Papers
Topics
Authors
Recent
Search
2000 character limit reached

Estimated Age of the Universe in Fractional Cosmology

Published 14 Oct 2023 in gr-qc | (2310.09464v3)

Abstract: Our proposed cosmological framework, which is based on fractional quantum cosmology, aims to address the issue of synchronicity in the age of the universe. To achieve this, we have developed a new fractional $\Lambda$CDM cosmological model. We obtained the necessary formalism by obtaining the fractional Hamiltonian constraint in a general minisuperspace. This formalism has allowed us to derive the fractional Friedmann and Raychaudhuri equations for a homogeneous and isotropic cosmology. Unlike the traditional de Sitter phase, our model exhibits a power-law accelerated expansion in the late-time universe, when vacuum energy becomes dominant. By fitting the model's parameters to cosmological observations, we determined that the fractional parameter of L\'{e}vy equals $\alpha=1.986$. Additionally, we have calculated the age of the universe to be 13.8196 Gyr. Furthermore, we have found that the ratio of the age to Hubble time from the present epoch to the distant future is finite and confined within the interval $0.9858\leq Ht<95.238$.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (105)
  1. On the Relation between the Expansion and the Mean Density of the Universe. Proc. Nat. Acad. Sci. USA 1932, 18, 213–214. https://doi.org/10.1073/pnas.18.3.213.
  2. A Lower limit on the age of the universe. Science 1996, 271, 957–961. https://doi.org/10.1126/science.271.5251.957.
  3. The dimensionless age of the Universe: A riddle for our time. Astrophys. J. 2016, 828, 35. https://doi.org/10.3847/0004-637X/828/1/35.
  4. Tonry, J.L.; et al. Cosmological results from high-z supernovae. Astrophys. J. 2003, 594, 1–24. https://doi.org/10.1086/376865.
  5. Casado, J. Linear expansion models vs. standard cosmologies: A critical and historical overview. Astrophys. Space Sci 2020, 365, 16. https://doi.org/10.1007/s10509-019-3720-z.
  6. Tian, S.X. Cosmological consequences of a scalar field with oscillating equation of state. IV. Primordial nucleosynthesis and the deuterium problem. Phys. Rev. D 2022, 106, 043524. https://doi.org/10.1103/PhysRevD.106.043524.
  7. Constraining cosmological scaling solutions of a Galileon field. Phys. Rev. D 2022, 105, 044056. https://doi.org/10.1103/PhysRevD.105.044056.
  8. Dark Energy: The Shadowy Reflection of Dark Matter? Entropy 2016, 18, 94. https://doi.org/10.3390/e18030094.
  9. Cosmological perturbations in the ΛΛ\Lambdaroman_ΛCDM-like limit of a polytropic dark matter model. Astron. Astrophys. 2017, 606, A116. https://doi.org/10.1051/0004-6361/201630364.
  10. Forecast Analysis on Interacting Dark Energy Models from Future Generation PICO and DESI Missions. Mon. Not. Roy. Astron. Soc. 2022, 519, 1809–1822. https://doi.org/10.1093/mnras/stac3586.
  11. Dissecting kinetically coupled quintessence: Phenomenology and observational tests. JCAP 2022, 11, 059. https://doi.org/10.1088/1475-7516/2022/11/059.
  12. Dark matter haloes in interacting dark energy models: Formation history, density profile, spin, and shape. Mon. Not. Roy. Astron. Soc. 2022, 511, 3076–3088. https://doi.org/10.1093/mnras/stac229.
  13. Nayak, B. Interacting Holographic Dark Energy, the Present Accelerated Expansion and Black Holes. Grav. Cosmol. 2020, 26, 273–280. https://doi.org/10.1134/S020228932003010X.
  14. A new parameterized interacting holographic dark energy. Eur. Phys. J. Plus 2022, 137, 254. https://doi.org/10.1140/epjp/s13360-022-02490-4.
  15. Landim, R.G. Note on interacting holographic dark energy with a Hubble-scale cutoff. Phys. Rev. D 2022, 106, 043527. https://doi.org/10.1103/PhysRevD.106.043527.
  16. Shimon, M. Elucidation of ’Cosmic Coincidence’ New Astron. 2024. 106, 102126. https://doi.org/10.1016/j.newast.2023.102126.
