标题： 相对论自引力玻色-爱因斯坦凝聚体和具有刚性状态方程的冷重子 显示英文标题

标题： Relativistic self-gravitating Bose-Einstein condensates and cold baryons with a stiff equation of state

摘要： 由于其超流体性质，一些致密的天体物理对象（例如中子星）可能以玻色-爱因斯坦凝聚态（BEC）的形式包含其物质的重要部分。 我们考虑了一个部分相对论性的自引力BEC模型，在该模型中，压力与静止质量密度之间的关系被假设为二次关系（类似于经典BEC的情况），但在能量密度与静止质量密度之间的关系中考虑了压力效应。 在高密度下，我们得到一个刚性状态方程，类似于Zel'dovich（1961年）在重子星背景下所考虑的刚性状态方程，其中重子通过矢量介子场相互作用。 我们利用Tooper（1965年）的形式主义确定由这个状态方程描述的一般相对论BEC恒星的最大质量。 这个最大质量略大于Chavanis和Harko（2012年）使用完全相对论模型获得的最大质量。 我们还考虑暗物质是由BEC组成的可能性，并将BEC的部分相对论模型应用于宇宙学。 在这个模型中，我们表明宇宙经历了一种刚性物质阶段，随后是一个尘埃物质阶段，最后是一个暗能量阶段（相当于宇宙常数）。 Zel'dovich（1972年）模型也得到了相同的演化过程，该模型假定最初，在宇宙奇点附近，宇宙充满冷重子。 有趣的是，在这种情况下，Friedmann方程可以解析求解，并提供了一个简单的$\Lambda$CDM模型的推广。 然而，我们指出了部分相对论性BEC模型的局限性，并展示了需要一个完全相对论性的模型。 显示英文摘要

摘要： Because of their superfluid properties, some compact astrophysical objects such as neutron stars may contain a significant part of their matter in the form of a Bose-Einstein condensate (BEC). We consider a partially-relativistic model of self-gravitating BECs where the relation between the pressure and the rest-mass density is assumed to be quadratic (as in the case of classical BECs) but pressure effects are taken into account in the relation between the energy density and the rest-mass density. At high densities, we get a stiff equation of state similar to the one considered by Zel'dovich (1961) in the context of baryon stars in which the baryons interact through a vector meson field. We determine the maximum mass of general relativistic BEC stars described by this equation of state by using the formalism of Tooper (1965). This maximum mass is slightly larger than the maximum mass obtained by Chavanis and Harko (2012) using a fully-relativistic model. We also consider the possibility that dark matter is made of BECs and apply the partially-relativistic model of BECs to cosmology. In this model, we show that the universe experiences a stiff matter phase, followed by a dust matter phase, and finally by a dark energy phase (equivalent to a cosmological constant). The same evolution is obtained in Zel'dovich (1972) model which assumes that initially, near the cosmological singularity, the universe is filled with cold baryons. Interestingly, the Friedmann equations can be solved analytically in that case and provide a simple generalization of the $\Lambda$CDM model. We point out, however, the limitations of the partially-relativistic model for BECs and show the need for a fully-relativistic one.