Journal of Holography Applications in Physics
Bouncing Universe for deformed non-minimally coupled inflation model
Document Type : Regular article
Author
India
Abstract
In this paper, we consider non-minimally coupled gravity model. We choose some suitable new variables and achieve the new Hamiltonian and Lagrangian which have harmonic oscillator form. The corresponding Lagrangian is deformed by non-commutative geometry. In order to have solution for the bouncing universe we specify the potential in the equation state. In that case we draw the equation of state in terms of time and show that the equation of state cross $-1$. Such bouncing behavior lead us to apply some conditions on $theta$ and $beta$ from non-commutative geometry. Here, also we can check the stability of system due to deformation of the non-minimally coupled to gravity model. In order to examine the stability of system we obtain the variation of pressure with respect to density energy. Also, we draw the variation of pressure with respect to energy density and show the condition of stability.
Keywords
Main Subjects
Article PDF
[1] S. Nojiri, S. D. Odintsov and E. N. Saridakis, "Holographic bounce", Nucl. Phys. B 949, 114790 (2019).
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[6] B. Wang, E. Abdalla and R. K. Su, "Constraints on the dark energy from holography", Phys. Lett. B 611, 21 (2005).
[7] M. Novello and S. E. Perez Bergliaa, "Bouncing Cosmologies", Phys. Rept. 463, 127 (2008).
[8] S. Mukherji and M. Peloso, "Bouncing and cyclic universes from brane models", Phys. Lett. B 547, 297 (2002).
[9] D. N. Vollick, "Negative Energies on the Brane", Gen. Relativ. Gravit. 34, 1 (2002).
[10] A. Biswas, S. Mukherji and S. S. Pal, "Nonsingluar cosmologies from branes", Int. J. Mod. Phys. A 19, 557 (2004).
[11] D. H. Coule, "Does brane cosmology have realistic principles?", Class. Quantum Grav. 18, 4265 (2001).
[12] S. Foa, "Bouncing pre-big bang on the brane", Phys. Rev. D 68, 043511 (2003).
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[15] A. J. Medved, "Of Bounces, Branes and Bounds", JHEP 0305, 008 (2003).
[16] Y. S. Myung, "Bouncing and cyclic universes in the charged AdS bulk background", Class. Quantum Grav. 20, 935 (2003).
[17] P. Astier and et al., "The Supernova Legacy Survey: measurement of ΩM , OmegaΛ and w from the rst year data set", Astron. Astrophys. 447, 31 (2006).
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[19] A. G. Riess and et al., "Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant (Supernova Search Team Collaboration)",
Astron. J. 116, 1009 (1998).
[20] K. Abazajian and et al., "The Second Data Release of the Sloan Digital Sky Survey (SDSS Collaboration)", Astron. J. 128, 502 (2004).
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[23] D. N. Spergel and et al., "Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Cosmology", Astrophys. J. Suppl. 170, 377 (2007).
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[25] P. J. Steinhardt, L. M. Wang and I. Zlatev, "Cosmological tracking solutions", Phys. Rev. D 59, 123504 (1999).
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[28] T. Padmanabhan, "Accelerated expansion of the universe driven by tachyonic matter", Phys. Rev. D 66, 021301 (2002).
[29] A. Sen, "Tachyon Matter", JHEP 0207, 065 (2002).
[30] N. Arkani-Hamed, H. C. Cheng, M. A. Luty and S. Mukohyama, "Ghost Condensation and a Consistent Infrared Modi cation of Gravity", JHEP 0405, 074 (2004).
[31] F. Piazza and S. Tsujikawa, "Dilatonic ghost condensate as dark energy", JCAP 0407, 004 (2004).
[32] P. S. Apostolopoulos and N. Tetradis, "Late acceleration and w = −1 crossing in induced gravity", Phys. Rev. D 74, 064021 (2006).
[33] B. Feng, X. Wang and X. Zhang, "Dark Energy Constraints from the Cosmic Age and Supernova", Phys. Lett. B 607, 35 (2005).
