Journal of Holography Applications in Physics
The Effects of Pole Dark Energy on Gravitational Waves
Document Type : Regular article
Authors
1 Center for Theoretical Physics, College of Physical Science and Technology, Sichuan University, Chengdu 610065, People’s Republic of China.
2 Department of Mathematics, Asutosh College, Kolkata-700 026, W. B., India
3 Department of Mathematics, Sister Nivedita University, DG-1/2, Action Area 1, New Town, Kolkata-700 156, India
4 Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711 103, India
Abstract
In this paper, we have studied the effects of pole dark energy on the evolution of gravitational waves. The background evolution of gravitational waves in a flat FRW universe is considered, and its dynamics are studied in the presence of pole dark energy. Two different potential functions are considered for the study. Using the field equations, we formulated the perturbed equations governing the evolution of gravitational waves with respect to redshift $z$ within the background of the FRW Universe. Subsequently, we delved into the characteristics of gravitational waves for the pole dark energy model and reached interesting results. We also probed the evolution of the gravitational waves for a universe driven by a cosmological constant and used it as a comparison for the results obtained for pole dark energy. From the analysis, we see that pole dark energy is superior as a dark energy model in driving the spacetime disturbances, compared to a cosmological constant.
Keywords
Main Subjects
Article PDF
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[26] T. W. B. Kibble, “Topology of Cosmic Domains and Strings”, J. Phys. A: Math. Gen. 9, 1387 (1976). DOI: 10.1088/0305-4470/9/8/029
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[47] H. Wei, R. G. Cai, Phys. Rev. D 72, 12350 (2005). DOI: 10.1103/PhysRevD.72.123507
[48] B. Gumjudpai, J. Ward, “Generalised DBI-Quintessence”, Phys. Rev. D 80, 023528 (2009). DOI: 10.1103/PhysRevD.80.023528
[49] J. Martin, M. Yamaguchi, “DBI-essence”, Phys. Rev. D 77, 123508 (2008). DOI: 10.1103/PhysRevD.77.123508
[50] N. Ogawa, “A note on classical solution of Chaplygin-gas as D-brane”, Phys. Rev. D 62, 085023 (2000). DOI: 10.1103/PhysRevD.62.085023
[51] A. Kamenshchik, U. Moschella, V. Pasquier, “Chaplygin-like gas and branes in black hole bulks”, Phys. Lett. B 487, 7 (2000). DOI: 10.1016/S0370-2693(00)00788-2
[52] M. Li, “A model of holographic dark energy”, Phys. Lett. B 603, 1 (2004). DOI: 10.1016/j.physletb.2004.10.014
[53] S. D. H. Hsu, “Entropy bounds and dark energy”, Phys. Lett. B 594, 13 (2004). DOI: 10.1016/j.physletb.2004.05.020
[54] H. Wei, R.-G. Cai, “A new model of agegraphic dark energy”, Phys. Lett. B 660, 113 (2008). DOI: 10.1016/j.physletb.2007.12.030
[55] H. Wei, R.-G. Cai, “Interacting agegraphic dark energy”, Eur. Phys. J. C 59, 99 (2009). DOI: 10.1140/epjc/s10052-008-0811-3
[56] E. V. Linder, “Pole dark energy”, Phys. Rev. D 101, 023506 (2020). DOI: 10.1103/PhysRevD.101.023506
[57] C. J. Feng, X. H. Zhai, X. Z. Li, “Multi-pole dark energy”, Chin. Phys. C 44, 105103 (2020). DOI: 10.1088/1674-1137/abab91
[58] E. V. Linder, “Detecting Helium Reionization with Fast Radio Bursts”, Phys. Rev. D 101, 103019 (2020). DOI: 10.1103/PhysRevD.101.103019
[59] B. J. Broy, M. Galante, D. Roest, A. Westphal, “Pole Inflation — Shift Symmetry and Universal Corrections”, J. High Energy Phys. 12, 149 (2015). DOI: 10.1007/JHEP12(2015)149
[60] T. Terada, “Generalized pole inflation: Hilltop, natural, and chaotic inflationary attractors”, Phys. Lett. B 760, 674 (2016). DOI: 10.1016/j.physletb.2016.07.050
