Constraints on multi-fluid cosmology in f(G) gravity with different observational data sets

Abstract In the present work, we incorporate redshift space distortion measurement to investigate the growth of large scale structure within the framework of multi-fluid cosmology in the context of f ( G ) gravity. Using 3 different f ( G ) gravity models, where f ( G ) is the function of Gauss–Bonnet invariant, we compare the predictions of f ( G ) gravity expansion history—through the Friedmann equation with Hubble data, BAO data sets and constrain models parameters such as $$\Omega _{m}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Ω</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:math> and $$H_{0}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> . Within the context of multi-fluid cosmology in f ( G ) gravity, we obtain the structure growth equation. This equation is then combined with $$\sigma _{8}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mn>8</mml:mn> </mml:msub> </mml:math> to get $$f\sigma _{8}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:msub> <mml:mi>σ</mml:mi> <mml:mn>8</mml:mn> </mml:msub> </mml:mrow> </mml:math> predictions—which is compared with redshift space distortion data to constrain models parameters to obtain best-fit values including $$\sigma _{8}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mn>8</mml:mn> </mml:msub> </mml:math> . This involves performing a Markov Chain Monte Carlo (MCMC) analysis for these specific forms of f ( G ) models. we also perform a statistical analysis incorporating the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), to assess the goodess-of-fit of the considered models.