Kaluza-Klein theory for teleparallel gravity
Chao-Qiang Geng, Chang Lai, Ling-Wei Luo, Huan-Hsin Tseng
TL;DR
This paper explores teleparallel gravity within the Kaluza-Klein framework, revealing that the 5D torsion scalar leads to an effective 4D theory similar to general relativity, with implications for cosmology.
Contribution
It provides the first detailed analysis of KK reduction of teleparallel gravity, showing the effective 4D theory's structure and its cosmological implications.
Findings
Effective 4D Lagrangian differs from Brans-Dicke type due to scalar-torsion coupling
Result is equivalent to general relativity in the effective theory
Cosmological analysis in FLRW universe shows consistent behavior
Abstract
We study teleparallel gravity in the \emph{original} Kaluza-Klein (KK) scenario. Our calculation of the KK reduction of teleparallel gravity indicates that the 5-dimensional torsion scalar generates the non-Brans-Dicke type effective Lagrangian in 4-dimension due to an additional coupling between the derivative of the scalar field and torsion, but the result is equivalent to that in general relativity. We also discuss the cosmological behavior in the FLRW universe based on the effective teleparallel gravity.
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