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.

宇宙的加速是由爱因斯坦-希尔伯特原理定义的，嵌入在五维体积空间中的四维时空的外在曲率造成的。使用Nash-Greene嵌入定理的线性逼近，我们获得了相关的扰动方程，其中只有引力-张量场方程有助于宇宙扰动的传播。根据大爆炸核合成和太阳约束，我们通过数值计算有效牛顿函数G _eff约束模型的相关参数。我们用数值方法求解了两个可能的解决方案族的增长密度方程，从而导致增长密度过大，并且在某些情况下，对增长曲线产生了温和的衰减，与ΛCDM和w CDM模型相比，增长扰动最大放大了约14％。还分析了有效引力Φ和牛顿曲率behavior的行为，显示出仅由外在曲率引起的，与ΛCDM标准不同的早期轻度扰动。