[34] B. Feng, M. Li, Y. Piao and X. Zhang, "Oscillating Quintom and the Recurrent Uni- verse", Phys. Lett. B 634, 101 (2006).
[35] Z. Guo, Y. Piao, X. Zhang and Y. Z. Zhang, "Cosmological Evolution of a Quintom Model of Dark Energy", Phys. Lett. B 608, 177 (2005).
[36] M. Li, B. Feng and X. Zhang, "A Single Scalar Field Model of Dark Energy with Equation of State Crossing -1", JCAP 0512, 002 (2005).
[37] X. F. Zhang and T. T. Qiu, "Avoiding the Big-Rip Jeopardy in a Quintom Dark Energy Model with Higher Derivatives", Phys. Lett. B 642, 187 (2006).
[38] H. S. Zhang and Z. H. Zhu, "Crossing w = −1 by a single scalar on a Dvali-Gabadadze-Porrati brane", Phys. Rev. D 75, 023510 (2007).
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[41] A. Yu. Kamenshchik, U. Moschella and V. Pasquier, "An alternative to quintessence", Phys. Lett. B 511, 265 (2001).
[42] H. Saadat and B. Pourhassan, "FRW Bulk Viscous Cosmology with Modi ed Chaplygin Gas in Flat Space", Astro. Space Science 343, 783 (2013).
[43] H. Saadat and B. Pourhassan, "FRW bulk viscous cosmology with modi ed cosmic Chaplygin gas", Astro. Space Science 344, 237 (2013).
[44] N. Bilic, G. B. Tupper and R. D. Viollier, "Uni cation of Dark Matter and Dark Energy: the Inhomogeneous Chaplygin Gas", Phys. Lett. B 535 17 (2002).
[45] M. C. Bento, O. Bertolami and A. A. Sen, "Generalized Chaplygin gas, accelerated expansion, and dark-energy-matter uni cation", Phys. Rev. D 66, 043507 (2002).
[46] J. C. Fabris, S. V. B. Goncalves and P. E. de Souza, "Density perturbations in an Universe dominated by the Chaplygin gas", Gen. Relativ. Gravit. 34, 53 (2002).
[47] B. Pourhassan, "Viscous Modi ed Cosmic Chaplygin Gas Cosmology", Int. J. Mod. Phys. D 22, 1350061 (2013).
[48] E. O. Kahya, B. Pourhassan and S. Uraz, "Constructing an in aton potential by mimicking modi ed Chaplygin gas", Phys. Rev. D 92, 103511 (2015).
[49] B. Pourhassan, "Uni ed universe history through phantom extended Chaplygin gas", Can. J. Phys. 94, 659 (2016).
[50] L. Amendola, "Coupled quintessence", Phys. Rev. D 62, 043511 (2000).
[51] M. Szydlowski, A. Kurek and A. Krawiec, "Top ten accelerating cosmological models", Phys. Lett. B 642, 171 (2006).
[52] C. Deayet, G. R. Dvali and G. Gabadadze, "Accelerated universe from gravity leaking
to extra dimensions", Phys. Rev. D 65, 044023 (2002).
[53] M. R. Setare, "Bulk-brane interaction and holographic dark energy", Phys. Lett. B 642, 421 (2006).
[54] A. G. Cohen, D. B. Kaplan and A. E. Nelson, "Eective Field Theory, Black Holes, and the Cosmological Constant", Phys. Rev. Lett. 82, 4971 (1999).
[55] P. Horava and D. Minic, "Probable Values of the Cosmological Constant in a Holographic Theory", Phys. Rev. Lett. 85, 1610 (2000).
[56] E. Elizalde, S. Nojiri, S. D. Odintsov and P. Wang, "Dark Energy: Vacuum Fluctuations, the Eective Phantom Phase, and Holography", Phys. Rev. D 71, 103504 (2005).
[57] M. R. Setare, J. Zhang and X. Zhang, "State nder diagnosis in a non- at universe and the holographic model of dark energy", JCAP 0703, 007 (2007).
