We consider a gravitational theory with an additional non-minimal coupling between baryonic matter fields and geometry. The coupling is second order in the energy momentum tensor and can be seen as a generalization of the energy–momentum squared gravity model. We will add a constraint through a Lagrange multiplier to ensure the conservation of the energy–momentum tensor. Background cosmological implications together with its dynamical system analysis will be investigated in details. Also we will consider the growth of matter perturbations at first order, and estimate the model parameter from observations on H and also \(f\sigma _8\). We will show that the model parameter should be small and positive in 2\(\sigma \) confidence interval. The theory is shown to be in a good agreement with observational data.

我们考虑一种重子理论，在重子物质场和几何之间还存在一个附加的非最小耦合。耦合在能量动量张量中是二阶的，可以看作是能量动量平方重力模型的推广。我们将通过拉格朗日乘数添加一个约束，以确保能量动量张量的守恒。我们将详细研究背景宇宙学的含义及其动力学系统分析。我们还将考虑一阶物质扰动的增长，并根据对H以及\（f \ sigma _8 \）的观测值估计模型参数。我们将显示模型参数应小且在2 \（\ sigma \）中为正置信区间。该理论与观测数据非常吻合。