We explore cosmological perturbations in a modified Gauss–Bonnet [Formula: see text] gravity, using a [Formula: see text] covariant formalism. In such a formalism, we define gradient variables to get perturbed linear evolution equations. We transform these linear evolution equations into ordinary differential equations using a spherical harmonic decomposition method. The obtained ordinary differential equations are time-dependent and then transformed into redshift-dependent. After these transformations, we analyze energy-density perturbations for two fluid systems, namely, for a Gauss–Bonnet field-dust system and for a Gauss–Bonnet field-radiation system for three different pedagogical [Formula: see text] models: trigonometric, exponential and logarithmic. For the Gauss–Bonnet field-dust system, energy-density perturbations decay with increase in redshift for all the three models. For the Gauss–Bonnet field-radiation system, the energy-density perturbations decay with increase in redshift for all of the three [Formula: see text] models for long wavelength modes whereas for short wavelength modes, the energy-density perturbations decay with increasing redshift for the logarithmic and exponential [Formula: see text] models and oscillate with decreasing amplitude for the trigonometric [Formula: see text] model.

This work treats cosmological perturbation in a mixture of standard matter, Chaplygin gas as well as Gauss–Bonnet fluids using a 1+3 covariant approach in the context of modified [Formula: see text] gravity. We define the gradient variables to obtain linear perturbation equations. After scalar and redshift transformations, we consider both an original Chaplygin and generalized Chaplygin gas models under Gauss–Bonnet gravity. For pedagogical purposes, the consideration of polynomial [Formula: see text] gravity model was used to solve the perturbation equations for short- and long-wavelength modes and investigate the late-time evolution. The numerical solutions were obtained. The results show that the energy overdensity perturbations decay with an increase in redshift. The treatment recovers GR results under limiting cases.

In this study, we present the evolution of cosmological perturbations in a universe consisting of standard matter and interacting vacuum. We use the [Formula: see text] covariant formalism in perturbation framework and consider two different models for the interacting vacuum; namely, a linear interacting model and interaction with creation pressure model. For both models, we derive the evolution equations governing the growth of linear perturbations for both radiation- and dust-dominated universe. We find numerical solutions in appropriate limits, namely long and short wavelengths. For both models, the perturbations grow with time (decay with redshift), showing that structure formation is possible in an accelerated cosmic background. The perturbation amplitudes — and their relative scalings with those of [Formula: see text]CDM — depend on the values of the interaction parameters considered, and in a way that can be used to constrain the models using existing and future large-scale structure data. In the vanishing limits of the coupling parameters of the interaction, we show that standard [Formula: see text]CDM cosmology, both background and perturbed, is recovered.

In this study, we present the evolution of cosmological perturbations in a universe consisting of standard matter and interacting vacuum. We use the 1 + 3 covariant formalism in perturbation framework and consider two different models for the interacting vacuum; namely, a linear interacting model and interaction with creation pressure model. For both models, we derive the evolution equations governing the growth of linear perturbations for both radiation-and dust-dominated Universe. We find numerical solutions in appropriate limits, namely long and short wavelengths. For both models, the perturbations grow with time (decay with redshift), showing that structure formation is possible in an accelerated cosmic background. The perturbation amplitudes -and their relative scalings with those of ΛCDM -depend on the values of the interaction parameters considered, and in a way that can be used to constrain the models using existing and future large-scale structure data. In the vanishing limits of the coupling parameters of the interaction, we show that standard ΛCDM cosmology, both background and perturbed, is recovered.