Journal of Holography Applications in Physics
Inflation driven by Barrow holographic dark energy
Document Type : Regular article
Authors
1 Department of Mathematics, Techno India Salt Lake, Sector-V, Kolkata-700 091, India.
2 Department of Mathematics, Asutosh College, Kolkata-700026, W. B., India
Abstract
In this work we have investigated the inflation mechanism driven by the Barrow Holographic dark energy (BHDE) in the early universe. BHDE is based on the Barrow relation for horizon entropy, which in turn is inspired from the shape of the COVID-19 virus. It was shown by Barrow that the quantum gravitational effects may instigate complex fractal features in the structure of a black hole. Since the length scale during the inflation is expected to be small, the energy density obtained from the application of the holographic principle in the early universe will be large enough to support the inflationary scenario. Using the Granda-Oliveros IR cut-off we have studied the inflationary scenario with the universe filled with BHDE. Various analytic solutions for the model were found out including the slow-roll parameters, scalar spectral index and tensor-to-scalar ratio. Since inflation is generally attributed to the presence of scalar fields, we have explored a correspondence between BHDE and scalar field models. Both canonical scalar field and the Tachyonic scalar field have been considered for this purpose. The evolution of the potential generated from the fields are plotted and found to be consistent with the observations. From the work we see that BHDE can be a model of dark energy that can successfully drive the early time inflation.
Keywords
Main Subjects
Article PDF
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[48] G. Wilk, Z. Wlodarczyk, ”Interpretation of the Nonextensivity Parameter q in Some Applications of Tsallis Statistics and Levy Distributions”, Phys. Rev. Lett. 84, 2770(2000).
[49] C. Tsallis, L. J. L. Cirto, ”Black hole thermodynamical entropy”, Eur. Phys. J. C 73, 2487 (2013).
[50] M. Tavayef, A. Sheykhi, K. Bamba, H. Moradpour, ”Tsallis holographic dark energy”, Phys. Lett. B 781, 195 (2018).
[51] A. S. Jahromi, S. Moosavi, H. Moradpour, J. M. Graca, I. Lobo, I. Salako, A. Jawad, ”Generalized entropy formalism and a new holographic dark energy model”, Phys. Lett. B 780, 21 (2018).
[52] E. N. Saridakis, K. Bamba, R. Myrzakulov, F. K. Anagnostopoulos, ”Holographic dark energy through Tsallis entropy”, J. Cosmol. Astropart. Phys. 12, 012 (2018).
[53] A. Sheykhi, ”Modified Friedmann equations from Tsallis entropy”, Phys. Lett. B 785, 118 (2018).
[54] A. A. Mamon, A. H. Ziaie, K. Bamba, ”A Generalized Interacting Tsallis Holographic Dark Energy Model and its thermodynamic implications”, Eur. Phys. J. C 80, 974 (2020).
[55] A. Mohammadi, T. Golanbari, K. Bamba, I. P. Lobo, ”Tsallis holographic dark energy for inflation”, Phys. Rev. D 103, 083505 (2021).
[56] S. Nojiri, S. D. Odintsov, E. N. Saridakis, ”Holographic inflation”, Phys. Lett. B 797, 134829 (2019).
[57] A. Oliveros, M. A. Acero, ”Inflation driven by a holographic energy density”, Europhys. Lett. 128, 59001 (2019).
[58] https://www.youtube.com/watch?v=pPb5NKEYCD8.
[59] J. D. Barrow, ”The Area of a Rough Black Hole”, Phys. Lett. B 808, 135643 (2020).
[60] E. N. Saridakis, ”Barrow holographic dark energy”, Phys. Rev. D 102, 123525 (2020).
[61] D. Kaiser, ”Primordial Spectral Indices from Generalized Einstein Theories”, Phys. Rev. D 52, 4295 (1995).
[62] M. Sasaki, E. D. Stewart, ”A General Analytic Formula for the Spectral Index of the Density Perturbations produced during Inflation”, Prog. Theor. Phys. 95, 71 (1996).
[63] J. Martin, C. Ringeval, V. Vennin, ”Encyclopaedia Inflationaris”, Phys. Dark Univ. 5-6, 75 (2014).
[64] R. P. Woodard, ”Perturbative quantum gravity comes of age”, Int. J. Mod. Phys. D 23, 1430020 (2014).
[65] K. Bamba, S. Capozziello, S. Nojiri, S. D. Odintsov, ”Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests”, Astrophys. Space Sci. 342, 155 (2012).
[66] A. Sen, ”Tachyon Matter”, J. High Energy Phys. 065, 0207 (2002).
[2] A. A. Starobinsky, ”A new type of isotropic cosmological models without singularity”, Phys. Lett. B 91, 99 (1980).
[3] A. Albrecht, P. J. Steinhardt, ”Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking”, Phys. Rev. Lett. 48, 1220 (1982).
[4] A. D. Linde, ”A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems”, Phys. Lett. B 108, 389 (1982).
[5] A. D. Linde, ”Chaotic inflation”, Phys. Lett. B 129, 177 (1983). [6] S. Perlmutter et. al., ”Measurements of Ω and Λ from 42 High-Redshift Supernovae”, Astrophys. J. 517, 565 (1999).
