Zero-Mass Scalar Field with Interacting and Non-interacting Two Fluids in f (R, T) Gravity

Kalpana Pawar¹ , N.T. Katre²

1. Department of Mathematics, Shivaji Science College, Nagpur, Dist. Nagpur (M.S.), India.
2. Department of Mathematics, Nabira Mahavidyalaya, Katol, Dist. Nagpur (M.S.), India.

Section:Research Paper, Product Type: Journal-Paper
Vol.11 , Issue.5 , pp.1-18, Oct-2023

Online published on Oct 31, 2023

Copyright © Kalpana Pawar, N.T. Katre . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

97 Views    177 Downloads    32 Downloads

Abstract :
This paper deals with the investigation of an accelerated expansion of a spatially homogeneous and isotropic flat Friedman-Lemaitre-Robertson-Walker (FLRW) universe in presence of zero-mass scalar fields associated with non-interacting and interacting barotropic fluid and dark energy in the framework of f (R, T) gravity. The exact solutions to the field equations have been obtained in two cases: power law and exponential law of volumetric expansion. Some physical and geometrical properties have been investigated for both power and exponential law models in non-interacting and interacting cases; in particular, the energy conditions and density parameters. The physical stability of the derived cosmological models has also been examined. We find that the models with exponential volumetric expansion are open, have accelerating expansion and physically stable; while, the models with power law volumetric expansion are open in both accelerating and decelerating cases, but physically stable and unstable in decelerating and accelerating case respectively.

Key-Words / Index Term :
FLRW space-time, f (R, T) gravity, Dark Energy, Zero-mass scalar field, Interacting and Non-interacting, Physical stability.

