a robust and unambiguous way.

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

Cited by 18 publications

References 25 publications

Pervasiveness of the breakdown of self-interacting vector field theories

Pervasiveness of the breakdown of self-interacting vector field theories

Proca-Higgs balls and stars in a UV completion for Proca self-interactions

Testing gravitational wave propagation with multiband detections

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