[58] R. R. Caldwell and M. Doran, "Dark-energy evolution across the cosmological-constant boundary", Phys. Rev. D 72, 043527 (2005).
[59] W. Hu, "Crossing the phantom divide: Dark energy internal degrees of freedom", Phys. Rev. D 71, 047301 (2005).
[60] A. Vikman, "Can dark energy evolve to the phantom?", Phys. Rev. D 71, 023515 (2005).
[61] G. B. Zhao, J. Q. Xia, M. Li, B. Feng and X. Zhang, "Perturbations of the Quintom Models of Dark Energy and the Eects on Observations", Phys. Rev. D 72, 123515 (2005).
[62] J. Sadeghi, M. R. Setare and A. Banijamali, "String inspired quintom model with non- minimally coupled modi ed gravity", Phys. Lett. B 678, 164 (2009).
[63] M. R. Setare, J. Sadeghi and A. Banijamali, "Bouncing Universe with Non-minimally Coupled Quintom Matter", Phys. Lett. B 669, 9 (2008).
[64] P. A. R. Ade and et al., "Planck 2015 results - XX. Constraints on in ation", Astron. Astrophys. 594, A20 (2016).
[65] T. Markkanen, T. Tenkanen, V. Vaskonen and H. Veermäe, "Quantum corrections to quartic in ation with a non-minimal coupling: metric vs. Palatini," JCAP 03, 029 (2018).
[66] J. Sadeghi, B. Pourhassan, Z. Nekouee and M. Shokri, "Deformation of the quintom cosmological model and its consequences", Int. J. Mod. Phys. D 27, 1850025 (2018).
[67] J. Sadeghi, F. Milani and A. R. Amani, "Bouncing universe with the non-minimally coupled scaler eld and its reconstructing", Mod. Phys. Lett. A 24, 2363 (2009).
[68] E. O Kahya, B. Pourhassan, E. O Kahya and B. Pourhassan, "The universe dominated by the extended Chaplygin gas", Mod. Phys. Lett. A 30, 1550070 (2015).
[69] B. Pourhassan, "Extended Chaplygin Gas in Horava-Lifshitz Gravity", Physics of the Dark Universe 13, 132 (2016).
[70] E.O. Kahya, M. Khurshudyan, B. Pourhassan, R. Myrzakulov and A. Pasqua, "Higher order corrections of the extended Chaplygin gas cosmology with varying G and Λ", Eur. Phys. J. C 75, 43 (2015).
[71] J. Sadeghi, H. Farahani and B. Pourhassan, "Interacting Holographic Extended Chap- lygin Gas and Phantom Cosmology in the Light of BICEP2", Eur. Phys. J. Plus 130, 84 (2015).
[72] E.O. Kahya and B. Pourhassan, "Observational constraints on the extended Chaplygin gas in ation", Astro. Space Science 353, 677 (2014).
[73] E. N. Saridakis, "Barrow holographic dark energy", Phys. Rev. D 102, 123525 (2020).
[74] S. Maity and P. Rudra, "In ation driven by Barrow holographic dark energy", Journal of Holography Applications in Physics 2(1), 1-12 (2022).
[2] X. Zhang and F. Q. Wu, "Constraints on holographic dark energy from type Ia supernova observations", Phys. Rev. D 72, 043524 (2005).
[3] M. Li, X. D. Li, S. Wang and X. Zhang, "Constraints on holographic dark energy from type Ia supernova observations", JCAP 0906, 036 (2009).
[4] J. Lu, E. N. Saridakis, M. R. Setare and L. Xu, "Observational constraints on holographic dark energy with varying gravitational constant", JCAP 1003, 031 (2010).
[5] Q. G. Huang and Y. G. Gong, "Supernova Constraints on a holographic dark energy model", JCAP 0408 (2004) 006. [astro-ph/0403590].
[6] B. Wang, E. Abdalla and R. K. Su, "Constraints on the dark energy from holography", Phys. Lett. B 611, 21 (2005).
