粒子产生的量子效应对f（R）引力背景演化和Cardy-Verlinde公式的影响
Quantum effects from particle production on background evolution and Cardy-Verlinde formula in f(R) gravity
摘要：
我们研究了膨胀宇宙中粒子的产生，假设拉格朗日量包含爱因斯坦项$R$加上一个形式为$R^α$的修正引力项，其中$α$是一个常数。暗流体被认为是宇宙的主要内容，出现了大撕裂奇点。分析了在奇点附近粒子产生的量子效应，发现对于$α\in ]1/2, 1[$，量子效应占主导地位，可以避免大撕裂，而对于$α\in J$，暗流体占主导地位，奇点仍然存在。还介绍了Cardy-Verlinde公式，并检查了它与宇宙总熵的等价性。发现这在爱因斯坦引力中总是可以发生，而在f（R）引力中，它只对$α=\frac{n+1}{2n+6}$成立，$n$是空间维，对应于大裂缝无法避免的情况。
英文摘要：
We investigate particle production in an expanding universe under the assumption that the Lagrangian contains the Einstein term $R$ plus a modified gravity term of the form $R^α$, where $α$ is a constant. Dark fluid is considered as the main content of the universe and the big rip singularity appears. Quantum effects due to particle creation is analysed near the singularity and we find that for $α\in ]1/2, 1[$, quantum effects are dominant and the big rip may be avoided whereas for $α\in J$ the dark fluid is dominant and the singularity remains. The Cardy-Verlinde formula is also introduced and its equivalence with the total entropy of the universe is checked. It is found that this can always occur in Einstein gravity while in f(R) gravity, it holds only for $α=\frac{n+1}{2n+6}$, $n$ being the space dimension, corresponding to the situation in which the big rip cannot be avoided.
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