Abstract
We present an application to cosmological models in f({{mathcal {R}}}) theories within the Palatini formalism of a method that combines cosmography and the explicit form of the field equations in the calculation of the redshift drift. The method yields a sequence of constraint equations which lead to limits on the parameter space of a given f({{mathcal {R}}})-model. Two particular families of f(mathcal{R})-cosmologies capable of describing the current dynamics of the universe are explored here: (i) power law theories of the type f({{mathcal {R}}})={{mathcal {R}}}-beta /{{mathcal {R}}}^n, and (ii) theories of the form f({{mathcal {R}}})={{mathcal {R}}}+alpha ln {{{mathcal {R}}}} -beta . The constraints on (n,beta ) and (alpha ,beta ), respectively, limit the values to intervals that are narrower than the ones previously obtained. As a byproduct, we show that when applied to General Relativity, the method yields values of the kinematic parameters with much smaller errors that those obtained directly from observations.
Highlights
The observational evidence of the accelerated expansion of the universe can be described by assuming that gravity is governed by a theory different from General Relativity (GR) at large scales and late times
The Einstein-Hilbert Lagrangian is replaced by a function f (R), where R is defined as R ≡ gμνRμν(Γ ), and Rμν is the Ricci tensor defined in terms of the independent connection
In this work we present the constraint relation for the (n, β) space, which must be satisfied by the parameters to be consistent with the cosmographic and dynamical approaches of the redshift drift
Summary
The observational evidence of the accelerated expansion of the universe can be described by assuming that gravity is governed by a theory different from General Relativity (GR) at large scales and late times. The constraint equations mentioned above can be used in two directions: (1) to get theoretical estimations of the kinematic parameters if General Relativity is assumed, and (2) to constrain the space-parameter of particular f (R)models if the kinematic parameters are derived from independent observational data. In this regard, cosmography has been widely used to distinguish between cosmological models (see for instance [23,24,25,26,27,28,29,30]).
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