[61] A. Achucarro, S. Cespedes, A-C. Davis, G. A. Palma, “Constraints on holographic multi-field inflation and models based on the Hamilton-Jacobi formalism”, Phys. Rev. Lett. 122, 191301 (2019). DOI: 10.1103/PhysRevLett.122.191301
[62] X. Zhang, “Holographic Ricci dark energy: Current observational constraints, quintom feature, and the reconstruction of scalar-field dark energy”, Phys. Rev. D. 79, 103509 (2009). DOI: 10.1103/PhysRevD.79.103509
[63] A. Tita, B. Gumjudpai, “Cosmological dynamics of holographic dark energy with non-minimally coupled scalar field”, Gen Relativ Gravit. 57, 106 (2025). DOI: 10.1007/s10714-025-03615-7
[64] P. Baisri, B. Gumjudpai, C. Kritpetch, P. Vanichchapongjaroen, “Cosmology in holographic non-minimal derivative coupling theory: Constraints from inflation and variation of gravitational constant”, Physics of the Dark Universe 41, 101251 (2023). DOI: 10.1016/j.dark.2023.101251
[65] R. Brustein, A. J. M. Medved, K. Yagi, “Lower limit on the entropy of black holes as inferred from gravitational wave observations”, Phys. Rev. D. 100, 104009 (2019). DOI: 10.1103/PhysRevD.100.104009
[66] F. Bigazzi, A. Caddeo, A. L. Cotrone, A. Paredes, “Dark Holograms and Gravitational Waves”, J. High Energ. Phys. 2021, 94 (2021). DOI: 10.1007/JHEP04(2021)094
[67] D. Bar, “Gravitational Wave Holography”, Int. J. Theor. Phys. 46, 503 (2007). DOI: 10.1007/s10773-006-9243-8
[2] R. Crittenden, R. L. Davis, P. J. Steinhardt, “Polarization of the microwave background due to primordial gravitational waves”, Astrophys. J. 417, L13 (1993). DOI:10.1086/187310
[3] A. Buonanno, M. Maggiore, C. Ungarelli, “Spectrum of relic gravitational waves in string cosmology”, Phys. Rev. D 55, 3330 (1997). DOI:10.1103/PhysRevD.55.3330
[4] M. Gasperini, “Tensor perturbations in high-curvature string backgrounds”, Phys. Rev. D 56, 4815 (1997). DOI:10.1103/PhysRevD.56.4815
[5] J. C. Fabris, S. V. B. Gonçalves, “Gravitational waves in an expanding Universe”, (1998). [arXiv:gr-qc/9808007v1]
[6] M. P. Infante, N. Sanchez, “The Primordial Gravitational Wave Background in String Cosmology”, Phys. Rev. D 61, 083515 (2000). DOI: 10.1103/PhysRevD.61.083515
[7] A. Riazuelo, J.-P. Uzan, “Quintessence and gravitational waves”, Phys. Rev. D 62, 083506 (2000). DOI: 10.1103/PhysRevD.62.083506
[8] J. C. Fabris, S. V. B. Goncalves, M. S. Santos, “Gravitational waves in the generalized Chaplygin gas model”, Gen. Relativity Gravitation 36, 2559 (2004). DOI: 10.1023/B:GERG.0000046183.62913.9e
[9] M. S. Santos, S. V. B. Goncalves, J. C. Fabris, E. M. de Gouveia Dal Pino, “Modeling the spectrum of gravitational waves in the primordial Universe”, AIP Conf. Proc. 784, 800 (2005). DOI: 10.1063/1.2077245
[10] M. B. Lopez, P. Frazao, A. B. Henriques, “Stochastic gravitational waves from a new type of modified Chaplygin gas”, Phys. Rev. D 81, 063504 (2010). DOI: 10.1103/PhysRevD.81.063504
[11] N. Zhang, Y.-K. E. Cheung, “Primordial gravitational waves spectrum in the Coupled-Scalar-Tachyon Bounce Universe”, Eur. Phys. J. C 80, 100 (2020). DOI: 10.1140/epjc/s10052-020-7659-6
[12] U. Debnath, “Gravitational waves for variable modified Chaplygin gas and some parametrizations of dark energy in the background of FRW universe”, Eur. Phys. J. Plus 135, 135 (2020). DOI: 10.1140/epjp/s13360-020-00221-1
[13] U. Debnath, Phys. Dark Univ. 32, 100832 (2021). DOI: 10.1016/j.dark.2021.100832
[14] S. Maity, P. Rudra, “Gravitational waves driven by Holographic dark energy”, Nucl. Phys. B 1009, 116724 (2024). DOI: 10.1016/j.nuclphysb.2024.116724
[15] P. Rudra, S. Maity, “Gravitational waves in f(Q) gravity”, Sayam 2, 39 (2024).