References :
[1] Garnavich, Peter M., Robert P. Kirshner, Peter Challis, John Tonry, Ron L. Gilliland, R. Chris Smith, Alejandro Clocchiatti et al. "Constraints on cosmological models from Hubble Space Telescope observations of high-z supernovae." The Astrophysical Journal 493, no. 2, L53, 1998.
[2] Garnavich, Peter M., Saurabh Jha, Peter Challis, Alejandro Clocchiatti, Alan Diercks, Alexei V. Filippenko, Ron L. Gilliland et al. "Supernova limits on the cosmic equation of state." The Astrophysical Journal 509, no. 1, 74, 1998.
[3] Riess, Adam G., Alexei V. Filippenko, Peter Challis, Alejandro Clocchiatti, Alan Diercks, Peter M. Garnavich, Ron L. Gilliland et al. "Observational evidence from supernovae for an accelerating universe and a cosmological constant." The astronomical journal 116, no. 3, 1009, 1998.
[4] Riess, Adam G., Louis-Gregory Strolger, John Tonry, Stefano Casertano, Henry C. Ferguson, Bahram Mobasher, Peter Challis et al. "Type Ia supernova discoveries at z> 1 from the Hubble Space Telescope: Evidence for past deceleration and constraints on dark energy evolution." The Astrophysical Journal 607, no. 2, 665, 2004.
[5] Perlmutter, Saul, Goldhaber Aldering, Gerson Goldhaber, R. A. Knop, Peter Nugent, Patricia G. Castro, Susana Deustua et al. "Measurements of ? and ? from 42 high-redshift supernovae." The Astrophysical Journal 517, no. 2, 565, 1999.
[6] Bennett, C. L. "First year Wilkinson microwave anisotropy probe (WMAP) observations: Preliminary maps and basic results." Astrophys. J. Suppl 148, no. 1, 2003.
[7] Spergel, David N., Licia Verde, Hiranya V. Peiris, Eiichiro Komatsu, M. R. Nolta, Charles L. Bennett, Mark Halpern et al. "First-year Wilkinson Microwave Anisotropy Probe (WMAP)* observations: determination of cosmological parameters." The Astrophysical Journal Supplement Series 148, no. 1, 175, 2003.
[8] Caldwell, Robert R., and Michael Doran. "Cosmic microwave background and supernova constraints on quintessence: concordance regions and target models." Physical Review D 69, no. 10, 103517, 2004.
[9] Huang, Zhuo-Yi, Bin Wang, Elcio Abdalla, and Ru-Keng Su. "Holographic explanation of wide-angle power correlation suppression in the cosmic microwave background radiation." Journal of Cosmology and Astroparticle Physics 2006, no. 05, 013, 2006.
[10] Tegmark, Max, Michael A. Strauss, Michael R. Blanton, Kevork Abazajian, Scott Dodelson, Havard Sandvik, Xiaomin Wang et al. "Cosmological parameters from SDSS and WMAP." Physical review D 69, no. 10, 103501, 2004.
[11] Tegmark, Max, Michael R. Blanton, Michael A. Strauss, Fiona Hoyle, David Schlegel, Roman Scoccimarro, Michael S. Vogeley et al. "The three-dimensional power spectrum of galaxies from the sloan digital sky survey." The Astrophysical Journal 606, no. 2 (2004): 702.
[12]Weinberg, Steven. "The cosmological constant problem." Reviews of modern physics 61, no. 1 (1989): 1.
[13] Carroll, Sean M. "The cosmological constant." Living reviews in relativity 4, no. 1 (2001): 1-56.
[14] Peebles, P. James E., and Bharat Ratra. "The cosmological constant and dark energy." Reviews of modern physics 75, no. 2 (2003): 559.
[15] Padmanabhan, Thanu. "Cosmological constant—the weight of the vacuum." Physics Reports 380, no. 5-6 (2003): 235-320.
[16] Eisenstein, Daniel J., Idit Zehavi, David W. Hogg, Roman Scoccimarro, Michael R. Blanton, Robert C. Nichol, Ryan Scranton et al. "Detection of the baryon acoustic peak in the large-scale correlation function of SDSS luminous red galaxies." The Astrophysical Journal 633, no. 2 (2005): 560.
[17] Nojiri, Shin`ichi, and Sergei D. Odintsov. "Introduction to modified gravity and gravitational alternative for dark energy." International Journal of Geometric Methods in Modern Physics 4, no. 01 (2007): 115-145.
[18] Aghanim, Nabila, Yashar Akrami, Mark Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday et al. "Planck 2018 results-VI. Cosmological parameters." Astronomy & Astrophysics 641 (2020): A6.
[19] Babourova, O. G., and B. Frolov. "The solution of the cosmological constant problem: the cosmological constant exponential decrease in the super-early Universe." Universe 6, no. 12 (2020): 230.
