Effective Pressure of the FRW Universe
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914219598807040 |
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| author | Kong, Shi-Bei |
| author_facet | Kong, Shi-Bei |
| contents | In this paper, we study the effective pressure of the $N$-dimensional FRW(Friedmann-Robertson-Walker) universe in Einstein gravity, Gauss-Bonnet gravity, and Lovelock gravity. The effective pressure is defined by $P_{eff}:=-d E/d V$, where $E=ρV$ is the effective energy and $V$ is the volume of the FRW universe inside the apparent horizon. The effective pressure in Einstein gravity is always negative and its absolute value decreases with the horizon radius $R_A$. The effective pressure in Gauss-Bonnet gravity is different with the one in Einstein gravity only when $N\geq6$. In this case, if $α>0$, the effective pressure is always negative, but if $α<0$, it is not always negative and has a minimum. The effective pressure in Lovelock gravity can have multiple zero-points and extreme points. The effective pressure in different dimensions has interesting relations. We also find that under certain condition, the effective pressure is equivalent with the `ordinary' pressure $p$ of the perfect fluid, and this condition do not depend on the specific choice of gravitational theories. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_17789 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Effective Pressure of the FRW Universe Kong, Shi-Bei General Relativity and Quantum Cosmology High Energy Physics - Theory In this paper, we study the effective pressure of the $N$-dimensional FRW(Friedmann-Robertson-Walker) universe in Einstein gravity, Gauss-Bonnet gravity, and Lovelock gravity. The effective pressure is defined by $P_{eff}:=-d E/d V$, where $E=ρV$ is the effective energy and $V$ is the volume of the FRW universe inside the apparent horizon. The effective pressure in Einstein gravity is always negative and its absolute value decreases with the horizon radius $R_A$. The effective pressure in Gauss-Bonnet gravity is different with the one in Einstein gravity only when $N\geq6$. In this case, if $α>0$, the effective pressure is always negative, but if $α<0$, it is not always negative and has a minimum. The effective pressure in Lovelock gravity can have multiple zero-points and extreme points. The effective pressure in different dimensions has interesting relations. We also find that under certain condition, the effective pressure is equivalent with the `ordinary' pressure $p$ of the perfect fluid, and this condition do not depend on the specific choice of gravitational theories. |
| title | Effective Pressure of the FRW Universe |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2507.17789 |