__C. S. Carvalho__, S. Basilakos

**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 H_{0}, the deceleration parameter q_{0}, and the jerk parameter j_{0}. 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 j_{0} due to the fluctuations of { H_{0},q_{0} } 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 q_{0} remains below the detection threshold. Although the backreaction effect on j_{0} is about ten times that on q_{0}, it is also below the detection threshold. Hence backreaction remains unobservable both in q_{0} and in j_{0}.

**Keywords**

methods: statistical, cosmological parameters

**Astronomy and Astrophysics**

Volume 592, Article Number A152, Number of pages 11

2016 August