标题： 宇宙无发猜想在二次齐次宇宙学中的证明 显示英文标题

标题： Proof of the Cosmic No-Hair Conjecture for Quadratic Homogeneous Cosmologies

摘要： 我们使用共形等价的爱因斯坦场方程，证明了在具有物质的$R+\beta R^2$理论中所有正交 Bianchi 宇宙的宇宙无发 conjecture，其中标量场具有完整的自相互作用势，在共形相关的物质场存在的情况下。我们特别表明，如果初始时标量三曲率不超过与共形变换相关的标量场的势，则 Bianchi IX 宇宙将渐近地趋近于 de Sitter 空间。我们的证明依赖于所谓的 Moss-Sahni 函数可能界限的严格估计，该函数服从某些微分不等式，并且需要一个非平凡的论证，将该函数的行为与标量曲率的空间部分的演化联系起来。 显示英文摘要

摘要： We prove the cosmic no-hair conjecture for all orthogonal Bianchi cosmologies with matter in the $R+\beta R^2$ theory using the conformally equivalent Einstein field equations, with the scalar field having the full self-interacting potential, in the presence of the conformally related matter fields. We show, in particular, that the Bianchi IX universe asymptotically approaches de Sitter space provided that initially the scalar three-curvature does not exceed the potential of the scalar field associated with the conformal transformation. Our proof relies on rigorous estimates of the possible bounds of the so-called Moss-Sahni function which obeys certain differential inequalities and a non-trivial argument which connects the behaviour of that function to evolution of the spatial part of the scalar curvature.