Cosmological perturbations in Palatini formalism
Cosmological perturbations in Palatini formalism
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DOI：
10.1088/1475-7516/2021/03/006
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发表时间：
2020-10
影响因子：
6.4
通讯作者：
Mio Kubota;Kin-ya Oda;K. Shimada;Masahide Yamaguchi
中科院分区：
文献类型：
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作者：
Mio Kubota;Kin-ya Oda;K. Shimada;Masahide Yamaguchi
我们研究Palatini形式的标量张量理论的宇宙学扰动。首先我们引入一个作用量，其中Ricci标量共形耦合到标量场的函数及其动力学项，并且还有一个由标量及其动力学项组成的k-本质项。这个作用有三个相互等价的框架：原始的约旦框架，重新定义度量的爱因斯坦框架，以及重新定义联系的黎曼框架。在文献中，我们第一次计算的平方作用和声速的标量和张量微扰在三个不同的框架，并明确表明，他们一致。此外，我们还证明了在这种作用下引力波的声速是单位的。因此，这个模型作为暗能量以及暴胀子，即使在非最小耦合的标量场的动力学项的依赖性的存在下，从度量形式主义的情况下不同。然后，我们继续构造L3的行动称为Galileon条款Palatini形式主义和计算其扰动。我们发现，基本上有10个不同的（不等价的）定义在Palatini形式主义为一个给定的Galileon长期度量形式主义。我们还看到，一般来说，由于Ostrogradsky不稳定性，L3项有一个鬼，引力波的声速可能偏离1，与度规形式主义的情况形成鲜明对比。有趣的是，一旦我们消除了这样的幽灵，引力波的声速也变成了1。因此，帕拉蒂尼形式主义中的无幽灵L3项仍然可以作为暗能量以及暴胀子，就像度规形式主义中的情况一样。
We investigate cosmological perturbations of scalar-tensor theories in Palatini formalism. First we introduce an action where the Ricci scalar is conformally coupled to a function of a scalar field and its kinetic term and there is also a k-essence term consisting of the scalar and its kinetic term. This action has three frames that are equivalent to one another: the original Jordan frame, the Einstein frame where the metric is redefined, and the Riemann frame where the connection is redefined. For the first time in the literature, we calculate the quadratic action and the sound speed of scalar and tensor perturbations in three different frames and show explicitly that they coincide. Furthermore, we show that for such action the sound speed of gravitational waves is unity. Thus, this model serves as dark energy as well as an inflaton even though the presence of the dependence of the kinetic term of a scalar field in the non-minimal coupling, different from the case in metric formalism. We then proceed to construct the L3 action called Galileon terms in Palatini formalism and compute its perturbations. We found that there are essentially 10 different (inequivalent) definitions in Palatini formalism for a given Galileon term in metric formalism. We also see that, in general, the L3 terms have a ghost due to Ostrogradsky instability and the sound speed of gravitational waves could potentially deviate from unity, in sharp contrast with the case of metric formalism. Interestingly, once we eliminate such a ghost, the sound speed of gravitational waves also becomes unity. Thus, the ghost-free L3 terms in Palatini formalism can still serve as dark energy as well as an inflaton, like the case in metric formalism.