标题： 具有刚性物质时代的宇宙学 显示英文标题

标题： Cosmology with a stiff matter era

摘要： 我们为由刚性物质、尘埃物质和暗能量组成的宇宙提供了Friedmann方程的一个简单解析解。 Zel'dovich（1972）的宇宙学模型中存在一个刚性物质时代，其中假设原始宇宙是由重子的冷气体组成的。 在某些暗物质由相对论性的自引力玻色-爱因斯坦凝聚体（BECs）组成的宇宙学模型中也会出现这种情况。 当刚性物质的能量密度为正值时，原始宇宙是奇点的。它起始于一个尺度因子为零且密度无限大的状态。 我们考虑刚性物质的能量密度为负值（反刚性物质）的可能性。 例如，当BECs具有吸引的自相互作用时就会发生这种情况。在这种情况下，原始宇宙是非奇点的。 它起始于一个尺度因子有限且能量密度等于零的状态。 为了普遍性，我们考虑任意符号的宇宙常数。 当宇宙常数为正时，宇宙渐近达到一个de Sitter相，在此阶段尺度因子呈指数增长。 这可以解释我们目前观测到的宇宙加速膨胀。 当宇宙常数为负（反de Sitter），宇宙的演化是循环的。 因此，根据刚性物质和暗能量的能量密度符号的不同，我们得到奇点或非奇点的膨胀或循环宇宙。 显示英文摘要

摘要： We provide a simple analytical solution of the Friedmann equations for a universe made of stiff matter, dust matter, and dark energy. A stiff matter era is present in the cosmological model of Zel'dovich (1972) where the primordial universe is assumed to be made of a cold gas of baryons. It also occurs in certain cosmological models where dark matter is made of relativistic self-gravitating Bose-Einstein condensates (BECs). When the energy density of the stiff matter is positive, the primordial universe is singular. It starts from a state with a vanishing scale factor and an infinite density. We consider the possibility that the energy density of the stiff matter is negative (anti-stiff matter). This happens, for example, when the BECs have an attractive self-interaction. In that case, the primordial universe is non-singular. It starts from a state in which the scale factor is finite and the energy density is equal to zero. For the sake of generality, we consider a cosmological constant of arbitrary sign. When the cosmological constant is positive, the universe asymptotically reaches a de Sitter phase where the scale factor increases exponentially rapidly. This can account for the accelerating expansion of the universe that we observe at present. When the cosmological constant is negative (anti-de Sitter), the evolution of the universe is cyclic. Therefore, depending on the sign of the energy density of the stiff matter and of the dark energy, we obtain singular and non-singular expanding or cyclic universes.