大尺度洛伦兹破缺与空间平坦性

doi:10.3969/j.issn.1000-5641.202022004

摘要/Abstract

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.

关键词: 洛伦兹破缺, 空间曲率, 哈勃常数

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

中图分类号:

O413.4

李静, 薛迅. 大尺度洛伦兹破缺与空间平坦性[J]. 华东师范大学学报（自然科学版）, 2021, 2021(1): 67-81.

Jing LI, Xun XUE. Spatial flatness and large-scale Lorentz violation[J]. Journal of East China Normal University(Natural Science), 2021, 2021(1): 67-81.

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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

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

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

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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