散焦暗能量：超越 $w < -1/3$ 的瑞查德利诊断与幽灵分界线
Defocusing dark energy: Raychaudhuri diagnostics beyond $w<-1/3$ and the phantom divide
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中文总结 AI 辅助
研究广义相对论中宇宙加速与能动张量相关问题，针对变号暗能量，用新组合替代传统指标，证明相关量性质，推导暗能量密度导数范围，结果表明应围绕(\(\rho,p,\mathcal{I},\mathcal{M}\))组织晚期推断而非仅\(w\)。
中文摘要 AI 辅助
在广义相对论中，宇宙加速是共动测地线汇的类时散焦，需要负的总有效引力质量密度\(\mathcal{M}_{\rm tot}=\rho_{\rm tot}+3p_{\rm tot}<0\)。\(w\equiv p/\rho<-1/3\)准则仅对\(\rho>0\)诊断扇区排斥：\(\rho<0\)时不等式反转，且\(\rho = 0\)时比率变量无定义，即使应力 - 能量张量有限。对于变号有效暗能量，如\(\Lambda_{\rm s}\)CDM型历史，我们改用带符号密度\(\rho_{\rm de}\)和两个与分支无关的组合。正则零能量条件（NEC）边界\(\mathcal{I}_{\rm de}=\rho_{\rm de}+p_{\rm de}=0\)取代幽灵分界线\(w_{\rm de}=-1\)，而\(\mathcal{M}_{\rm de}=\rho_{\rm de}+3p_{\rm de}<0\)控制扇区级别的瑞查德利排斥。对于在\(z_\dagger\)处有有限奇数次\(n\)的从负到正密度平滑穿越的单独守恒暗能量扇区，我们证明\(\mathcal{I}_{\rm de}\)和\(\mathcal{M}_{\rm de}\)在穿孔邻域为负且在穿越处非正，而\(w_{\rm de}\)发展出具有通用留数\(n(1 + z_\dagger)/3\)的运动极点。如果\(\mathcal{M}_{\rm de}\)在某个足够高的红移处\(>0\)，连续性要求至少有一个排斥边界\(z_{\rm rep}>z_\dagger\)：该扇区在\(\rho_{\rm de}<0\)时就已经是排斥的。我们推导了在满足总NEC的穿越处加速时\(\rho_{\rm de}'(z_\dagger)\)的精确范围。在所述单脉冲和平稳点假设下，减速参数有一个或三个变号零点。平滑的\(\Lambda_{\rm s}\)CDM轮廓、指数红外\(f(T)\)模型和最小幽灵膜说明了结果。这些结果促使围绕\((\rho,p,\mathcal{I},\mathcal{M})\)而非仅围绕\(w\)组织晚期推断。
英文摘要
In general relativity, cosmic acceleration is timelike defocusing of the comoving congruence and requires a negative total active gravitational mass density, $\mathcal{M}_{\rm tot}=ρ_{\rm tot}+3p_{\rm tot}<0$. The criterion $w\equiv p/ρ<-1/3$ diagnoses sector repulsion only for $ρ>0$: the inequality reverses for $ρ<0$, and ratio variables are ill-defined at $ρ=0$ even when the stress-energy tensor is finite. For sign-changing effective dark energy (DE), as in $Λ_{\rm s}$CDM-type histories, we instead use the signed density $ρ_{\rm de}$ and two branch-independent combinations. The regular null energy condition (NEC) boundary $\mathcal{I}_{\rm de}=ρ_{\rm de}+p_{\rm de}=0$ replaces the phantom divide $w_{\rm de}=-1$, while $\mathcal{M}_{\rm de}=ρ_{\rm de}+3p_{\rm de}<0$ governs sector-level Raychaudhuri repulsion. For a separately conserved DE sector with a smooth negative-to-positive density crossing of finite odd order $n$ at $z_\dagger$, we prove that $\mathcal{I}_{\rm de}$ and $\mathcal{M}_{\rm de}$ are negative in a punctured neighborhood and non-positive at the crossing, while $w_{\rm de}$ develops a kinematic pole with universal residue $n(1+z_\dagger)/3$. If $\mathcal{M}_{\rm de}>0$ at some sufficiently high redshift, continuity requires at least one repulsion boundary $z_{\rm rep}>z_\dagger$: the sector is already repulsive while $ρ_{\rm de}<0$. We derive the exact range of $ρ_{\rm de}'(z_\dagger)$ for acceleration at the crossing with the total NEC satisfied. Under the stated single-impulse and stationary-point assumptions, the deceleration parameter has one or three sign-changing zeros. A smooth $Λ_{\rm s}$CDM profile, an exponential infrared $f(T)$ model, and the minimal phantom brane illustrate the results. These results motivate organizing late-time inference around $(ρ,p,\mathcal{I},\mathcal{M})$ rather than around $w$ alone.
