Holographic Complexity of Braneworld in Horndeski Gravity

• Published in: Fortschritte der Physik Vol. 71; no. 2-3
• Main Authors: Santos, Fabiano F., Sokoliuk, Oleksii, Baransky, Alexander
• Format: Journal Article
• Language: English
• Published: Weinheim Wiley Subscription Services, Inc 01.03.2023
• Subjects: braneworld; Complexity; cosmology; holographic principle; Holography; Hyperspaces; Initial conditions; modified gravity; Scalars
• ISSN: 0015-8208; 1521-3978
• DOI: 10.1002/prop.202200141

This work investigates the influence of a probe string on a complexity of braneworld according to the CA (Complexity equals action) conjecture within the Horndeski gravity. In the current study, it is considered that scalar fields that source Horndeski gravity have a spatial dependence. In addition, our system contains a particle moving on the boundary, which corresponds to the insertion of a fundamental string in the higher dimensional bulk. Such an effect is given by the Nambu‐Goto term, that also incorporates the time‐dependence and evolution in our system. Both warp factor, scalar field and superpotential values are derived numerically assuming appropriate initial conditions and the growth rate of holographic complexity is analysed within the so‐called Wheeler‐De Witt (WDW) patch with null‐like hypersurfaces present. This work investigates the influence of a probe string on a complexity of braneworld according to the CA (Complexity equals action) conjecture within the Horndeski gravity. In the current study, it is considered that scalar fields that source Horndeski gravity have a spatial dependence. In addition, the system used contains a particle moving on the boundary, which corresponds to the insertion of a fundamental string in the higher dimensional bulk. Such an effect is given by the Nambu‐Goto term, that also incorporates the time‐dependence and evolution in our system. Both warp factor, scalar field and superpotential values are derived numerically assuming appropriate initial conditions and the growth rate of holographic complexity is analysed within the so‐called Wheeler‐De Witt (WDW) patch with null‐like hypersurfaces present.