论文标题
$ f（r）$ f（r）中的二进制系统的重力辐射：一种半古典方法
Gravitational radiation from binary systems in $f(R)$ gravity: A semi-classical approach
论文作者
论文摘要
准稳定的紧凑型二进制系统的能量损失和轨道周期衰减的速率是在$ f（r）$重力理论中得出的，它使用经典源的单个顶点重力发射过程的方法。在爱因斯坦框架中以同等标量张量格式编写的$ f（r）$动作线性后，我们确定了无质量的旋转2张量张量模式，大量标量模式和能量动量张量之间的适当相互作用项。标量字段的定义与$ f（r）$模型有关。然后，使用相互作用顶点，我们计算自旋2四极辐射引起的能量损失速率，该辐射与具有乘法因子的Peter-Mathews公式相同，也是标量偶极辐射引起的能量损失。总能量损失是这两个贡献的总和。我们的推导是最笼统的，因为它适用于二元轨道的任意偏心率和标量场的任意质量。使用二进制系统期间衰减的衍生理论公式，我们比较了$ f（r）$重力和一般相对性的预测，即观察到四个二进制系统，即Hulse-Taylor Binary，PSR J1141-6545，PSR J1141-6545，PSR J1738+0333+0333，以及PSR J0333，以及PSR J0348+0432。因此，我们将三种著名的$ F（R）$ Dark Energy模型（即Hu-Sawicki，Starobinsky和Tsujikawa模型）进行了限制。我们从Tsujikawa模型，即$ \ vert f'（r_0）-1 \ vert <2.09 <2.09 \ times 10^{ - 4} $。这种结合比大多数天体物理观察甚至一些宇宙学观察的强度都要强。
The rate of energy loss and orbital period decay of quasi-stable compact binary systems are derived in $f(R)$ theory of gravity using the method of a single vertex graviton emission process from a classical source. After linearising the $f(R)$ action written in an equivalent scalar-tensor format in the Einstein frame, we identify the appropriate interaction terms between the massless spin-2 tensor mode, massive scalar mode, and the energy momentum tensor. The definition of the scalar field is related to the $f(R)$ models. Then using the interaction vertex we compute the rate of energy loss due to spin-2 quadrupole radiation, which comes out to be the same as the Peter-Mathews formula with a multiplication factor, and also the energy loss due to the scalar dipole radiation. The total energy loss is the sum of these two contributions. Our derivation is most general as it is applicable for both arbitrary eccentricity of the binary orbits and arbitrary mass of the scalar field. Using the derived theoretical formula for the period decay of the binary systems, we compare the predictions of $f(R)$ gravity and general relativity for the observations of four binary systems, i.e. Hulse-Taylor Binary, PSR J1141-6545, PSR J1738+0333, and PSR J0348+0432. Thus we put bound on three well-known $f(R)$ dark energy models, namely the Hu-Sawicki, the Starobinsky, and the Tsujikawa model. We get the best constraint on $f'(R_0)-1$ (where $R_0$ is the scalar curvature of the Universe at the present epoch) from the Tsujikawa model, i.e $\vert f'(R_0)-1\vert < 2.09\times 10^{-4}$. This bound is stronger than those from most of the astrophysical observations and even some cosmological observations.
