Evolution of growth density equation by constraints on effective Newtonian constant G eff

Abstract

The acceleration of the Universe is described as a consequence of the extrinsic curvature of a four dimensional space–time embedded in a five dimensional bulk space, defined by the Einstein–Hilbert principle. Using the linear approximation of the Nash–Greene embedding theorem, we obtain the related perturbed equations in which only the gravitational-tensor field equations contribute to the propagation of the cosmological perturbations. In accordance with big bang nucleosynthesis and solar constraints, we calculate numerically the effective Newtonian function G eff to constrain the related parameters of the model. We numerically solve the growth density equation for two possible family of solutions leading to growth overdensities and, in some cases, a mild damping of the growth profiles, with a top amplification of the growth perturbations around 14% in comparison with ΛCDM and wCDM models. The behaviour of the effective gravitational potential Φ and the Newtonian curvature Ψ is also analysed showing mild perturbations in early times induced only by the extrinsic curvature differently from the ΛCDM standards.