Curvature dark energy reconstruction through different cosmographic distance definitions

Abstract

In the context of f (R) gravity, dark energy is a geometrical fluid with negative equation of state. Since the function f (R) is not known a priori, the need of a model independent reconstruction of its shape represents a relevant technique to determine which f (R) model is really favored with respect to others. To this aim, cosmography is related to a generic f (R) and its derivatives in order to provide a model-independent investigation at redshift z ∼ 0. The analysis is based on the use of three different cosmological distance definitions, in order to alleviate the duality problem, i.e. the problem of which cosmological distance to use with specific cosmic data sets. Therefore, the luminosity, d L , flux, d F , and angular, d A , distances are considered and numerical constraints by the Union 2.1 supernovae compilation and measurement of baryonic acoustic oscillations, at z B AO = 0.35 are found. It was noticed that all distances reduce to the same expression, i.e. d L;F ;A ∼ 1 H 0 z, at first order. Thus, to fix the cosmographic series of observables, the initial value of H 0 was imposed by fitting H 0 through supernovae only, in the redshift regime z < 0.4. The pressure of curvature dark energy fluid was found to be slightly lower than the one related to the cosmological constant. This indicates that a possible evolving curvature dark energy realistically fills the current universe. Moreover, the combined use of d L , d F and d A shows that the sign of the acceleration parameter agrees with theoretical bounds, while its variation, namely the jerk parameter, is compatible with j 0 > 1. Finally, the functional form of f (R) is infered by means of a truncated polynomial approximation, in terms of fourth order scale factor a(t).

On the theory and applications of modern cosmography

“…The same hypothesis holds for the other distance definitions, which can be thought as standard cosmographic indicators, as also proposed in [31]. In such an approach, one argues the need of using all the distances for a complete cosmographic test, since all the various cosmological distances assume the total photon number is conserved on all cosmic scales.…”

“…, it is possible to get bounds with cosmic data within shorter redshift intervals 31 , in which one can recover an acceptable value for H 0 to use in any cosmographic analyses, performed at arbitrary expansion order 32 . The second possibility is to fix H 0 by means of other types of measurements, either through a χ square analysis or by fixing it.…”

“…More recently, however, it was demonstrated that the use of alternative versions of the luminosity distance are predictive and useful to determine viable priors which may calibrate the luminosity distance itself. A possible 31 A viable interval would be z ≤ 0.5, in which the union 2.1 data are deeply concentrated. 32 In general, this procedure consists in fixing a coefficient, instead of marginalising over it.…”

Cosmology in Poincaré gauge gravity with a pseudoscalar torsion

“…The contributions of the modifications of gravity can be identified with some kind of geometric dark energy. This is specially advantageous since one can define an equation of state associated with such dark energy and compare it with the ΛCDM model [27][28][29]. However, the function f (R) is not known a priori, none introduces a new fundamental principle that can be used as a guiding line, it is usually constructed by trial and error.…”

“…We also note that although we do not introduce a cosmological constant Λ in the action (2.1), it automatically emerges in these equations. In (2.18) the pseudoscalar torsion f is a function of ρ and p rather than a constant, in contrast to [27][28][29]. It should be noted that although (2.8) …”