Angular distribution of cosmological parameters as a probe of inhomogeneities: a kinematic parametrisation

¹ Institute of Astrophysics and Space Sciences, University of Lisbon, Tapada da Ajuda, 1349–018 Lisbon, Portugal
e-mail: cscarvalho@oal.ul.pt
² Research Center for Astronomy and Applied Mathematics, Academy of Athens, Soranou Efessiou 4, 11–527 Athens, Greece

Received: 22 March 2016
Accepted: 20 May 2016

Abstract

We use a kinematic parametrisation of the luminosity distance to measure the angular distribution on the sky of time derivatives of the scale factor, in particular the Hubble parameter H₀, the deceleration parameter q₀, and the jerk parameter j₀. We apply a recently published method to complement probing the inhomogeneity of the large-scale structure by means of the inhomogeneity in the cosmic expansion. This parametrisation is independent of the cosmological equation of state, which renders it adequate to test interpretations of the cosmic acceleration alternative to the cosmological constant. For the same analytical toy model of an inhomogeneous ensemble of homogenous pixels, we derive the backreaction term in j₀ due to the fluctuations of { H₀,q₀ } and measure it to be of order 10^-2 times the corresponding average over the pixels in the absence of backreaction. In agreement with that computed using a ΛCDM parametrisation of the luminosity distance, the backreaction effect on q₀ remains below the detection threshold. Although the backreaction effect on j₀ is about ten times that on q₀, it is also below the detection threshold. Hence backreaction remains unobservable both in q₀ and in j₀.