Search

COSMOGRAPHIC TRANSITION REDSHIFT IN F(R) GRAVITY // Tomsk State Pedagogical University Bulletin. 2014. Issue 12 (153). P. 39-43

We propose a strategy to infer the transition redshift zda, which characterizes the passage through the universe decelerated to accelerated phases, in the framework f(R) gravities. To this end, we numerically reconstruct f(z), i. e. the corresponding f(R) function re-expressed in terms of the redshift z and we show how to match f(z) with cosmography. In particular, we relate f(z) and its derivatives to the cosmographic coefficients, i. e. H0, q0 and j0 and demonstrate that its corresponding evolution may be framed by means of an effective logarithmic dark energy term ΩX, slightly departing from the case of a pure cosmological constant. Afterwards, we show that our model predicts viable transition redshift constraints, which agree with ΛCDM. To do so, we compute the corresponding zda in terms of cosmographic outcomes and find that zda ≤ 1. Finally, we reproduce an effective f(z) and show that this class of models is fairly well compatible with present-time data. To do so, we get numerical constraints employing Monte Carlo fits with the Union 2.1 supernova survey and with the Hubble measurement data set.

Keywords: cosmography, f(R) gravity, transition redshift, dark energy

COMPLEX COORDINATE TRANSFORMATIONS TO GET EXACT AXIALLY SYMMETRIC SOLUTIONS IN F(R)-GRAVITY // Tomsk State Pedagogical University Bulletin. 2014. Issue 12 (153). P. 53-57

We present a strategy to get axially symmetric solutions in f(R) gravity by starting from spherically symmetric space-times. To do so, we assume the validity of a complex coordinate transformation, which acts on the spherically symmetric metric and permits one to infer the corresponding f(R) modification. The consequences of this recipe are here described, giving particular emphasis to define a class of compatible axially symmetric solutions, which fairly well describe the motion in cylindrical geometries in the field of f(R), in two different classes of coordinates. We demonstrate that our approach is general and may be applied for several cases of interest. We also show that our treatment is compatible with the standard approach of general relativity, evaluating the motion of a freely falling particle in the context of our metric.

Keywords: complex coordinate transformations, axially symmetric solutions, f(R)-gravity