Free Access

A closed universe with hybrid nonlocality

Institute of Physics, University of Belgrade, 11080 Belgrade, Serbia

Mathematical Institute of the Serbian Academy of Sciences and Arts, 11000 Belgrade, Serbia

https://doi.org/10.1142/S0219887824400127Cited by:0 (Source: Crossref)

This article is part of the issue:

20th Anniversary Special Issue — From Quantum Information to Cosmology: Exploring the Frontiers of Geometric Methods in Physics

Abstract

In this paper, we explore some cosmological solutions of the Friedmann–Lemaître–Robertson–Walker (FLRW) closed universe with nonlocal de Sitter gravity $\sqrt{d S}$ and nonlocal scalar field which has its origin in $p$ -adic string theory. In this case, we have that both geometrical and matter sectors of equations of motion (EoM) are nonlocal. The cosmological constant $Λ$ plays a role of dark energy (DE) and is related to the mass of scalar field as $m = \frac{ℏ}{c} \sqrt{\frac{Λ}{6}} = 1.5 \times 1 0^{- 69} kg$ . We found that the cosmological constant $Λ$ depends on prime number $p$ as a discrete parameter and we conjectured that $Λ$ is not constant during the universe evolution.

Keywords:

References

1. G. F. R. Ellis, 100 years of general relativity, preprint (2015), arXiv:1509.01772[gr-qc]. Google Scholar
2. N. Aghanim et al., Planck 2018 results. VI. Cosmological parameters, Planck 118 collaboration, A&A 641 (2020) A6, arXiv:1807.06209 [astro-ph.CO]. Crossref, Google Scholar
3. M. Novello and S. E. P. Bergliaffa , Bouncing cosmologies, Phys. Rep. 463 (2008) 127–213, arXiv:0802.1634 [astro-ph]. Crossref, Web of Science, Google Scholar
4. A. S. Koshelev and S. Yu. Vernov , On bouncing solutions in non-local gravity, Phys. Part. Nucl. 43 (2012) 666–668, arXiv:1202.1289v1 [hep-th]. Crossref, Web of Science, Google Scholar
5. T. P. Sotiriou and V. Faraoni , $f (R)$ theories of gravity, Rev. Mod. Phys. 82 (2010) 451, arXiv:0805.1726v4 [gr-qc]. Crossref, Web of Science, Google Scholar
6. S. Nojiri and S. D. Odintsov , Unified cosmic history in modified gravity: From $F (R)$ theory to Lorentz non-invariant models, Phys. Rep. 505 (2011) 59–144, arXiv:1011.0544v4 [gr-qc]. Crossref, Web of Science, Google Scholar
7. T. Clifton, P. G. Ferreira, A. Padilla and C. Skordis , Modified gravity and cosmology, Phys. Rep. 513 (2012) 1, arXiv:1106.2476v2 [astro-ph.CO]. Crossref, Web of Science, Google Scholar
8. S. Nojiri, S. D. Odintsov and V. K. Oikonomou , Modified gravity theories on a nutshell: Inflation, bounce and late-time evolution, Phys. Rep. 692 (2017) 1–104, arXiv:1705.11098 [gr-qc]. Crossref, Web of Science, Google Scholar
9. S. Capozziello and F. Bajardi , Nonlocal gravity cosmology: An overview, Int. J. Mod. Phys. D 31 (2022) 2230009, arXiv:2201.04512 [gr-qc]. Link, Web of Science, Google Scholar
10. B. Dragovich , On nonlocal modified gravity and cosmology, Springer Proc. Math. & Stat. 111 (2014) 251–262. Google Scholar
11. I. Dimitrijevic, B. Dragovich, Z. Rakic and J. Stankovic, On a nonlocal de Sitter gravity, preprint, arXiv:2312.16673 [gr-qc]. Google Scholar
12. T. Biswas, A. Mazumdar and W. Siegel , Bouncing universes in string-inspired gravity, J. Cosmol. Astropart. Phys. 0603 (2006) 009, arXiv:hep-th/0508194. Crossref, Web of Science, Google Scholar
13. T. Biswas, T. Koivisto and A. Mazumdar , Towards a resolution of the cosmological singularity in non-local higher derivative theories of gravity, J. Cosmol. Astropart. Phys. 1011 (2010) 008, arXiv:1005.0590v2 [hep-th]. Crossref, Web of Science, Google Scholar
14. T. Biswas, E. Gerwick, T. Koivisto and A. Mazumdar , Towards singularity and ghost free theories of gravity, Phys. Rev. Lett. 108 (2012) 031101, arXiv:1110.5249v2 [gr-qc]. Crossref, Web of Science, Google Scholar