  17. Constant-roll, cosmic acceleration, and massive neutrinos. JCAP 2022, 7, 043. https://doi.org/10.1088/1475-7516/2022/07/043.
  18. A quantum cosmology approach to cosmic coincidence and inflation. Phys. Dark Univ. 2023, 40, 101227. https://doi.org/10.1016/j.dark.2023.101227.
  19. Kolb, E.W. A coasting cosmology. Astrophys. J. 1989, 344, 543–550. https://doi.org/10.1086/167825.
  20. Allen, R.E. Four testable predictions of instanton cosmology. AIP Conf. Proc. 1999, 478, 204–207. https://doi.org/10.1063/1.59392.
  21. Coasting Cosmologies with Time Dependent Cosmological Constant. Int. J. Mod. Phys. A 1998, 14, 1523–1529. https://doi.org/10.1142/S0217751X99000762.
  22. The Rh=c⁢tsubscript𝑅ℎ𝑐𝑡R_{h}=ctitalic_R start_POSTSUBSCRIPT italic_h end_POSTSUBSCRIPT = italic_c italic_t universe. Mon. Not. Roy. Astron. Soc. 2012, 419, 2579–2586. https://doi.org/10.1111/j.1365-2966.2011.19906.x.
  23. Lewis, G.F. Matter matters: Unphysical properties of the Rh=c⁢tsubscript𝑅ℎ𝑐𝑡R_{h}=ctitalic_R start_POSTSUBSCRIPT italic_h end_POSTSUBSCRIPT = italic_c italic_t universe. Mon. Not. Roy. Astron. Soc. 2013, 432, 2324–2330. https://doi.org/10.1093/mnras/stt592.
  24. From Fractional Quantum Mechanics to Quantum Cosmology: An Overture. Mathematics 2020, 8, 313. https://doi.org/10.3390/math8030313.
  25. Broadening quantum cosmology with a fractional whirl. Mod. Phys. Lett. A 2021, 36, 2140005. https://doi.org/10.1142/S0217732321400058.
  26. Prospecting black hole thermodynamics with fractional quantum mechanics. Eur. Phys. J. C 2021, 81, 632. https://doi.org/10.1140/epjc/s10052-021-09438-5.
  27. de Sitter fractional quantum cosmology. Phys. Rev. D 2022, 105, L121901. https://doi.org/10.1103/PhysRevD.105.L121901.
  28. Inflation and fractional quantum cosmology. Fractal Fract. 2022, 6, 655. https://doi.org/10.3390/fractalfract6110655.
  29. Challenging Routes in Quantum Cosmology; World Scientific: Singapore, 2022. https://doi.org/10.1142/8540.
  30. Laskin, N. Fractional Quantum Mechanics. Phys. Rev. E 2000, 62, 3135–3145. https://doi.org/10.1103/PhysRevE.62.3135.
  31. Laskin, N. Fractional Schrodinger equation. Phys. Rev. E 2002, 66, 056108. https://doi.org/10.1103/PhysRevE.66.056108.
  32. Laskin, N. Principles of Fractional Quantum Mechanics. arXiv 2010, arXiv:1009.5533.
  33. Calcagni, G. Classical and Quantum Cosmology; Graduate Texts in Physics; Springer: Berlin/Heidelberg, Germany, 2017. https://doi.org/10.1007/978-3-319-41127-9.
  34. Horizon Problem Remediation via Deformed Phase Space. Gen. Rel. Grav. 2011, 43, 2895–2910. https://doi.org/10.1007/s10714-011-1208-4.
  35. Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space. Phys. Rev. D 2014, 89, 044028. https://doi.org/10.1103/PhysRevD.89.044028.
  36. Quantum cosmology, minimal length and holography. Phys. Rev. D 2014, 90, 023541. https://doi.org/10.1103/PhysRevD.90.023541.
  37. Noncommutative minisuperspace, gravity-driven acceleration, and kinetic inflation. Phys. Rev. D 2014, 90, 083533. https://doi.org/10.1103/PhysRevD.90.083533.
  38. Non-singular Brans–Dicke collapse in deformed phase space. Annals Phys. 2016, 375, 154–178. https://doi.org/10.1016/j.aop.2016.09.007.
