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Abstract
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In the context of general relativity, the geodesic
deviation equation (GDE) relates the Riemann curvature tensor
to the relative acceleration of two neighboring geodesics.
In this paper,we consider the GDE for the generalized hybrid
metric-Palatini gravity and apply it in this model to investigate
the structure of time-like, space-like, and null geodesics
in the homogeneous and isotropic universe. We propose a
particular case f (R,R) = R + R to study the numerical
behavior of the deviation vector η(z) and the observer area–
distance r0(z) with respect to redshift z.Also, we consider the
GDE in the framework of the scalar–tensor representation of
the generalized hybrid metric-Palatini gravity, i.e., f (R,R),
in which the model can be considered as dynamically equivalent
to a gravitational theory with two scalar fields. Finally,
we extend our calculations to obtain the modification of the
Mattig relation in this model.
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