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

**Authors:** Guillermo Lara, Miguel Bezares, Enrico Barausse  
**arXiv:** [2112.09186](https://arxiv.org/abs/2112.09186)  
**Date:** 2021-12-16  
**Summary page:** https://www.summarizepaper.com/en/paper/2112.09186v1/

## Key points

- Authors explore behavior of scalar-tensor theories with first-derivative self interactions, known as $k$-essence
- Investigate limitations of $k$-essence on smaller scales
- Initial value evolutions play crucial role in predicting behavior of astrophysical systems on smaller scales
- Ultraviolet completions to $k$-essence considered to address instabilities in Cauchy problem
- Ultraviolet completions render Cauchy evolutions well-posed at all times
- Relationship between nonlinearities and range of validity of low-energy theory checked in ultraviolet completion
- No breakdown in well-posedness observed in Cauchy problem with ultraviolet completion
- Evolutions within regime of validity agree with predictions from low-energy theory
- Nonlinear behavior of $k$-essence mostly lies outside regime of validity
- Study provides insights into mitigating instabilities related to Cauchy problem in $k$-essence using ultraviolet completions
- Highlights limitations of capturing nonlinear behavior on local scales

## Summary

In their paper titled "UV completions, fixing the equations and nonlinearities in $k$-essence," authors Guillermo Lara, Miguel Bezares, and Enrico Barausse explore the behavior of scalar-tensor theories with first-derivative self interactions, known as $k$-essence. While $k$-essence has shown interesting phenomenology on cosmological scales, the authors investigate its limitations on smaller scales. On smaller scales, initial value evolutions play a crucial role in predicting the behavior of astrophysical systems such as binaries of compact objects. However, these evolutions may encounter instabilities due to the Cauchy problem potentially becoming ill-posed. To address these issues, the authors consider ultraviolet completions to $k$-essence. These completions have been known to exist and offer potential solutions by rendering Cauchy evolutions well-posed at all times. Furthermore, they allow for checking the relationship between nonlinearities and the range of validity of the low-energy theory. They confirm that the ultraviolet completion does not lead to any breakdown in well-posedness of the Cauchy problem. Moreover, they find that when within its regime of validity, evolutions in this completion agree with those predicted by the low-energy theory. However, they also observe that most of the nonlinear behavior of $k$-essence lies outside this regime. Overall, this study provides insights into how ultraviolet completions can mitigate instabilities related to the Cauchy problem in $k$-essence and highlights its limitations in capturing its nonlinear behavior on local scales. The findings contribute to a better understanding of scalar-tensor theories and their applicability on different scales.