  39. Gravity-Driven Acceleration and Kinetic Inflation in Noncommutative Brans-Dicke Setting. Odessa Astron. Pub. 2016, 29, 19. https://doi.org/10.18524/1810-4215.2016.29.84956.
  40. Inflationary Universe in Deformed Phase Space Scenario. Annals Phys. 2018, 393, 288–307. https://doi.org/10.1016/j.aop.2018.04.014.
  41. Kinetic inflation in deformed phase space Brans–Dicke cosmology. Phys. Dark Univ. 2019, 24, 100269. https://doi.org/10.1016/j.dark.2019.100269.
  42. Rasouli, S.M.M. Noncommutativity, Sáez–Ballester Theory and Kinetic Inflation. Universe 2022, 8, 165. https://doi.org/10.3390/universe8030165.
  43. Shchigolev, V. Cosmological models with fractional derivatives and fractional action functional. Commun. Theor. Phys. 2011, 56, 389. https://doi.org/10.1088/0253-6102/56/2/34.
  44. Varieschi, G.U. Relativistic Fractional-Dimension Gravity. Universe 2021, 7, 387. https://doi.org/10.3390/universe7100387.
  45. Cosmology under the fractional calculus approach. Mon. Not. Roy. Astron. Soc. 2022, 517, 4813–4826. https://doi.org/10.1093/mnras/stac3006.
  46. Cosmology under the fractional calculus approach: A possible H0subscript𝐻0H_{0}italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT tension resolution? arXiv 2023, arXiv:2304.14465.
  47. Shchigolev, V.K. Cosmic Evolution in Fractional Action Cosmology. Discontinuitynlinearity Complex. 2013, 2, 115–123. https://doi.org/10.5890/DNC.2013.04.002.
  48. Shchigolev, V.K. Fractional Einstein-Hilbert Action Cosmology. Mod. Phys. Lett. A 2013, 28, 1350056. https://doi.org/10.1142/S0217732313500569.
  49. Calcagni, G. Multi-scale gravity and cosmology. JCAP 2013, 12, 041. https://doi.org/10.1088/1475-7516/2013/12/041.
  50. Shchigolev, V.K. Testing Fractional Action Cosmology. Eur. Phys. J. Plus 2016, 131, 256. https://doi.org/10.1140/epjp/i2016-16256-6.
  51. Calcagni, G. Multifractional theories: An unconventional review. JHEP 2017, 3, 138. Erratum in 2017, 6, 20. https://doi.org/10.1007/JHEP03(2017)138.
  52. Shchigolev, V.K. Fractional-order derivatives in cosmological models of accelerated expansion. Mod. Phys. Lett. A 2021, 36, 2130014. https://doi.org/10.1142/S0217732321300147.
  53. Dark energy in multifractional spacetimes. Phys. Rev. D 2020, 102, 103529. https://doi.org/10.1103/PhysRevD.102.103529.
  54. Calcagni, G. Multifractional theories: An updated review. Mod. Phys. Lett. A 2021, 36, 2140006. https://doi.org/10.1142/S021773232140006X.
  55. Calcagni, G. Classical and quantum gravity with fractional operators. Class. Quant. Grav. 2021, 38, 165005. Erratum in 2021, 38, 169601. https://doi.org/10.1088/1361-6382/ac1bea.
  56. Exact solutions and cosmological constraints in fractional cosmology. Fractal Fract. 2023, 7, 368. https://doi.org/10.3390/fractalfract7050368.
  57. Quantum Fractionary Cosmology: K-Essence Theory. Universe 2023, 9, 185. https://doi.org/10.3390/universe9040185.
  58. Stochastic gravitational-wave background in quantum gravity. JCAP 2021, 3, 019. https://doi.org/10.1088/1475-7516/2021/03/019.
  59. Quantum gravity and gravitational-wave astronomy. JCAP 2019, 10, 012. https://doi.org/10.1088/1475-7516/2019/10/012.
  60. Calcagni, G. Complex dimensions and their observability. Phys. Rev. D 2017, 96, 046001. https://doi.org/10.1103/PhysRevD.96.046001.
  61. Cosmic microwave background and inflation in multi-fractional spacetimes. JCAP 2016, 8, 039. https://doi.org/10.1088/1475-7516/2016/08/039.