[16] B. P. Abbott et al., “Observation of Gravitational Waves from a Binary Black Hole Merger”, Phys. Rev. Lett. 116, 061102 (2016). DOI: 10.1103/PhysRevLett.116.061102
[17] J. Cervantes-Cota, S. Galindo-Uribarri, G. Smoot, “A Brief History of Gravitational Waves”, Universe 2, 22 (2016). DOI: 10.3390/universe2030022
[18] J. H. Taylor, J. M. Weisberg, “A new test of general relativity: Gravitational radiation and the binary pulsar PSR 1913+16”, Astrophys. J. 253, 908 (1982). DOI: 10.1086/15969
[19] R. A. Hulse, J. H. Taylor, “Discovery of a pulsar in a binary system”, Astrophys. J. 195, L51 (1975). DOI: 10.1086/181708
[20] A. G. Riess et al. (Supernova Search Team Collaboration), “Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant”, Astron. J. 116, 1009 (1998). DOI: 10.1086/300499
[21] R. Abbott et al., “GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run”, Phys. Rev. X 13, 041039 (2023). DOI: 10.1103/PhysRevX.13.041039
[22] M. Rajagopal, R. W. Romani, “Ultralow-frequency Gravitational Radiation from Massive Black Hole Binaries”, Astrophys. J. 446, 543 (1995). DOI: 10.1086/175813
[23] A. H. Jaffe, D. C. Backer, “Gravitational Waves Probe the Coalescence Rate of Massive Black Hole Binaries”, Astrophys. J. 583, 616 (2003). DOI: 10.1086/345361
[24] J. S. B. Wyithe, A. Loeb, “Low-Frequency Gravitational Waves from Massive Black Hole Binaries: Predictions for LISA and Pulsar Timing”, Astrophys. J. 590, 691 (2003). DOI: 10.1086/375187
[25] A. A. Starobinsky, “A New Type of Isotropic Cosmological Models Without Singularity”, Phys. Lett. B 91, 99 (1980). DOI: 10.1016/0370-2693(80)90670-X
[26] T. W. B. Kibble, “Topology of Cosmic Domains and Strings”, J. Phys. A: Math. Gen. 9, 1387 (1976). DOI: 10.1088/0305-4470/9/8/029
[27] M. Maggiore, “Gravitational Wave Experiments and Early Universe Cosmology”, [arXiv:gr-qc/0008027] (2000).