15. T. Biswas, A. Conroy, A. S. Koshelev and A. Mazumdar , Generalized gost-free quadratic curvature gravity, Class. Quantum Grav. 31 (2014) 015022, arXiv:1308.2319 [hep-th]. Crossref, Web of Science, Google Scholar
16. T. Biswas, A. S. Koshelev, A. Mazumdar and S. Yu. Vernov , Stable bounce and inflation in non-local higher derivative cosmology, J. Cosmol. Astropart. Phys. 08 (2012) 024, arXiv:1206.6374v2 [astro-ph.CO]. Crossref, Google Scholar
17. I. Dimitrijevic, B. Dragovich, A. S. Koshelev, Z. Rakic and J. Stankovic , Cosmological solutions of a nonlocal square-root gravity, Phys. Lett. B 797 (2019) 134848, arXiv:1906.07560 [gr-qc]. Crossref, Web of Science, Google Scholar
18. S. Deser and R. Woodard , Nonlocal cosmology, Phys. Rev. Lett. 99 (2007) 111301, arXiv:0706.2151 [astro-ph]. Crossref, Web of Science, Google Scholar
19. A. S. Koshelev, K. Sravan Kumar, A. Mazumdar and A. A. Starobinsky , Non-gaussianities and tensor-to-scalar ratio in non-local $R^{2}$ -like inflation, J. High Energy Phys. 06 (2020) 152, arXiv:2003.00629 [hep-th]. Crossref, Web of Science, Google Scholar
20. L. Buoninfante, A. S. Koshelev, G. Lambiase and A. Mazumdar , Classical properties of non-local, ghost- and singularity-free gravity, J. Cosmol. Astropart. Phys. 09 (2018) 034, arXiv:1802.00399 [gr-qc]. Crossref, Web of Science, Google Scholar
21. E. Elizalde, E. O. Pozdeeva and S. Yu. Vernov , Stability of de Sitter solutions in non-local cosmological models, Proceedings of Science, QFTHEP2011, 138 (2012) 1–9, arXiv:1202.0178. Google Scholar
22. S. Capozziello, E. Elizalde, Sh. Nojiri and S. D. Odintsov , Accelerating cosmologies from non-local higher-derivative gravity, Phys. Lett. B 671(1) (2009) 193–198. Crossref, Web of Science, Google Scholar
23. B. Craps, T. De Jonckheere and A. S. Koshelev , Cosmological perturbations in non-local higher-derivative gravity, J. Cosmol. Astropart. Phys. 11 (2014) 022. Crossref, Google Scholar
24. R. P. Woodard , Nonlocal models of cosmic acceleration, Found. Phys. 44 (2014) 213–233, arXiv:1401.0254 [astro-ph.CO]. Crossref, Web of Science, Google Scholar
25. E. Belgacem, Y. Dirian, S. Foffa and M. Maggiore , Nonlocal gravity. Conceptual aspects and cosmological predictions, J. Cosmol. Astropart. Phys. 03 (2018) 002, arXiv:1712.07066 [hep-th]. Crossref, Google Scholar
26. A. O. Barvinsky , Dark energy and dark matter from nonlocal ghost-free gravity theory, Phys. Lett. B 710 (2012) 12. Crossref, Web of Science, Google Scholar
27. L. Modesto , Super-renormalizable quantum gravity, Phys. Rev. D 86 (2012) 044005, arXiv:1107.2403 [hep-th]. Crossref, Web of Science, Google Scholar
28. L. Modesto and L. Rachwal , Super-renormalizable and finite gravitational theories, Nucl. Phys. B 889 (2014) 228, arXiv:1407.8036 [hep-th]. Crossref, Web of Science, Google Scholar
29. I. Dimitrijevic, B. Dragovich, Z. Rakic and J. Stankovic , Nonlocal de Sitter gravity and its exact cosmological solutions, J. High Energy Phys. 12 (2022) 054, arXiv:2206.13515v1 [gr-qc]. Crossref, Web of Science, Google Scholar
30. I. Dimitrijevic, B. Dragovich, J. Grujic, A. S. Koshelev and Z. Rakic , Cosmology of non-local $f (R)$ gravity, Filomat 33 (2019) 1163, arXiv:1509.04254v2 [hep-th]. Crossref, Google Scholar
31. I. Dimitrijevic, B. Dragovich, J. Stankovic, A. S. Koshelev and Z. Rakic , On nonlocal modified gravity and its cosmological solutions, Springer Proc. Math. & Stat. 191 (2016) 35–51, arXiv:1701.02090 [hep-th]. Google Scholar