[7] A. G. Riess et al., ”Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant”, Astron. J. 116, 1009 (1998).
[8] A. D. Linde, ”Inflationary cosmology”, Phys. Rep. 333, 575 (2000). [9] A. D. Linde, ”Current understanding of inflation”, New Astron. Rev. 49, 35 (2005).
[10] A. D. Linde, ”Prospects of Inflation”, Phys. Scr. T117, 40 (2005). [11] A. Berera, ”Warm Inflation”, Phys. Rev. Lett. 75, 3218 (1995).
[12] R. Maartens, D.Wands, B. A. Bassett, I. P. Heard, ”Chaotic inflation on the brane”, Phys. Rev. D 62, 041301 (2000).
[13] S. Mukohyama, ”Brane cosmology driven by the rolling tachyon”, Phys. Rev. D 66, 024009 (2002).
[14] A. Feinstein, ”Power-law inflation from the rolling tachyon”, Phys. Rev. D 66, 063511 (2002).
[15] T. Padmanabhan, ”Accelerated expansion of the universe driven by tachyonic matter”, Phys. Rev. D 66, 021301 (2002).
[16] G. Barenboim, W. H. Kinney, ”Slow roll in simple non-canonical inflation”, J. Cosmol. Astropart. Phys. 03, 014 (2007) .
[17] P. Franche, R. Gwyn, B. Underwood, A. Wissanji, ”Initial conditions for noncanonical inflation”, Phys. Rev. D 82, 063528 (2010).
[18] S. Unnikrishnan, V. Sahni, A. Toporensky, ”Refining inflation using non-canonical scalars”, J. Cosmol. Astropart. Phys. 08, 018 (2012) .
[19] K.-i. Maeda, K. Yamamoto, ”Stability analysis of inflation with an SU(2) gauge field”, J. Cosmol. Astropart. Phys. 12, 018 (2013).
[20] A. Mohammadi, T. Golanbari, S. Nasri, K. Saaidi, ”Constant-roll brane inflation”, Phys. Rev. D 101, 123537 (2020).
[21] P. Brax, ”What makes the Universe accelerate? A review on what dark energy could be and how to test it”, Rep. Prog. Phys. 81, 016902 (2018).
[22] A. Kamenshchik, U. Moschella, V. Pasquier, ”Antiprotons stopping in xenon”, Phys. Lett. B 511, 265 (2001).
[23] V. Gorini, A. Kamenshchik, U. Moschella, ”Can the Chaplygin gas be a plausible model for dark energy?”, Phys. Rev. D 67, 063509 (2003).
[24] U. Alam, V. Sahni, T. D. Saini, A. A. Starobinsky, ”Exploring the expanding Universe and dark energy using the statefinder diagnostic”, Mon. Not. R. Astron. Soc. 344, 1057 (2003).
[25] P. Rudra, U. Debnath, R. Biswas, ”Dynamics of modified Chaplygin gas in brane world scenario: phase plane analysis”, Astrophys. Space. Sci. 339, 53 (2012).
[26] R. Chowdhury, P.Rudra, ”Interacting Generalized Cosmic Chaplygin Gas in Loop Quantum Cosmology: A Singularity Free Universe”, Int. J. Theor. Phys. 52, 489 (2013)
[27] P. Rudra, ”Dynamics of interacting generalized cosmic Chaplygin gas in brane-world scenario”, Astrophys. Space. Sci. 342, 579 (2012)
[28] S. D. H. Hsu, ”Entropy bounds and dark energy”, Phys. Lett. B 594, 13 (2004).
[29] R. Horvat, ”Holography and Variable Cosmological Constant”, Phys. Rev. D 70, 087301 (2004).
[30] M. Li, ”A Model of Holographic Dark Energy”, Phys. Lett. B 603, 1 (2004).
[31] G.’t Hooft, ”Dimensional Reduction in Quantum Gravity”, Conf. Proc. C 930308, 284 (1993).
[32] L. Susskind, ”The World as a Hologram”, J. Math. Phys. (N.Y.) 36, 6377 (1995).
[33] R. Bousso, ”The holographic principle”, Rev. Mod. Phys. 74, 825 (2002).
[34] L. Susskind, ”Entanglement and Chaos in De Sitter Space Holography: An SYK Ex- ample”, Journal of Holography Applications in Physics 1, 1 (2021).
[35] S. Nojiri, S. D. Odintsov, ”Unifying phantom inflation with late-time acceleration: scalar phantom-non-phantom transition model and generalized holographic dark energy”, Gen. Relativ. Gravit. 38, 1285 (2006).
[36] S. Nojiri, S. D. Odintsov, E. N. Saridakis, ”Modified cosmology from extended entropy with varying exponent”, Eur. Phys. J. C 79, 242 (2019).
[37] S. Nojiri, S. Odintsov, V. Oikonomou, T. Paul, ”Unifying holographic inflation with holographic dark energy: A covariant approach”, Phys. Rev. D 102, 023540 (2020).