[28] M. T. Miles et al., Mon. Not. R. Astron. Soc. 519, 3976 (2023). DOI: 10.1093/mnras/stac3721
[29] M. T. Miles et al., “The MeerKAT Pulsar Timing Array: the first search for gravitational waves with the MeerKAT radio telescope”, Mon. Not. R. Astron. Soc. 536, 1489 (2025). DOI: 10.1093/mnras/stae1590
[30] S. J. Perlmutter et al., “Discovery of a supernova explosion at half the age of the Universe.”, Nature 391, 51 (1998). DOI: 10.1038/34124
[31] D. N. Spergel et al., “First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters”, Astrophys. J. Suppl. 148, 175 (2003). DOI: 10.1086/377226
[32] S. Briddle et al., “Precision cosmology? Not just yet”, Science 299, 1532 (2003). DOI: 10.1126/science.1082158
[33] A. R. Liddle, D. H. Lyth, Cosmological Inflation and Large-Scale Structure, Cambridge University Press (2000). ISBN: 9780521660220
[34] D. N. Spergel et al. (WMAP Collaboration), Astrophys. J. Suppl. 148, 175 (2003). DOI: 10.1086/377226
[35] E. Komatsu et al. (WMAP Collaboration), “Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation.”, Astrophys. J. Suppl. 180, 330 (2009). DOI: 10.1088/0067-0049/180/2/33
[36] E. J. Copland, M. Sami, S. Tsujikawa, “Dynamics of dark energy”, Int. J. Mod. Phys. D 15, 1753 (2006). DOI: 10.1142/S021827180600942X
[37] M. Li, X.-D. Li, S. Wang, Y. Wang, Commun. Theor. Phys. 56, 525 (2011). DOI: 10.1088/0253-6102/56/3/20
[38] P. J. E. Peebles, B. Ratra, “Cosmology with a time-variable cosmological “constant””, Astrophys. J. 325, L17 (1988). DOI: 10.1086/185100
[39] R. R. Caldwell, R. Dave, P. J. Steinhardt, “Cosmological imprint of an energy component with general equation of state”, Phys. Rev. Lett. 80, 1582 (1998). DOI: 10.1103/PhysRevLett.80.1582
[40] A. Sen, “Rolling Tachyon”, J. High Energy Phys. 0204, 048 (2002). DOI: 10.1088/1126- 6708/2002/04/048
[41] A. Sen, “Tachyon Matter”, J. High Energy Phys. 0207, 065 (2002). DOI: 10.1088/1126- 6708/2002/07/065
[42] M. Gasperini et al., Phys. Rev. D 65, 023508 (2002). DOI: 10.1103/PhysRevD.65.023508
[43] L. Amendola, M. Gasperini, D. Tocchini-Valentini, C. Ungarelli, Phys. Rev. D 67, 043512 (2003). DOI: 10.1103/PhysRevD.67.043512
[44] C. Armendariz-Picon, V. F. Mukhanov, P. J. Steinhardt, “A dynamical solution to the problem of a small cosmological constant and late-time cosmic acceleration”, Phys. Rev. Lett. 85, 4438 (2000). DOI: 10.1103/PhysRevLett.85.4438
[45] C. Armendariz-Picon, V. F. Mukhanov, P. J. Steinhardt, “Essentials of k-essence”, Phys. Rev. D 63, 103510 (2001). DOI: 10.1103/PhysRevD.63.103510
[46] H. Wei, R. G. Cai, D. F. Zeng, Class. Quantum Grav. 22, 3189 (2005). DOI: 10.1088/0264-9381/22/16/002
[47] H. Wei, R. G. Cai, Phys. Rev. D 72, 12350 (2005). DOI: 10.1103/PhysRevD.72.123507
[48] B. Gumjudpai, J. Ward, “Generalised DBI-Quintessence”, Phys. Rev. D 80, 023528 (2009). DOI: 10.1103/PhysRevD.80.023528
[49] J. Martin, M. Yamaguchi, “DBI-essence”, Phys. Rev. D 77, 123508 (2008). DOI: 10.1103/PhysRevD.77.123508