[20] Geng, C. Q., C. C. Lee, and L. Yin. "Constraints on a special running vacuum model." The European Physical Journal C 80, no. 1 (2020): 69.
[21] Wetterich, Christof. "Cosmology and the fate of dilatation symmetry." Nuclear Physics B 302, no. 4 (1988): 668-696.
[22] Ratra, Bharat, and Philip JE Peebles. "Cosmological consequences of a rolling homogeneous scalar field." Physical Review D 37, no. 12, 3406, 1988.
[23] Cicoli, Michele, Francisco G. Pedro, and Gianmassimo Tasinato. "Natural quintessence in string theory." Journal of Cosmology and Astroparticle Physics 2012, no. 07, 044, 2012.
[24] Wetterich, Christof. "Inflation, quintessence, and the origin of mass." Nuclear Physics B 897 (2015): 111-178.
[25] Tsujikawa, Shinji. "Quintessence: a review." Classical and Quantum Gravity 30, no. 21 (2013): 214003.
[26] Turner, M. S., and M. White. "CDM models with a smooth component." Physical Review D 56, no. 8 (1997): R4439.
[27] Xu, L., Y. Wang, M. Tong, and H. Noh. "CMB temperature and matter power spectrum in a decay vacuum dark energy model." Physical Review D 84, no. 12 (2011): 123004.
[28] Armendariz-Picon, C., T. Damour, and V. Mukhanov. "k-Inflation." Physics Letters B 458, no. 2-3 (1999): 209-218.
[29] Chiba, Takeshi, Takahiro Okabe, and Masahide Yamaguchi. "Kinetically driven quintessence." Physical Review D 62, no. 2 (2000): 023511.
[30] Varshney, Gunjan, Umesh Kumar Sharma, and Anirudh Pradhan. "Reconstructing the k-essence and the dilation field models of the THDE in f (R, T) gravity." The European Physical Journal Plus 135, no. 7 (2020): 541.
[31] Caldwell, Robert R. "A phantom menace? Cosmological consequences of a dark energy component with super-negative equation of state." Physics Letters B 545, no. 1-2 (2002): 23-29.
[32] Caldwell, Robert R., Marc Kamionkowski, and Nevin N. Weinberg. "Phantom energy: dark energy with w[33] Elizalde, Emilio, Shin’ichi Nojiri, and Sergei D. Odintsov. "Late-time cosmology in a (phantom) scalar-tensor theory: dark energy and the cosmic speed-up." Physical Review D 70, no. 4 (2004): 043539.
[34] Anisimov, Alexey, Eugeny Babichev, and Alexander Vikman. "B-inflation." Journal of Cosmology and Astroparticle Physics 2005, no. 06 (2005): 006.
[35] Sen, Ashoke. "Rolling tachyon." Journal of High Energy Physics 2002, no. 04 (2002): 048.
[36] Padmanabhan, T., and T. Roy Choudhury. "Can the clustered dark matter and the smooth dark energy arise from the same scalar field?." Physical Review D 66, no. 8 (2002): 081301.
[37] Khoury, Justin, and Amanda Weltman. "Chameleon fields: Awaiting surprises for tests of gravity in space." Physical review letters 93, no. 17 (2004): 171104.
[38] Nojiri, Shin’ichi, Sergei D. Odintsov, V. K. Oikonomou, and Tanmoy Paul. "Unifying holographic inflation with holographic dark energy: A covariant approach." Physical Review D 102, no. 2 (2020): 023540.
[39] Shekh, S. H. "Models of holographic dark energy in f (Q) gravity." Physics of the dark Universe 33 (2021): 100850.
[40] Wang, Shuang, Yi Wang, and Miao Li. "Holographic dark energy." Physics reports 696 (2017): 1-57.
[41] S. D. Katore, S. V. Gore, and A. Y. Shaikh, “Holographic Dark Energy Cosmological Models in f(G) Theory,” New Astron., vol. 80, p. 101420, Oct. 2020, doi: 10.1016/j.newast.2020.101420.
[42] Pawar, D. D., R. V. Mapari, and P. K. Agrawal. "A modified holographic Ricci dark energy model in f (R, T) theory of gravity." Journal of Astrophysics and Astronomy 40, pp.1-8, 2019.
[43] Zhang, Jing-Fei, Yun-He Li, and Xin Zhang. "A global fit study on the new agegraphic dark energy model." The European Physical Journal C 73, no. 1, 2280, 2013.
[44] Pourbagher, A., and Alireza Amani. "Thermodynamics of the viscous f (T, B) gravity in the new agegraphic dark energy model." Modern Physics Letters A 35, no. 20, 2050166, 2020.
[45] Pourhassan, Behnam. "Viscous modified cosmic Chaplygin gas cosmology." International Journal of Modern Physics D 22, no. 09, 1350061, 2013.
[46] Pourhassan, Behnam, and E. O. Kahya. "Extended Chaplygin gas model." Results in Physics 4, 101, 2014.