  62. El-Nabulsi, R.A. Gravitons in fractional action cosmology. Int. J. Theor. Phys. 2012, 51, 3978–3992. https://doi.org/10.1007/s10773-012-1290-8.
  63. El-Nabulsi, R.A. A Cosmology Governed by a Fractional Differential Equation and the Generalized Kilbas-Saigo-Mittag-Leffler Function. Int. J. Theor. Phys. 2016, 55, 625–635. https://doi.org/10.1007/s10773-015-2700-5.
  64. Fractional Action Cosmology with Power Law Weight Function. J. Phys. Conf. Ser. 2012, 354, 012008. https://doi.org/10.1088/1742-6596/354/1/012008.
  65. El-Nabulsi, R.A. Nonstandard fractional exponential Lagrangians, fractional geodesic equation, complex general relativity, and discrete gravity. Can. J. Phys. 2013, 91, 618–622. https://doi.org/10.1139/cjp-2013-0145.
  66. El-Nabulsi, A.R. Non-minimal coupling in fractional action cosmology. Indian J. Phys. 2013, 87, 835–840. https://doi.org/10.1007/s12648-013-0295-3.
  67. Rami, E.N.A. Fractional action oscillating phantom cosmology with conformal coupling. Eur. Phys. J. Plus 2015, 130, 102. https://doi.org/10.1140/epjp/i2015-15102-9.
  68. El-Nabulsi, R.A. Implications of the Ornstein-Uhlenbeck-like fractional differential equation in cosmology. Rev. Mex. Fis. 2016, 62, 240.
  69. El-Nabulsi, R.A. Fractional Action Cosmology with Variable Order Parameter. Int. J. Theor. Phys. 2017, 56, 1159–1182. https://doi.org/10.1007/s10773-016-3260-z.
  70. El-Nabulsi, R.A. Wormholes in fractional action cosmology. Can. J. Phys. 2017, 95, 605–609. https://doi.org/10.1139/cjp-2017-0109.
  71. El-Nabulsi, R.A. New Metrics from a Fractional Gravitational Field. Commun. Theor. Phys. 2017, 68, 309. https://doi.org/10.1088/0253-6102/68/3/309.
  72. Fractional Action Cosmology: Emergent, Logamediate, Intermediate, Power Law Scenarios of the Universe and Generalized Second Law of Thermodynamics. Int. J. Theor. Phys 2012, 51, 812–837. https://doi.org/10.1007/s10773-011-0961-1.
  73. Fractional action cosmology: Some dark energy models in emergent, logamediate, and intermediate scenarios of the universe. Int. J. Theor. Phys 2013, 7, 25. https://doi.org/10.1186/2251-7235-7-25.
  74. Calcagni, G. Quantum field theory, gravity and cosmology in a fractal universe. JHEP 2010, 3, 120. https://doi.org/10.1007/JHEP03(2010)120.
  75. Calcagni, G. Fractal universe and quantum gravity. Phys. Rev. Lett. 2010, 104, 251301. https://doi.org/10.1103/PhysRevLett.104.251301.
  76. Emergence of fractal cosmic space from fractional quantum gravity. Eur. Phys. J. Plus 2023, 138, 862. https://doi.org/10.1140/epjp/s13360-023-04506-z.
  77. Extending Friedmann equations using fractional derivatives using a Last Step Modification technique: The case of a matter dominated accelerated expanding Universe. Symmetry 2021, 13, 174. https://doi.org/10.3390/sym13020174.
  78. Landim, R.G. Fractional dark energy. Phys. Rev. D 2021, 103, 083511. https://doi.org/10.1103/PhysRevD.103.083511.
  79. Calcagni, G. Quantum scalar field theories with fractional operators. Class. Quant. Grav. 2021, 38, 165006. https://doi.org/10.1088/1361-6382/ac103c.
  80. Landim, R.G. Fractional dark energy: Phantom behavior and negative absolute temperature. Phys. Rev. D 2021, 104, 103508. https://doi.org/10.1103/PhysRevD.104.103508.
  81. Giusti, A. MOND-like Fractional Laplacian Theory. Phys. Rev. D 2020, 101, 124029. https://doi.org/10.1103/PhysRevD.101.124029.
  82. Quantum Cosmology of Fab Four John Theory with Conformable Fractional Derivative. Universe 2020, 6, 50. https://doi.org/10.3390/universe6040050.
