Spatial flatness and large-scale Lorentz violation
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摘要: 局域测量得到的哈勃参数(
$ {H_0}$ )与基于$\Lambda {\rm{CDM}}$ (Lambda Cold Dark Matter Model)模型从微波背景辐射(Cosmic Microwave Background, CMB)测出来的哈勃参数之间存在不一致性, 促使人们超越标准宇宙学模型去考察新宇宙学模型, 比如空间非平坦的大尺度洛伦兹破缺模型. 由于空间曲率项、 宇宙学常数项和宇宙学扭曲(contortion)对于解释观测数据的贡献存在重叠简并, 这使得现有的模型对于解释观测数据具有存活空间. 通过对光度距离模量红移关系观测与模型预言的对比, 以及计算物质密度和有效宇宙学常数随时间的演化等途径, 将空间曲率密度限制在一定的范围以内, 并在此取值范围内讨论了空间不平坦的大尺度洛伦兹破缺模型的表现.Abstract: There is an inconsistency between the Hubble parameter obtained from local measurements and model-based parameters obtained from cosmic microwave background (CMB) measurements. This inconsistency motivated us to consider new cosmological models based on$\Lambda {\rm{CDM}}$ (Lambda Cold Dark Matter Model), such as a large-scale Lorentz violation model with non-vanishing spatial curvature. The degeneracy among the spatial curvature, cosmological constant, and cosmological contortion distribution makes the model viable for interpretation of the observation data. By comparing the luminosity distance modulus and redshift with the model prediction and calculating the change in matter density as well as the cosmological constant over time, we limit the spatial curvature density to a certain range. Accordingly, we discuss the performance of the large-scale Lorentz violation model with non-vanishing spatial curvature under these constraints.-
Key words:
- Lorentz violation /
- spatial curvature /
- Hubble constant
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图 16
$\ddot a$ 随尺度因子的演化: a)$K = +1 ,{a_0}{H_0} = 3.5 ,{\varLambda _0} = - 0.02 \varLambda$ ; b)$K = -1 ,{a_0}{H_0} = 3.5 ,{\varLambda _0} = - 0.02\varLambda$ Fig. 16
$\ddot a$ changes with the scale factor: a)$K = +1 ,{a_0}{H_0} = 3.5 ,{\varLambda _0} = - 0.02\varLambda$ ; b)$K = -1 ,{a_0}{H_0} = 3.5 ,{\varLambda _0} = - 0.02\varLambda$ 表 1
$K = + 1$ 情况下${\varLambda _{\max}}$ 的值Tab. 1 The value of
${\varLambda _{\max}}$ when$K = + 1$ 情形 ${a_0}{H_0}{\rm{ = } }2.0$ ${a_0}{H_0}{\rm{ = }}2.5$ ${a_0}{H_0}{\rm{ = 3.0} }$ ${a_0}{H_0}{\rm{ = 3}}{\rm{.5}}$ CaseA1 0.0008Λ 0.0007Λ 0.0006Λ 0.0007Λ CaseA2 0.0012Λ 0.0014Λ 0.0015Λ 0.0015Λ CaseB1 0.0008Λ 0.0007Λ 0.0007Λ 0.0006Λ CaseB2 0.0012Λ 0.0014Λ 0.0015Λ 0.0016Λ CaseC1(w0 = –1) 0.0008Λ 0.0007Λ 0.0007Λ 0.0006Λ CaseC2(w0 = –1) 0.0012Λ 0.0015Λ 0.0015Λ 0.0016Λ CaseC1(w0 = $-\frac{8}{9} $) 0.0008Λ 0.0007Λ 0.0007Λ 0.0006Λ CaseC2(w0 = $-\frac{8}{9} $) 0.0013Λ 0.0016Λ 0.0017Λ 0.0018Λ CaseC1(w0 = $-\frac{7}{9} $) 0.0008Λ 0.0007Λ 0.0007Λ 0.0006Λ CaseC2(w0 = $-\frac{7}{9} $) 0.0013Λ 0.0016Λ 0.0018Λ 0.0019Λ CaseC1(w0 = $-\frac{2}{3} $) 0.0008Λ 0.0007Λ 0.0006Λ 0.0006Λ CaseC2(w0 = $-\frac{2}{3} $) 0.0014Λ 0.0018Λ 0.0020 0.0022Λ CaseC1(w0 = $-\frac{1}{3} $) 0.0008Λ 0.0006Λ 0.0006Λ 0.0006Λ CaseC2(w0 = $-\frac{1}{3} $) 0.0025Λ 0.0046Λ 0.0056Λ 0.0062Λ 表 2
