https://doi.org/10.1140/epjc/s10052-023-12381-2
Regular Article – Theoretical Physics
On covariant perturbations with scalar field in modified Gauss–Bonnet gravity
1
Department of Physics, Mbarara University of Science and Technology, Mbarara, Uganda
2
Department of Physics, College of Science and Technology, University of Rwanda, Kigali, Rwanda
3
Rwanda Academy of Science, Kigali, Rwanda
4
ICTP-East Africa Institute for Fundamental Research, Kigali, Rwanda
5
Rochester Institute of Technology, Rochester, NY, USA
Received:
19
October
2023
Accepted:
22
December
2023
Published online:
18
January
2024
We investigate cosmological perturbations of f(G) gravity in the presence of a scalar field. Using the 
covariant formalism, we present the energy overdensity perturbation equations responsible for large scale structure formation. After applying harmonic decomposition method together with the redshift transformation technique, we obtain the fully perturbed equations in redshift space. The equations are solved to study the growth of matter overdensities contrast with redshift. For both short- and long-wavelength modes, we obtain numerical results for particular functional form f(G) models and scalar field. We find that, for this choice the energy overdensity perturbations decay with increase in redshift. However, for both short- and long-wavelength modes, the perturbations which include amplitude effects due to the f(G) models with a scalar field do differ remarkably from those in 
CDM. The results reduce to GR results in the limit of 
and in the absence of scalar field.
© The Author(s) 2024
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