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We investigate propagations of graviton and additional scalar on four-dimensional anti de Sitter (AdS$_4$) space using $f(R)$ gravity models with external sources.
- It is shown that there is the van Dam-Veltman-Zakharov (vDVZ) discontinuity in $f(R)$ gravity models because $f(R)$ gravity implies GR with additional scalar.
- This indicates a difference between general relativity and $f(R)$ gravity clearly.
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