[7] M. Novello and S. E. Perez Bergliaa, "Bouncing Cosmologies", Phys. Rept. 463, 127 (2008).
[8] S. Mukherji and M. Peloso, "Bouncing and cyclic universes from brane models", Phys. Lett. B 547, 297 (2002).
[9] D. N. Vollick, "Negative Energies on the Brane", Gen. Relativ. Gravit. 34, 1 (2002).
[10] A. Biswas, S. Mukherji and S. S. Pal, "Nonsingluar cosmologies from branes", Int. J. Mod. Phys. A 19, 557 (2004).
[11] D. H. Coule, "Does brane cosmology have realistic principles?", Class. Quantum Grav. 18, 4265 (2001).
[12] S. Foa, "Bouncing pre-big bang on the brane", Phys. Rev. D 68, 043511 (2003).
[13] J. Hovdebo and R. Myers, "Bouncing braneworlds go crunch!", JCAP 011, 012 (2003). [14] P. Kanti and K. Tamvakis, "Challenges and obstacles for a bouncing universe in brane models", Phys. Rev. D 68, 024014 (2003).
[15] A. J. Medved, "Of Bounces, Branes and Bounds", JHEP 0305, 008 (2003).
[16] Y. S. Myung, "Bouncing and cyclic universes in the charged AdS bulk background", Class. Quantum Grav. 20, 935 (2003).
[17] P. Astier and et al., "The Supernova Legacy Survey: measurement of ΩM , OmegaΛ and w from the rst year data set", Astron. Astrophys. 447, 31 (2006).
[18] S. Perlmutter and et al., "Measurements of Ω and Λ from 42 High-Redshift Supernovae (Supernova Cosmology Project Collaboration)", Astrophys. J. 517, 565 (1999).
[19] A. G. Riess and et al., "Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant (Supernova Search Team Collaboration)",
Astron. J. 116, 1009 (1998).
[20] K. Abazajian and et al., "The Second Data Release of the Sloan Digital Sky Survey (SDSS Collaboration)", Astron. J. 128, 502 (2004).
[21] K. Abazajian and et al., "The Third Data Release of the Sloan Digital Sky Survey (SDSS Collaboration)", Astron. J. 129, 1755 (2005).
[22] D. N. Spergel and et al., "First-Year Wilkinson Microwave Anisotropy Probe (WMAP)*Observations: Determination of Cosmological Parameters (WMAP Collaboration)", Astrophys. J. Suppl. 148, 175 (2003).
[23] D. N. Spergel and et al., "Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Cosmology", Astrophys. J. Suppl. 170, 377 (2007).
[24] R. R. Caldwell, R. Dave and P. J. Steinhardt, "Cosmological Imprint of an Energy Component with General Equation of State", Phys. Rev. Lett. 80, 1582 (1998).
[25] P. J. Steinhardt, L. M. Wang and I. Zlatev, "Cosmological tracking solutions", Phys. Rev. D 59, 123504 (1999).
[26] C. Wetterich, "Cosmology and the fate of dilatation symmetry", Nucl. Phys. B 302, 668 (1988).
[27] C. Armendariz-Picon, V. F. Mukhanov and P. J. Steinhardt, "Essentials of k-essence", Phys. Rev. D 63 103510 (2001).
[28] T. Padmanabhan, "Accelerated expansion of the universe driven by tachyonic matter", Phys. Rev. D 66, 021301 (2002).
[29] A. Sen, "Tachyon Matter", JHEP 0207, 065 (2002).
[30] N. Arkani-Hamed, H. C. Cheng, M. A. Luty and S. Mukohyama, "Ghost Condensation and a Consistent Infrared Modi cation of Gravity", JHEP 0405, 074 (2004).
[31] F. Piazza and S. Tsujikawa, "Dilatonic ghost condensate as dark energy", JCAP 0407, 004 (2004).
[32] P. S. Apostolopoulos and N. Tetradis, "Late acceleration and w = −1 crossing in induced gravity", Phys. Rev. D 74, 064021 (2006).