$K = - 1$ 情况下${\varLambda _{\max}}$ 的值Tab. 2 The value of
${\varLambda _{\max}}$ when$K = - 1$ 情形 ${a_0}{H_0}{\rm{ = 1}}{\rm{.5}}$ ${a_0}{H_0}{\rm{ = } }2.0$ ${a_0}{H_0}{\rm{ = }}2.5$ ${a_0}{H_0}{\rm{ = 3.0} }$ ${a_0}{H_0}{\rm{ = 3}}{\rm{.5}}$ CaseA1 0.0004Λ 0.0005Λ 0.0005Λ 0.0005Λ 0.0005Λ CaseA2 0.0023Λ 0.002Λ 0.0019Λ 0.0018Λ 0.0018Λ CaseB1 0.0004Λ 0.0004Λ 0.0005Λ 0.0005Λ 0.0005Λ CaseB2 0.0023Λ 0.002Λ 0.0019Λ 0.0019Λ 0.0018Λ CaseC1(w0 = –1) 0.0003Λ 0.0004Λ 0.0005Λ 0.0005Λ 0.0005Λ CaseC2(w0 = –1) 0.015Λ 0.0027Λ 0.0023Λ 0.0021Λ 0.002Λ CaseC1(w0 = $-\frac{8}{9} $) 0.0003Λ 0.0004Λ 0.0005Λ 0.0005Λ 0.0005Λ CaseC2(w0 = $-\frac{8}{9} $) 0.0033Λ 0.0033Λ 0.0026Λ 0.0024Λ 0.0023Λ CaseC1(w0 = $-\frac{7}{9} $) 0.0003Λ 0.0004Λ 0.0005Λ 0.0005Λ 0.0005Λ CaseC2(w0 = $-\frac{7}{9} $) 0.0032Λ 0.0032Λ 0.0032Λ 0.0028Λ 0.0026Λ CaseC1(w0 = $-\frac{2}{3} $) 0.0003Λ 0.0004Λ 0.0004Λ 0.0004Λ 0.0005Λ CaseC2(w0 = $-\frac{2}{3} $) 0.0185Λ 0.0091Λ 0.0054Λ 0.0037Λ 0.0031Λ CaseC1(w0 = $-\frac{1}{3} $) 0.001Λ 0.0005Λ 0.0005Λ 0.0005Λ 0.0005Λ CaseC2(w0 = $-\frac{1}{3} $) 0.0147Λ 0.0119Λ 0.0105Λ 0.0097Λ 0.0092Λ 表 3
$K = + 1$ 时Λ0-crit的值Tab. 3 The value of Λ0-crit when
$K = + 1$ 情形 ${a_0}{H_0}{\rm{ = }}2.5$ ${a_0}{H_0}{\rm{ = 3.0} }$ ${a_0}{H_0}{\rm{ = 3}}.5$ $K = 0$ CaseA1 –0.072Λ –0.064Λ –0.059Λ 0.05Λ CaseA2 –0.14Λ –0.159Λ –0.167Λ –0.18Λ CaseB1 –0.094Λ –0.083Λ –0.078Λ –0.066Λ CaseB2 –0.154Λ –0.176Λ –0.187Λ –0.2144Λ CaseC1(w0 = –1) 0Λ 0Λ 0Λ 0Λ CaseC2(w0 = –1) 0Λ 0Λ 0Λ 0Λ CaseC1(w0 = $-\frac{8}{9} $) 0.162Λ 0.152Λ 0.146Λ 0.119Λ CaseC2(w0 = $-\frac{8}{9} $) 0.09Λ 0.086Λ 0.083Λ 0.075Λ CaseC1(w0 = $-\frac{7}{9} $) CaseC2(w0 = $-\frac{7}{9} $) 0.173Λ 0.164Λ 0.164Λ 0.152Λ CaseC1(w0 = $-\frac{2}{3} $) CaseC2(w0 = $-\frac{2}{3} $) 0.246Λ 0.235Λ 0.228Λ 0.225Λ CaseC1(w0 = $-\frac{1}{3} $) CaseC2(w0 = $-\frac{1}{3} $) 0.354Λ 0.368Λ 0.375Λ 0.397Λ 表 4
$K = - 1$ 时Λ0-crit的值Tab. 4 The value of Λ0-crit when
$K = - 1$ 情形 ${a_0}{H_0}{\rm{ = 1}}.5$ ${a_0}{H_0}{\rm{ = } }2.0$ ${a_0}{H_0}{\rm{ = }}2.5$ ${a_0}{H_0}{\rm{ = 3.0} }$ ${a_0}{H_0}{\rm{ = 3}}.5$ $K = 0$ CaseA1 –0.023Λ –0.033Λ –0.038Λ –0.041Λ –0.044Λ –0.05Λ CaseA2 –0.214Λ –0.208Λ –0.203Λ –0.198Λ –0.195Λ –0.187Λ CaseB1 –0.03Λ –0.042Λ –0.049Λ –0.053Λ –0.056Λ –0.066Λ CaseB2 –0.284Λ –0.262Λ –0.248Λ –0.239Λ –0.233Λ –0.214Λ CaseC1(w0 = –1) 0Λ 0Λ 0Λ 0Λ 0Λ 0Λ CaseC2(w0 = –1) 0Λ 0Λ 0Λ 0Λ 0Λ 0Λ CaseC1(w0 = $\frac{8}{9} $) 0.05Λ 0.086Λ 0.102Λ 0.107Λ 0.115Λ 0.119Λ CaseC2(w0 = $\frac{8}{9} $) 0.03Λ 0.052Λ 0.059Λ 0.064Λ 0.075Λ CaseC1(w0 = $\frac{7}{9} $) CaseC2(w0 = $\frac{7}{9} $) 0.079Λ 0.104Λ 0.118Λ 0.131Λ 0.152Λ CaseC1(w0 = $\frac{2}{3} $) CaseC2(w0 = $\frac{2}{3} $) 0.03Λ 0.15Λ 0.173Λ 0.189Λ 0.198Λ 0.225Λ CaseC1(w0 = $\frac{1}{3} $) CaseC2(w0 = $\frac{1}{3} $) 0.203Λ 0.25Λ 0.278Λ 0.309Λ 0.343Λ 0.397Λ -
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