In this work we shall study the implications of a subclass of $E$-models cosmological attractors, namely of $a$-attractors, on hydrodynamically stable slowly rotating neutron stars. Specifically, we shall present the Jordan frame theory of the $a$-attractors, and by using a conformal transformation we shall derive the Einstein frame theory. We discuss the inflationary context of $a$-attractors in order to specify the allowed range of values for the free parameters of the model based on the latest cosmic-microwave-background-based Planck 2018 data. Accordingly, using the notation and physical units frequently used in theoretical astrophysics contexts, we shall derive the Tolman–Oppenheimer–Volkoff equations in the Einstein frame. Assuming a piecewise polytropic equation of state, the lowest density part of which shall be chosen to be the WFF1, or APR or the SLy EoS, we numerically solve the Tolman–Oppenheimer–Volkoff equations using a double shooting python-based “LSODA” numerical code. The resulting picture depends on the value of the parameter $a$ characterizing the $a$-attractors. As we show, for large values of $a$, which do not produce a viable inflationary era, the $M$–$R$ graphs are nearly identical to the general relativistic result, and these two are discriminated at large central densities values. Also, for large $a$-values, the WFF1 equation of state is excluded, due to the GW170817 constraints on the radius of an $M\sim 1.6M_{\odot }$ neutron star, which must be larger than $R=10.68_{-0.04}^{+15}$km and on the radius corresponding to the maximum mass which must be larger than $R=9.6_{-0.03}^{+0.14}$km. In addition, the small $a$ cases produce larger masses and radii compared to the general relativistic case and are compatible with the GW170817 constraints on the radii of neutron stars. A notable feature is that as the parameter $a$ decreases, the radii of the static hydrodynamically stable neutron stars increase. Our results indicate deep and not yet completely understood connections between non-minimal inflationary attractors and neutron stars phenomenology in scalar–tensor theory.

在这项工作中，我们将研究一个子类的含义。 $E$-模型宇宙吸引子，即 $\mathrm{一个}$吸引子，在流体力学稳定的缓慢旋转的中子星上。具体来说，我们将介绍约旦框架理论$\mathrm{一个}$吸引子，并通过使用保形变换，我们将得出爱因斯坦框架理论。我们讨论了通货膨胀的背景$\mathrm{一个}$-吸引子，以便基于最新的基于宇宙微波背景的Planck 2018数据为模型的自由参数指定允许的值范围。因此，使用在理论天体物理学中经常使用的符号和物理单位，我们将在爱因斯坦框架中推导Tolman–Oppenheimer–Volkoff方程。假设一个分段的多态状态方程，其最低密度部分应选择为WFF1或APR或SLy EoS，我们使用基于python的两次射击“ LSODA”数值对Tolman–Oppenheimer–Volkoff方程进行数值求解代码。生成的图片取决于参数的值$\mathrm{一个}$ 表征 $\mathrm{一个}$吸引人。如我们所示，对于$\mathrm{一个}$，这不会产生可行的通货膨胀时代， $\mathrm{中号}$–$\mathrm{[R}$图与一般相对论结果几乎相同，并且在较大的中心密度值时将这两个图区分开。另外，对于大$\mathrm{一个}$值，则由于GW170817限制了WFF1状态方程的半径，因此排除了WFF1状态方程。 $\mathrm{中号}〜\mathrm{1个}。6{\mathrm{中号}}_{\odot }$ 中子星，必须大于 $\mathrm{[R}=10。68_{-0。04}^{+15}$km，并且在对应于最大质量的半径上，该最大质量必须大于 $\mathrm{[R}=9。6_{-0。03}^{+0。14}$公里 另外，小$\mathrm{一个}$与一般相对论情况相比，这种情况产生的质量和半径更大，并且与GW170817对中子星半径的约束兼容。一个显着的特点是作为参数$\mathrm{一个}$减小，静水动力稳定的中子星的半径增加。我们的结果表明，在标量-张量理论中，非最小膨胀吸引子与中子星现象学之间的联系尚未完全理解。