On covariant perturbations with scalar field in modified Gauss–Bonnet gravity
Albert Munyeshyaka, Joseph Ntahompagaze, Tom Mutabazi, Manasse R. Mbonye
Abstract
Abstract We investigate cosmological perturbations of f ( G ) gravity in the presence of a scalar field. Using the $$1+3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> 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 $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM. The results reduce to GR results in the limit of $$f(G)\rightarrow G$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> <mml:mo>→</mml:mo> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> and in the absence of scalar field.