https://doi.org/10.1140/epjc/s10052-022-10561-0
Regular Article - Theoretical Physics
Inferring 
and 
with cosmic growth rate measurements using machine learning
1
Observatório Nacional, Rua General José Cristino 77, São Cristóvão, 20921-400, Rio de Janeiro, RJ, Brazil
2
Departamento de Física, Universidade Federal de Juiz de Fora, 36036-330, Juiz de Fora, MG, Brazil
3
Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970, Porto Alegre, RS, Brazil
4
Instituto Nacional de Pesquisas Espaciais, Av. dos Astronautas 1758, Jardim da Granja, São José dos Campos, SP, Brazil
Received:
12
May
2022
Accepted:
26
June
2022
Published online:
6
July
2022
Measurements of the cosmological parameter 
provided by cosmic microwave background and large scale structure data reveal some tension between them, suggesting that the clustering features of matter in these early and late cosmological tracers could be different. In this work, we use a supervised learning method designed to solve Bayesian approach to regression, known as Gaussian Processes regression, to quantify the cosmic evolution of up to 
. For this, we propose a novel approach to find firstly the evolution of the function 
, then we find the function . As a sub-product we obtain a minimal cosmological model-dependent 
and 
estimates. We select independent data measurements of the growth rate f(z) and of 
according to criteria of non-correlated data, then we perform the Gaussian reconstruction of these data sets to obtain the cosmic evolution of , , and the growth index . Our statistical analyses show that is compatible with Planck 
CDM cosmology; when evaluated at the present time we find 
and 
. Applying our methodology to the growth index, we find 
. Moreover, we compare our results with others recently obtained in the literature. In none of these functions, i.e. , , and , do we find significant deviations from the standard cosmology predictions.
© The Author(s) 2022
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