[33] B. Feng, X. Wang and X. Zhang, "Dark Energy Constraints from the Cosmic Age and Supernova", Phys. Lett. B 607, 35 (2005).
[34] B. Feng, M. Li, Y. Piao and X. Zhang, "Oscillating Quintom and the Recurrent Uni- verse", Phys. Lett. B 634, 101 (2006).
[35] Z. Guo, Y. Piao, X. Zhang and Y. Z. Zhang, "Cosmological Evolution of a Quintom Model of Dark Energy", Phys. Lett. B 608, 177 (2005).
[36] M. Li, B. Feng and X. Zhang, "A Single Scalar Field Model of Dark Energy with Equation of State Crossing -1", JCAP 0512, 002 (2005).
[37] X. F. Zhang and T. T. Qiu, "Avoiding the Big-Rip Jeopardy in a Quintom Dark Energy Model with Higher Derivatives", Phys. Lett. B 642, 187 (2006).
[38] H. S. Zhang and Z. H. Zhu, "Crossing w = −1 by a single scalar on a Dvali-Gabadadze-Porrati brane", Phys. Rev. D 75, 023510 (2007).
[39] X. F. Zhang, H. Li, Y. S. Piao and X. M. Zhang, "Two- eld Models of Dark Energy with Equation of State Across -1", Mod. Phys. Lett. A 21, 231 (2006).
[40] A. Y. Kamenshchik, U. Moschella and V. Pasquier, "Chaplygin-like gas and branes in black hole bulks", Phys. Lett. B 487, 7 (2000).
[41] A. Yu. Kamenshchik, U. Moschella and V. Pasquier, "An alternative to quintessence", Phys. Lett. B 511, 265 (2001).
[42] H. Saadat and B. Pourhassan, "FRW Bulk Viscous Cosmology with Modi ed Chaplygin Gas in Flat Space", Astro. Space Science 343, 783 (2013).
[43] H. Saadat and B. Pourhassan, "FRW bulk viscous cosmology with modi ed cosmic Chaplygin gas", Astro. Space Science 344, 237 (2013).
[44] N. Bilic, G. B. Tupper and R. D. Viollier, "Uni cation of Dark Matter and Dark Energy: the Inhomogeneous Chaplygin Gas", Phys. Lett. B 535 17 (2002).
[45] M. C. Bento, O. Bertolami and A. A. Sen, "Generalized Chaplygin gas, accelerated expansion, and dark-energy-matter uni cation", Phys. Rev. D 66, 043507 (2002).
[46] J. C. Fabris, S. V. B. Goncalves and P. E. de Souza, "Density perturbations in an Universe dominated by the Chaplygin gas", Gen. Relativ. Gravit. 34, 53 (2002).
[47] B. Pourhassan, "Viscous Modi ed Cosmic Chaplygin Gas Cosmology", Int. J. Mod. Phys. D 22, 1350061 (2013).
[48] E. O. Kahya, B. Pourhassan and S. Uraz, "Constructing an in aton potential by mimicking modi ed Chaplygin gas", Phys. Rev. D 92, 103511 (2015).
[49] B. Pourhassan, "Uni ed universe history through phantom extended Chaplygin gas", Can. J. Phys. 94, 659 (2016).
[50] L. Amendola, "Coupled quintessence", Phys. Rev. D 62, 043511 (2000).
[51] M. Szydlowski, A. Kurek and A. Krawiec, "Top ten accelerating cosmological models", Phys. Lett. B 642, 171 (2006).
[52] C. Deayet, G. R. Dvali and G. Gabadadze, "Accelerated universe from gravity leaking
to extra dimensions", Phys. Rev. D 65, 044023 (2002).
[53] M. R. Setare, "Bulk-brane interaction and holographic dark energy", Phys. Lett. B 642, 421 (2006).
[54] A. G. Cohen, D. B. Kaplan and A. E. Nelson, "Eective Field Theory, Black Holes, and the Cosmological Constant", Phys. Rev. Lett. 82, 4971 (1999).
