Limitations of cosmography in extended theories of gravity

Abstract

The cosmographic approach, which only relies upon the homogeneity and isotropy of the Universe on large scales, has become an essential tool in dealing with an increasing number of theoretical possibilities for explaining the late-time acceleration of the Universe, ranging from Modified Gravity theories to Dark Energy alternatives passing from testing the cosmological concordance ΛCDM model. Despite its generality, we show that this method has a number of shortcomings when trying to adequately reconstruct theories with higher-order derivatives in either the gravitational or the matter sector. Herein some paradigmatic examples of such an inability, explanations of the limitations and prospective cures will be presented.

Model-independent limits and constraints on extended theories of gravity from cosmic reconstruction techniques

“…To overcome this problem, cosmographic reconstructions often employ auxiliary parametrisations of cosmic distances, which commonly involve new choices of independent variables 5 built up in terms of the redshift z. However, the viability of such analyses has recently been put into question, due to increasing propagation of errors and difficulties in understanding what the most suitable parametrisation at a statistical level is [23,24]. Such combinations of redshift z seemed to lead to biased results, not being for instance even able to unveil ΛCDM as the theory responsible for mock data precisely generated from an exact ΛCDM model.…”

“…Finally, let us mention that Refs. [21][22][23][24] only dealt with SNIa data whereas our present analysis has included both Union 2.1 supernovae catalogue, baryonic acoustic oscillation data and H(z) differential age compilations, which indeed probe cosmology on different scales of the cosmological evolution. In this sense also, our analysis overcome previous attempts to prove the validity and competitiveness of the cosmographic approach.…”

“…Cosmographic studies in these theories have been limited to recent research [23,24] which proved how limited such a technique is when compared to Gaussian processes of reconstruction [25]. Moreover the usual approximation that the matter content today can be related to the cosmographic parameter q 0 as happens in ΛCDM was made, limiting the generality of the obtained results therein.…”

“…In the event of those parameters not being fixed, a one-to-one correspondence between the f (R)-derivatives and the cosmographic parameters is no longer possible [23,24] which forces a sensible prior assumption over these derivatives or complementary tests. Anyhow, these attempts led to limited constraints on f (R) models [23,24] that we intend to extend herein.…”

Towards New Constraints in Extended Theories of Gravity: Cosmography and Gravitational-Wave Signals from Neutron Stars

“…Cosmography of the Universe indeed belongs to this class of techniques [39]. Cosmographic studies in extended theories have been limited to recent research [40,41] proving how much disfavoured such a technique is in comparison with Gaussian processes of reconstruction [42].…”