[50] N. Ogawa, “A note on classical solution of Chaplygin-gas as D-brane”, Phys. Rev. D 62, 085023 (2000). DOI: 10.1103/PhysRevD.62.085023
[51] A. Kamenshchik, U. Moschella, V. Pasquier, “Chaplygin-like gas and branes in black hole bulks”, Phys. Lett. B 487, 7 (2000). DOI: 10.1016/S0370-2693(00)00788-2
[52] M. Li, “A model of holographic dark energy”, Phys. Lett. B 603, 1 (2004). DOI: 10.1016/j.physletb.2004.10.014
[53] S. D. H. Hsu, “Entropy bounds and dark energy”, Phys. Lett. B 594, 13 (2004). DOI: 10.1016/j.physletb.2004.05.020
[54] H. Wei, R.-G. Cai, “A new model of agegraphic dark energy”, Phys. Lett. B 660, 113 (2008). DOI: 10.1016/j.physletb.2007.12.030
[55] H. Wei, R.-G. Cai, “Interacting agegraphic dark energy”, Eur. Phys. J. C 59, 99 (2009). DOI: 10.1140/epjc/s10052-008-0811-3
[56] E. V. Linder, “Pole dark energy”, Phys. Rev. D 101, 023506 (2020). DOI: 10.1103/PhysRevD.101.023506
[57] C. J. Feng, X. H. Zhai, X. Z. Li, “Multi-pole dark energy”, Chin. Phys. C 44, 105103 (2020). DOI: 10.1088/1674-1137/abab91
[58] E. V. Linder, “Detecting Helium Reionization with Fast Radio Bursts”, Phys. Rev. D 101, 103019 (2020). DOI: 10.1103/PhysRevD.101.103019
[59] B. J. Broy, M. Galante, D. Roest, A. Westphal, “Pole Inflation — Shift Symmetry and Universal Corrections”, J. High Energy Phys. 12, 149 (2015). DOI: 10.1007/JHEP12(2015)149
[60] T. Terada, “Generalized pole inflation: Hilltop, natural, and chaotic inflationary attractors”, Phys. Lett. B 760, 674 (2016). DOI: 10.1016/j.physletb.2016.07.050
[61] A. Achucarro, S. Cespedes, A-C. Davis, G. A. Palma, “Constraints on holographic multi-field inflation and models based on the Hamilton-Jacobi formalism”, Phys. Rev. Lett. 122, 191301 (2019). DOI: 10.1103/PhysRevLett.122.191301
[62] X. Zhang, “Holographic Ricci dark energy: Current observational constraints, quintom feature, and the reconstruction of scalar-field dark energy”, Phys. Rev. D. 79, 103509 (2009). DOI: 10.1103/PhysRevD.79.103509
[63] A. Tita, B. Gumjudpai, “Cosmological dynamics of holographic dark energy with non-minimally coupled scalar field”, Gen Relativ Gravit. 57, 106 (2025). DOI: 10.1007/s10714-025-03615-7
[64] P. Baisri, B. Gumjudpai, C. Kritpetch, P. Vanichchapongjaroen, “Cosmology in holographic non-minimal derivative coupling theory: Constraints from inflation and variation of gravitational constant”, Physics of the Dark Universe 41, 101251 (2023). DOI: 10.1016/j.dark.2023.101251
[65] R. Brustein, A. J. M. Medved, K. Yagi, “Lower limit on the entropy of black holes as inferred from gravitational wave observations”, Phys. Rev. D. 100, 104009 (2019). DOI: 10.1103/PhysRevD.100.104009
[66] F. Bigazzi, A. Caddeo, A. L. Cotrone, A. Paredes, “Dark Holograms and Gravitational Waves”, J. High Energ. Phys. 2021, 94 (2021). DOI: 10.1007/JHEP04(2021)094
[67] D. Bar, “Gravitational Wave Holography”, Int. J. Theor. Phys. 46, 503 (2007). DOI: 10.1007/s10773-006-9243-8
)
Volume 5, Issue 4
October 2025Pages 50-67
- Receive Date: 10 August 2025
- Revise Date: 08 September 2025
- Accept Date: 12 September 2025