[55] P. Horava and D. Minic, "Probable Values of the Cosmological Constant in a Holographic Theory", Phys. Rev. Lett. 85, 1610 (2000).
[56] E. Elizalde, S. Nojiri, S. D. Odintsov and P. Wang, "Dark Energy: Vacuum Fluctuations, the Eective Phantom Phase, and Holography", Phys. Rev. D 71, 103504 (2005).
[57] M. R. Setare, J. Zhang and X. Zhang, "State nder diagnosis in a non- at universe and the holographic model of dark energy", JCAP 0703, 007 (2007).
[58] R. R. Caldwell and M. Doran, "Dark-energy evolution across the cosmological-constant boundary", Phys. Rev. D 72, 043527 (2005).
[59] W. Hu, "Crossing the phantom divide: Dark energy internal degrees of freedom", Phys. Rev. D 71, 047301 (2005).
[60] A. Vikman, "Can dark energy evolve to the phantom?", Phys. Rev. D 71, 023515 (2005).
[61] G. B. Zhao, J. Q. Xia, M. Li, B. Feng and X. Zhang, "Perturbations of the Quintom Models of Dark Energy and the Eects on Observations", Phys. Rev. D 72, 123515 (2005).
[62] J. Sadeghi, M. R. Setare and A. Banijamali, "String inspired quintom model with non- minimally coupled modi ed gravity", Phys. Lett. B 678, 164 (2009).
[63] M. R. Setare, J. Sadeghi and A. Banijamali, "Bouncing Universe with Non-minimally Coupled Quintom Matter", Phys. Lett. B 669, 9 (2008).
[64] P. A. R. Ade and et al., "Planck 2015 results - XX. Constraints on in ation", Astron. Astrophys. 594, A20 (2016).
[65] T. Markkanen, T. Tenkanen, V. Vaskonen and H. Veermäe, "Quantum corrections to quartic in ation with a non-minimal coupling: metric vs. Palatini," JCAP 03, 029 (2018).
[66] J. Sadeghi, B. Pourhassan, Z. Nekouee and M. Shokri, "Deformation of the quintom cosmological model and its consequences", Int. J. Mod. Phys. D 27, 1850025 (2018).
[67] J. Sadeghi, F. Milani and A. R. Amani, "Bouncing universe with the non-minimally coupled scaler eld and its reconstructing", Mod. Phys. Lett. A 24, 2363 (2009).
[68] E. O Kahya, B. Pourhassan, E. O Kahya and B. Pourhassan, "The universe dominated by the extended Chaplygin gas", Mod. Phys. Lett. A 30, 1550070 (2015).
[69] B. Pourhassan, "Extended Chaplygin Gas in Horava-Lifshitz Gravity", Physics of the Dark Universe 13, 132 (2016).
[70] E.O. Kahya, M. Khurshudyan, B. Pourhassan, R. Myrzakulov and A. Pasqua, "Higher order corrections of the extended Chaplygin gas cosmology with varying G and Λ", Eur. Phys. J. C 75, 43 (2015).
[71] J. Sadeghi, H. Farahani and B. Pourhassan, "Interacting Holographic Extended Chap- lygin Gas and Phantom Cosmology in the Light of BICEP2", Eur. Phys. J. Plus 130, 84 (2015).
[72] E.O. Kahya and B. Pourhassan, "Observational constraints on the extended Chaplygin gas in ation", Astro. Space Science 353, 677 (2014).
[73] E. N. Saridakis, "Barrow holographic dark energy", Phys. Rev. D 102, 123525 (2020).
[74] S. Maity and P. Rudra, "In ation driven by Barrow holographic dark energy", Journal of Holography Applications in Physics 2(1), 1-12 (2022).
)
Volume 3, Issue 1
March 2023Pages 57-70
- Receive Date: 02 February 2023
- Revise Date: 01 March 2023
- Accept Date: 10 March 2023