论文标题
$λ$ CDM背景的弱重力
Weak gravity on a $Λ$CDM background
论文作者
论文摘要
我们认为Horndeski修饰的重力模型遵守稳定性，重力波的速度$ C_T $等于$ C $和Subhorizon量表上的准近似近似（QSA）。 We assume further a $Λ$CDM background expansion and a monotonic evolution on the cosmic background of the $α$ functions as $α_i= α_{i0}~a^s$ where $i=M,B$, $a$ is the scale factor and $α_{i0}$ ($α_{M0}, α_{B0}$), $s$ are arbitrary parameters.我们表明，生长和镜头减少（无量纲）重力耦合$μ\ equiv g _ {\ rm增长}/g $，$σ\ equiv g _ {\ rm镜头}/g $如今显示以下通用属性：$σ_0<1 $ $ nise $ $ $ $ $ $μ0<1 <1 <1 <1 <1 <1 $μ_0> 1 $对大$ S $受到青睐。我们还始终建立关系$ \geqσ$。考虑到$fσ_8$和$ e_g $ data将参数$ s $限制为满足$ s \ S \ Lessim 2 $。因此，这些数据基本上选择了今天的弱重力制度（$μ_0<1 $），而当$ s <2 $，而$μ_0> 1 $仅对$ s \ 2 $少少。至少在没有筛选的情况下，将排除间隔$ 0.5 \ Lessim S \ Lessim 2 $。我们进一步考虑增长指数$γ（z）$，并确定$（α_{m0}，α_{b0}，s），s）$参数区域，与差异$γ_0-γ_0^{λcdm} $相对应的特定迹象γ\ bigl | _ {z = 0} $和$γ_1\ equiv \ frac {{\ rm d}γ} {\ rm d z} \ rm d z} \ bigl | _ {z = 0} $。这样，重要的信息就会获得$μ$的过去发展。我们特别在选定的弱重力区域中获得$ s <2 $的签名$γ_0>γ_0^{λcdm} $。
We consider Horndeski modified gravity models obeying stability, velocity of gravitational waves $c_T$ equals $c$ and quasistatic approximation (QSA) on subhorizon scales. We assume further a $Λ$CDM background expansion and a monotonic evolution on the cosmic background of the $α$ functions as $α_i= α_{i0}~a^s$ where $i=M,B$, $a$ is the scale factor and $α_{i0}$ ($α_{M0}, α_{B0}$), $s$ are arbitrary parameters. We show that the growth and lensing reduced (dimensionless) gravitational couplings $μ\equiv G_{\rm growth}/G$, $Σ\equiv G_{\rm lensing}/G$ exhibit the following generic properties today: $Σ_0 < 1$ for all viable parameters, $μ_0<1$ (weak gravity today) is favored for small $s$ while $μ_0>1$ is favored for large $s$. We establish also the relation $μ\geq Σ$ at all times. Taking into account the $fσ_8$ and $E_G$ data constrains the parameter $s$ to satisfy $s\lesssim 2$. Hence these data select essentially the weak gravity regime today ($μ_0<1$) when $s<2$, while $μ_0>1$ subsists only marginally for $s\approx 2$. At least the interval $0.5\lesssim s \lesssim 2$ would be ruled out in the absence of screening. We consider further the growth index $γ(z)$ and identify the $(α_{M0},α_{B0},s)$ parameter region that corresponds to specific signs of the differences $γ_0-γ_0^{ΛCDM}$, and $γ_1-γ_1^{ΛCDM}$, where $γ_0\equiv γ\bigl|_{z=0}$ and $γ_1\equiv \frac{{\rm d}γ}{\rm d z}\bigl|_{z=0}$. In this way important information is gained on the past evolution of $μ$. We obtain in particular the signature $γ_0>γ_0^{ΛCDM}$ for $s<2$ in the selected weak gravity region.
