Diffeomorphism invariant cosmological sector in loop quantum gravity

被引:9
作者
Beetle, C. [1 ]
Engle, J. S. [1 ]
Hogan, M. E. [1 ,2 ]
Mendonca, P. [1 ]
机构
[1] Florida Atlantic Univ, Dept Phys, 777 Glades Rd, Boca Raton, FL 33431 USA
[2] Wells Coll, Dept Math & Phys Sci, 170 Main St, Aurora, NY 13026 USA
基金
美国国家科学基金会;
关键词
loop quantum gravity; cosmology; symmetry reduction; CONNECTIONS; SPACE; GEOMETRY; STATES; REAL; AREA;
D O I
10.1088/1361-6382/aa89c6
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
In this paper we work out in detail a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, and propose how to compare in detail the physics of this sector with that of loop quantum cosmology. The key technical steps we have completed are (a) to formulate conditions for homogeneity and isotropy in a diffeomorphism covariant way on the classical phase space of general relativity, and (b) to translate these conditions consistently using well-understood techniques to loop quantum gravity. To impose the symmetry at the quantum level, on both the connection and its conjugate momentum, the method used necessarily has similiarities to the Gupta-Bleuler method of quantizing the electromagnetic field. Lastly, a strategy for embedding states of loop quantum cosmology into this new homogeneous isotropic sector, and using this embedding to compare the physics, is presented.
引用
收藏
页数:30
相关论文
共 61 条
  • [1] Agullo I., 2017, LOOP QUANTUM GRAVITY
  • [2] Agullo I, 2014, SPRINGER HANDBOOK OF SPACETIME, P809
  • [3] Extension of the quantum theory of cosmological perturbations to the Planck era
    Agullo, Ivan
    Ashtekar, Abhay
    Nelson, William
    [J]. PHYSICAL REVIEW D, 2013, 87 (04)
  • [4] Quantum Gravity Extension of the Inflationary Scenario
    Agullo, Ivan
    Ashtekar, Abhay
    Nelson, William
    [J]. PHYSICAL REVIEW LETTERS, 2012, 109 (25)
  • [5] [Anonymous], 2012, The principles of quantum mechanics
  • [6] [Anonymous], 2013, Spacetime and geometry: An introduction togeneral relativity
  • [7] [Anonymous], 2022, Back to reichenbach, DOI DOI 10.1017/CBO9780511755804
  • [8] [Anonymous], 1964, GENERALIZED FUNCTION
  • [9] DIFFERENTIAL GEOMETRY ON THE SPACE OF CONNECTIONS VIA GRAPHS AND PROJECTIVE-LIMITS
    ASHTEKAR, A
    LEWANDOWSKI, J
    [J]. JOURNAL OF GEOMETRY AND PHYSICS, 1995, 17 (03) : 191 - 230
  • [10] Quantum nature of the big bang
    Ashtekar, A
    Pawlowski, T
    Singh, P
    [J]. PHYSICAL REVIEW LETTERS, 2006, 96 (14)