扩展的帕拉蒂尼理论中丰富的现象学
Enriched Phenomenology in Extended Palatini Theories
摘要：
我们证明了在Palatini公式中具有拉格朗日函数f（R，R_{μν} R^{μν}）的广义引力理论具有比简单的f（R）或f（R_{μν} R^{μν}）理论丰富得多的唯象性。实际上，我们发现标量R和Q= R_{μν} R^{μν}可以写成能量动量张量的能量密度和压强的代数函数。在f（R）或f（R_{μν} R^{μν}）理论的简单情况下，R和Q只是能量-动量张量的迹T的函数。因此，在辐射主导的宇宙中，f（R）和f（R_{μν} R^{μν}）理论表现出与广义相对论相同的动力学，具有有效的宇宙学常数。f（R，R_{μν} R^{μν}）模型的情况并非如此，其中R=R（ρ，P）且Q=Q（ρ，P），因此，即使对于无迹源，也存在修改的动力学。
英文摘要：
We show that extended theories of gravity with Lagrangian f(R,R_{μν}R^{μν}) in the Palatini formulation possess a phenomenology much richer than the simpler f(R) or f(R_{μν}R^{μν}) theories. In fact, we find that the scalars R and Q=R_{μν}R^{μν} can be written as algebraic functions of the energy density and pressure of the energy momentum tensor. In the simpler cases of f(R) or f(R_{μν}R^{μν}) theories, R and Q are just functions of the trace T of the energy-momentum tensor. As a result, in radiation dominated universes f(R) and f(R_{μν}R^{μν}) theories exhibit the same dynamics as general relativity with an effective cosmological constant. This is not the case of f(R,R_{μν}R^{μν}) models, in which R=R(ρ,P) and Q=Q(ρ,P) and, therefore, modified dynamics exists even for traceless sources.
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