Gravity's Rainbow
It is worth noting that the above two equations are modified by the rainbow function and these equations can be transformed to the standard ones when setting \(\tildef=1\). Let us next consider the deformed Starobinsky model in which f(R) takes the following form [14]:
Gravity's Rainbow
where \(\tildef(t)\) denotes the rainbow function. Notice that this perturbed metric has been written in the Newtonian gauge. Let us define a new variable \(A \equiv 3(H\Phi +\dot\Psi )\). With the metric (19) and Eq. (4), we obtain the following system of equations [11]
Regarding our present work, the study the cosmological dynamics of isotropic and anisotropic universe in f(R) gravity, see e.g. [8, 55, 56] and references therein, via the dynamical system technique can be further studied. Interestingly, the swampland criteria in the deformed Starobinsky model can be worth investigating by following the work done by Ref. [52]. The reheating process in the present work is an interesting topic to be investigated [53, 54]. Moreover, the effects of rainbow functions on the structure of compact objects are also worth investigating, see e.g. [57, 58]. 041b061a72