Reconstruction method of $f(R)$ gravity for isotropic and anisotropic spacetimes

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We present the reconstruction method of $f(R)$ gravity for the homogeneous and anisotropic Bianchi-I spacetime, which was previously formulated only for homogeneous and isotropic FLRW spacetime.

• We argue in this paper that for anisotropic spacetimes, the total anisotropy behaves as an independent metric degree of freedom on top of the average scale factor in $f(R)$ gravity.
• This is not like $GR$, where specifying the form of the average scale factor as a function of time also specify the total anisotropy as a function of time uniqely.
• We link this peculiar fact to an interesting intertwining between the definition of Ricci scalar for anisotropic metric and anisotropy evolution equation in $f(R)$ gravity.