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Mathematical Formulation of the No-Go Theorem in Horndeski Theory^{ †}

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## Abstract

**:**

## 1. Introduction and Summary

## 2. No-Go Theorem

**Theorem**

**1.**

**Set up:**We consider functions on ${\mathbb{R}}^{1}$ with the following relations (it is exactly the case of the general Horndeski theory):

**Assumptions:**- (1) ${\mathcal{G}}_{\mathcal{T}}$, ${\mathcal{F}}_{\mathcal{T}}$, Σ, Θ, and a are smooth functions of coordinate q1.
- (2) $\phantom{\rule{3.33333pt}{0ex}}\exists \u03f5>0:\phantom{\rule{3.33333pt}{0ex}}{\mathcal{G}}_{\mathcal{T}}>{\mathcal{F}}_{\mathcal{T}}>\u03f5,\phantom{\rule{1.em}{0ex}}{\mathcal{G}}_{\mathcal{S}}>{\mathcal{F}}_{\mathcal{S}}>\u03f5,\phantom{\rule{1.em}{0ex}}a>\u03f5.$
**Statement:**- The only relevant function choice to satisfy the assumptions is $\mathsf{\Theta}=0$ everywhere.

**Proof.**

## 3. Discussion

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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1. | Coordinate q stands for time coordinate in a cosmological setup and radial coordinate in a static, spherically symmetric case, for instance, in a wormhole setup. |

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**MDPI and ACS Style**

Mironov, S.
Mathematical Formulation of the No-Go Theorem in Horndeski Theory. *Universe* **2019**, *5*, 52.
https://doi.org/10.3390/universe5020052

**AMA Style**

Mironov S.
Mathematical Formulation of the No-Go Theorem in Horndeski Theory. *Universe*. 2019; 5(2):52.
https://doi.org/10.3390/universe5020052

**Chicago/Turabian Style**

Mironov, Sergey.
2019. "Mathematical Formulation of the No-Go Theorem in Horndeski Theory" *Universe* 5, no. 2: 52.
https://doi.org/10.3390/universe5020052