[38] L. Granda, A. Oliveros, ”Infrared cut-off proposal for the Holographic density”, Phys. Lett. B 669, 275 (2008).
[39] L. Granda, A. Oliveros, ”New infrared cut-off for the holographic scalar fields models of dark energy”, Phys. Lett. B 671, 199 (2009).
[40] R. B. Mann, S. N. Solodukhin, ”Quantum scalar field on a three-dimensional (BTZ) black hole instanton: Heat kernel, effective action, and thermodynamics”, Phys. Rev. D 55, 3622 (1997).
[41] C. Rovelli, ”Black Hole Entropy from Loop Quantum Gravity”, Phys. Rev. Lett. 77, 3288 (1996).
[42] A. Ashtekar, J. Baez, A. Corichi, K. Krasnov, ”Quantum Geometry and Black Hole Entropy”, Phys. Rev. Lett. 80, 904 (1998).
[43] R. K. Kaul, P. Majumdar, ”Logarithmic Correction to the Bekenstein-Hawking Entropy”, Phys. Rev. Lett. 84, 5255 (2000).
[44] S. Das, S. Shankaranarayanan, S. Sur, ”Power-law corrections to entanglement entropy of horizons”, Phys. Rev. D 77, 064013 (2008).
[45] N. Radicella, D. Pavon, ”The generalized second law in universes with quantum corrected entropy relations”, Phys. Lett. B 691, 121 (2010).
[46] C. Tsallis, ”Possible generalization of Boltzmann-Gibbs statistics”, J. Stat. Phys. 52, 479 (1988).
[47] M. Lyra, C. Tsallis, ”Nonextensivity and Multifractality in Low-Dimensional Dissipative Systems”, Phys. Rev. Lett. 80, 53 (1998).
[48] G. Wilk, Z. Wlodarczyk, ”Interpretation of the Nonextensivity Parameter q in Some Applications of Tsallis Statistics and Levy Distributions”, Phys. Rev. Lett. 84, 2770(2000).
[49] C. Tsallis, L. J. L. Cirto, ”Black hole thermodynamical entropy”, Eur. Phys. J. C 73, 2487 (2013).
[50] M. Tavayef, A. Sheykhi, K. Bamba, H. Moradpour, ”Tsallis holographic dark energy”, Phys. Lett. B 781, 195 (2018).
[51] A. S. Jahromi, S. Moosavi, H. Moradpour, J. M. Graca, I. Lobo, I. Salako, A. Jawad, ”Generalized entropy formalism and a new holographic dark energy model”, Phys. Lett. B 780, 21 (2018).
[52] E. N. Saridakis, K. Bamba, R. Myrzakulov, F. K. Anagnostopoulos, ”Holographic dark energy through Tsallis entropy”, J. Cosmol. Astropart. Phys. 12, 012 (2018).
[53] A. Sheykhi, ”Modified Friedmann equations from Tsallis entropy”, Phys. Lett. B 785, 118 (2018).
[54] A. A. Mamon, A. H. Ziaie, K. Bamba, ”A Generalized Interacting Tsallis Holographic Dark Energy Model and its thermodynamic implications”, Eur. Phys. J. C 80, 974 (2020).
[55] A. Mohammadi, T. Golanbari, K. Bamba, I. P. Lobo, ”Tsallis holographic dark energy for inflation”, Phys. Rev. D 103, 083505 (2021).
[56] S. Nojiri, S. D. Odintsov, E. N. Saridakis, ”Holographic inflation”, Phys. Lett. B 797, 134829 (2019).
[57] A. Oliveros, M. A. Acero, ”Inflation driven by a holographic energy density”, Europhys. Lett. 128, 59001 (2019).
[58] https://www.youtube.com/watch?v=pPb5NKEYCD8.
[59] J. D. Barrow, ”The Area of a Rough Black Hole”, Phys. Lett. B 808, 135643 (2020).
[60] E. N. Saridakis, ”Barrow holographic dark energy”, Phys. Rev. D 102, 123525 (2020).
[61] D. Kaiser, ”Primordial Spectral Indices from Generalized Einstein Theories”, Phys. Rev. D 52, 4295 (1995).
[62] M. Sasaki, E. D. Stewart, ”A General Analytic Formula for the Spectral Index of the Density Perturbations produced during Inflation”, Prog. Theor. Phys. 95, 71 (1996).
[63] J. Martin, C. Ringeval, V. Vennin, ”Encyclopaedia Inflationaris”, Phys. Dark Univ. 5-6, 75 (2014).
[64] R. P. Woodard, ”Perturbative quantum gravity comes of age”, Int. J. Mod. Phys. D 23, 1430020 (2014).
[65] K. Bamba, S. Capozziello, S. Nojiri, S. D. Odintsov, ”Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests”, Astrophys. Space Sci. 342, 155 (2012).
[66] A. Sen, ”Tachyon Matter”, J. High Energy Phys. 065, 0207 (2002).
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Volume 2, Issue 1
We would like to dedicate this issue to the memory of Prof. John D. Barrow.January 2022Pages 1-12
- Receive Date: 05 October 2021
- Revise Date: 06 November 2021
- Accept Date: 06 January 2022