32. I. Dimitrijevic, B. Dragovich, J. Grujic and Z. Rakic , Some cosmological solutions of a nonlocal modified gravity, Filomat 29 (2015) 619, arXiv:1508.05583 [hep-th]. Crossref, Web of Science, Google Scholar
33. I. Dimitrijevic , Cosmological solutions in modified gravity with monomial nonlocality, Appl. Math. Comput. 285 (2016) 195. Crossref, Web of Science, Google Scholar
34. I. Dimitrijevic, B. Dragovich, Z. Rakic and J. Stankovic , Variations of infinite derivative modified gravity, Springer Proc. Math. & Stat. 263 (2018) 91. Google Scholar
35. I. Dimitrijevic, B. Dragovich, A. S. Koshelev, Z. Rakic and J. Stankovic , Some cosmological solutions of a new nonlocal gravity model, Symmetry 12 (2020) 917, arXiv:2006.16041 [gr-qc]. Crossref, Web of Science, Google Scholar
36. I. Dimitrijevic, B. Dragovich, Z. Rakic and J. Stankovic , New cosmological solutions of a nonlocal gravity model, Symmetry 14 (2022) 3, arXiv:2112.06312 [gr-qc]. Crossref, Web of Science, Google Scholar
37. I. Dimitrijevic , Some exact anisotropic cosmological solutions of a simple nonlocal de Sitter gravity, Int. J. Mod. Phys. A 38(32) (2024) 2343011, https://doi.org/10.1142/S0217751X2343011X. Link, Google Scholar
38. I. Ya. Aref’eva, L. V. Joukovskaya and S. Yu. Vernov , Bouncing and accelerating solutions in nonlocal stringy models, J. High Energy Phys. 0707 (2007) 087, arXiv:hep-th/0701184. Crossref, Web of Science, Google Scholar
39. B. Dragovich , A $p$ -Adic matter in a closed universe, Symmetry 14 (2022) 73, arXiv:2201.02200 [hep-th]. Crossref, Google Scholar
40. L. Brekke and P. G. O. Freund , $p$ -Adic numbers in physics, Phys. Rep. 233(1) (1993) 1–66. Crossref, Web of Science, Google Scholar
41. V. S. Vladimirov, I. V. Volovich and E. I. Zelenov , p-Adic Analysis and Mathematical Physics (World Scientific, Singapore, 1994). Link, Google Scholar
42. B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev, I. V. Volovich and E. I. Zelenov , $p$ -Adic mathematical physics: The first 30 years, p-Adic Numbers Ultrametric Anal. Appl. 9(2) (2017) 87–121 arXiv:1705.04758 [math-ph]. Crossref, Google Scholar
43. L. Brekke, P. G. O. Freund, M. Olson and E. Witten , Nonarchimedean string dynamics, Nucl. Phys. B 302 (1988) 365–402. Crossref, Web of Science, Google Scholar
44. P. H. Frampton and Y. Okada , Effective scalar field theory of $p$ -adic string, Phys. Rev. D 37 (1988) 3077–3084. Crossref, Web of Science, Google Scholar
45. D. Ghoshal and A. Sen , Tachyon condensation and brane descent relations in $p$ -adic string theory, Nucl. Phys. B 584 (2000) 300–312. Crossref, Google Scholar
46. N. Moeller and B. Zwiebach , Dynamics with infinitely many time derivatives and rolling tachyons, J. High Energy Phys. 0210 (2002) 034. Crossref, Google Scholar
47. V. S. Vladimirov , On some exact solutions in $p$ -adic open-closed string theory, p-Adic Numbers Ultrametric Anal. Appl. 4 (2012) 57–63. Crossref, Google Scholar
48. N. Barnaby, T. Biswas and J. M. Cline , $p$ -Adic inflation, J. High Energy Phys. 0704 (2007) 056. Crossref, Web of Science, Google Scholar
49. M. Bocardo-Gaspar, H. Garcia-Compean and W. A. Zuñiga-Galindo , On $p$ -adic string amplitudes in the limit $p$ approaches to one, J. High Energy Phys. 08 (2018) 043. Crossref, Google Scholar
50. B. Dragovich , Towards $p$ -adic matter in the universe, Springer Proc. Math. & Stat. 36 (2013) 13–24. Google Scholar
51. B. Dragovich , $p$ -Adic and adelic cosmology: $p$ -adic origin of dark energy and dark energy, AIP Conf. Proc. 826 (2006) 25–42. Crossref, Google Scholar
52. B. Dragovich , From $p$ -adic to zeta strings, in Proc. 1st Conf. Nonlinearity (Serbian Academy of Nonlinear Sciences, Belgrade, Serbia, 2020), pp. 14–28, arXiv:2007.13628 [hep-th]. Google Scholar