  83. Theory and applications Of Fractional Differential Equations. North-Holland Math. Stud. 2006, 204,7–10. https://doi.org/10.1016/S0304-0208(06)80001-0.
  84. Podlubny, I. Fractional Differential Equations; Elsevier: Amsterdam, The Netherlands, 1998; Volume 198.
  85. Laskin, N. Fractional quantum mechanics and Levy paths integrals. Phys. Lett. A 2000, 268, 298–305. https://doi.org/10.1016/S0375-9601(00)00201-2.
  86. Pozrikidis, C. The Fractional Laplacian; CRC Press: Boca Raton, FL, USA, 2018. https://doi.org/10.1201/9781315367675.
  87. Laskin, N. Fractional Quantum Mechanics; World Scientific: Singapore, 2018. https://doi.org/10.1142/10541.
  88. Riesz, M. L’intégrale de Riemann-Liouville et le problème de Cauchy. Acta Mathematica 1949, 81, 1 – 222.
  89. Tarasov, V.E. Fractional Derivative Regularization in QFT. Adv. High Energy Phys. 2018, 2018, 7612490. https://doi.org/10.1155/2018/7612490.
  90. Relativistic S Matrix of Dynamical Systems with Boson and Fermion Constraints. Phys. Lett. B 1977, 69, 309–312. https://doi.org/10.1016/0370-2693(77)90553-6.
  91. The Large Scale Structure of Space-Time; Cambridge Monographs on Mathematical Physics; Cambridge University Press: Cambridge, UK, 1973. https://doi.org/10.1017/CBO9780511524646.
  92. Quantum Hamilton-Jacobi cosmology and classical-quantum correlation. Int. J. Theor. Phys. 2017, 56, 2167–2177. https://doi.org/10.1007/s10773-017-3363-1.
  93. The Quantum State Of The Universe From Deformation Quantization and Classical-Quantum Correlation. Gen. Rel. Grav. 2017, 49, 14. https://doi.org/10.1007/s10714-016-2178-3.
  94. Dirac observables and boundary proposals in quantum cosmology. Phys. Rev. D 2014, 89, 083504. https://doi.org/10.1103/PhysRevD.89.083504.
  95. Classical Universe emerging from quantum cosmology without horizon and flatness problems. Eur. Phys. J. C 2016, 76, 527. https://doi.org/10.1140/epjc/s10052-016-4373-5.
  96. Holography from quantum cosmology. Phys. Rev. D 2015, 91, 023501. https://doi.org/10.1103/PhysRevD.91.023501.
  97. Lectures on Hyperbolic Geometry; Springer: Berlin/Heidelberg, Germany, 1992. https://doi.org/10.1007/978-3-642-58158-8_1.
  98. Hubble parameter measurement constraints on the cosmological deceleration-acceleration transition redshift. Astrophys. J. Lett. 2013, 766, L7. https://doi.org/10.1088/2041-8205/766/1/L7.
  99. Scolnic, D.M.; et al. The Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample. Astrophys. J. 2018, 859, 101. https://doi.org/10.3847/1538-4357/aab9bb.
  100. Impact of the cosmic variance on H0subscript𝐻0H_{0}italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT on cosmological analyses. Phys. Rev. D 2018, 98, 023537. https://doi.org/10.1103/PhysRevD.98.023537.
  101. Hinshaw, G.; et al. Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results. Astrophys. J. Suppl. 2013, 208, 19. https://doi.org/10.1088/0067-0049/208/2/19.
  102. Distance Priors from Planck Final Release. JCAP 2019, 2, 028. https://doi.org/10.1088/1475-7516/2019/02/028.
  103. MOG cosmology without dark matter and the cosmological constant. Mon. Not. Roy. Astron. Soc. 2021, 507, 3387–3399. https://doi.org/10.1093/mnras/stab2350.
  104. No Evidence for Dark Energy Dynamics from a Global Analysis of Cosmological Data. Phys. Rev. D 2009, 80, 121302. https://doi.org/10.1103/PhysRevD.80.121302.
  105. Null tests of the standard model using the linear model formalism. Phys. Rev. D 2018, 97, 083510. https://doi.org/10.1103/PhysRevD.97.083510.
Citations (10)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up