Borde–Guth–Vilenkin theorem (English Wikipedia)

Borde, Arvind; Guth, Alan H.; Vilenkin, Alexander (15 April 2003). "Inflationary space-times are incomplete in past directions". Physical Review Letters. 90 (15): 151301. arXiv:gr-qc/0110012. Bibcode:2003PhRvL..90o1301B. doi:10.1103/PhysRevLett.90.151301. PMID 12732026. S2CID 46902994.
Mithani, Audrey; Vilenkin, Alexander (20 April 2012). "Did the universe have a beginning?". arXiv:1204.4658 [hep-th].
Carroll, Sean M. (2018-06-04). "Why Is There Something, Rather Than Nothing?". arXiv:1802.02231 [physics.hist-ph].
Vilenkin, Alexander (2013). "Arrows of time and the beginning of the universe". Physical Review D. 88 (4): 043516. arXiv:1305.3836. Bibcode:2013PhRvD..88d3516V. doi:10.1103/PhysRevD.88.043516. S2CID 119213877.
Lesnefsky, J. E.; Easson, D. A.; Davies, P. C. W. (2023). "Past-completeness of inflationary spacetimes". Physical Review D. 107 (4): 044024. arXiv:2207.00955. doi:10.1103/PhysRevD.107.044024.
Pavlović, Petar; Sossich, Marko (2024). "Geodesically complete cyclic cosmologies and entropy". European Physical Journal C. 84 (3) 242. arXiv:2305.06719. doi:10.1140/epjc/s10052-024-12621-z.

books.google.com

Borde, Arvind; Guth, Alan H.; Vilenkin, Alexander (15 April 2003). "Inflationary space-times are incomplete in past directions". Physical Review Letters. 90 (15): 151301. arXiv:gr-qc/0110012. Bibcode:2003PhRvL..90o1301B. doi:10.1103/PhysRevLett.90.151301. PMID 12732026. S2CID 46902994.
Vilenkin, Alexander (2013). "Arrows of time and the beginning of the universe". Physical Review D. 88 (4): 043516. arXiv:1305.3836. Bibcode:2013PhRvD..88d3516V. doi:10.1103/PhysRevD.88.043516. S2CID 119213877.
Lesnefsky, J. E.; Easson, D. A.; Davies, P. C. W. (2023). "Past-completeness of inflationary spacetimes". Physical Review D. 107 (4): 044024. arXiv:2207.00955. doi:10.1103/PhysRevD.107.044024.
Pavlović, Petar; Sossich, Marko (2024). "Geodesically complete cyclic cosmologies and entropy". European Physical Journal C. 84 (3) 242. arXiv:2305.06719. doi:10.1140/epjc/s10052-024-12621-z.

Borde, Arvind; Guth, Alan H.; Vilenkin, Alexander (15 April 2003). "Inflationary space-times are incomplete in past directions". Physical Review Letters. 90 (15): 151301. arXiv:gr-qc/0110012. Bibcode:2003PhRvL..90o1301B. doi:10.1103/PhysRevLett.90.151301. PMID 12732026. S2CID 46902994.
Vilenkin, Alexander (2013). "Arrows of time and the beginning of the universe". Physical Review D. 88 (4): 043516. arXiv:1305.3836. Bibcode:2013PhRvD..88d3516V. doi:10.1103/PhysRevD.88.043516. S2CID 119213877.

Vilenkin, Alexander (2015-10-23). "The Beginning of the Universe". Inference. 1 (4). Archived from the original on 27 December 2023.

Borde, Arvind; Guth, Alan H.; Vilenkin, Alexander (15 April 2003). "Inflationary space-times are incomplete in past directions". Physical Review Letters. 90 (15): 151301. arXiv:gr-qc/0110012. Bibcode:2003PhRvL..90o1301B. doi:10.1103/PhysRevLett.90.151301. PMID 12732026. S2CID 46902994.

Carroll, Sean (2014-02-24). "Post-Debate Reflections". Sean Carroll Blog. Archived from the original on 2014-02-25. Retrieved 2019-11-19.

Borde, Arvind; Guth, Alan H.; Vilenkin, Alexander (15 April 2003). "Inflationary space-times are incomplete in past directions". Physical Review Letters. 90 (15): 151301. arXiv:gr-qc/0110012. Bibcode:2003PhRvL..90o1301B. doi:10.1103/PhysRevLett.90.151301. PMID 12732026. S2CID 46902994.
Vilenkin, Alexander (2013). "Arrows of time and the beginning of the universe". Physical Review D. 88 (4): 043516. arXiv:1305.3836. Bibcode:2013PhRvD..88d3516V. doi:10.1103/PhysRevD.88.043516. S2CID 119213877.

Vilenkin, Alexander (2015-10-23). "The Beginning of the Universe". Inference. 1 (4). Archived from the original on 27 December 2023.
Carroll, Sean (2014-02-24). "Post-Debate Reflections". Sean Carroll Blog. Archived from the original on 2014-02-25. Retrieved 2019-11-19.