[47] Kahya, Emre Onur, and B. Pourhassan. "The universe dominated by the extended Chaplygin gas." Modern Physics Letters A 30, no. 13, 1550070, 2015.
[48] Campos, Juliano P., JĂşlio C. Fabris, Rafael Perez, Oliver F. Piattella, and Hermano Velten. "Does Chaplygin gas have salvation?." The European Physical Journal C 73, 1-15, 2013.
[49] Avelino, P. P., K. Bolejko, and G. F. Lewis. "Nonlinear Chaplygin gas cosmologies." Physical Review D 89, no. 10 (2014): 103004.
[50] Buchdahl, Hans A. "Non-linear Lagrangians and cosmological theory." Monthly Notices of the Royal Astronomical Society 150, no. 1 (1970): 1-8.
[51] Ferraro, R., and F. Fiorini. "Modified teleparallel gravity: Inflation without an inflaton." Physical Review D 75, no. 8 (2007): 084031.
[52] Bengochea, G. R., and R. Ferraro. "Dark torsion as the cosmic speed-up." Physical Review D 79, no. 12 (2009): 124019.
[53] Harko, Tiberiu, Francisco SN Lobo, Shin’ichi Nojiri, and Sergei D. Odintsov. "f (R, T) gravity." Physical Review D 84, no. 2 (2011): 024020.
[54] Felice, A. De, and S. Tsujikawa. "Construction of cosmologically viable f (G) gravity models." Physics Letters B 675, no. 1, (2009): 1-8.
[55] Bamba, K., M. Ilyas, M. Z. Bhatti, and Z. Yousaf. "Energy conditions in modified f (G) gravity." General Relativity and Gravitation 49 (2017): 1-17.
[56] Goheer, N., R. Goswami, P. KS Dunsby, and K. Ananda. "Coexistence of matter dominated and accelerating solutions in f (G) gravity." Physical Review D 79, no. 12 (2009): 121301.
[57] Elizalde, E., R. Myrzakulov, V. V. Obukhov, and D. Sáez-Gómez. "?CDM epoch reconstruction from F (R, G) and modified Gauss–Bonnet gravities." Classical and Quantum Gravity 27, no. 9 (2010): 095007.
[58] Bamba, K., S. D. Odintsov, L. Sebastiani, and S. Zerbini. "Finite-time future singularities in modified Gauss–Bonnet and ? (R, G) gravity and singularity avoidance." The European Physical Journal C 67(2010): 295-310.
[59] Bahamonde, S., M. Marciu, and P. Rudra. "Generalised teleparallel quintom dark energy non-minimally coupled with the scalar torsion and a boundary term." Journal of Cosmology and Astroparticle Physics 2018, no. 04 (2018): 056.
[60] Jiménez, J. B., L. Heisenberg, and T. Koivisto. "Coincident general relativity." Physical Review D 98, no. 4 (2018): 044048.
[61] Jiménez, J. B., L. Heisenberg, T. Koivisto.and S. Pekar. "Cosmology in f (Q) geometry." Physical Review D 101, no. 10 (2020): 103507.
[62] Xu, Y., G. Li, T. Harko, and S. D. Liang. "f (Q, T) gravity." The European Physical Journal C 79 (2019): 1-19.
[63] Xu, Y., T. Harko, S. Shahidi, and S. D. Liang. "Weyl type f (Q, T) gravity, and its cosmological implications." The European Physical Journal C 80, no. 5 (2020): 1-22.
[64] Miranda, V., S. E. Jorás, L. Waga, and M. Quartin. "Viable singularity-free f (R) gravity without a cosmological constant." Physical Review Letters 102, no. 22 (2009): 221101.
[65] Sharif, M., and Z. Yousaf. "Instability of a dissipative restricted non-static axial collapse with shear viscosity in f (R) gravity." Journal of Cosmology and Astroparticle Physics 2014, no. 06, 019, 2014.
[66] Chirde, V. R., and S. H. Shekh. "Isotropic background for interacting two fluid scenario coupled with zero mass scalar field in modified gravity." Bulg. J. Phys 43 (2016): 156-169.
[67] Pawar, K., N. T. Katre, and S. H. Shekh. “Accelerating expansion of two fluid Universe coupled with zero mass scalar field in f(R) gravity”. J. of Emerging Tech. and Research, 9, no. 12, pp. e294-e300, 2022.
[68] Houndjo, M. J. S., and O. F. Piattella. "Reconstructing f (R, T) gravity from holographic dark energy." International Journal of Modern Physics D 21, no. 03, 1250024, 2012.
[69] Samanta, G. C. "Universe filled with dark energy (DE) from a wet dark fluid (WDF) in f (R, T) gravity." International Journal of Theoretical Physics 52, pp.2303-2315, 2013.
[70] Singh, J. K., A. Singh, G. K. Goswami, and J. Jena. "Dynamics of a parametrized dark energy model in f (R, T) gravity." Annals of Physics 443 (2022): 168958.
[71] Houndjo, M. J. S. "Reconstruction of f (R, T) gravity describing matter dominated and accelerated phases." International Journal of Modern Physics D 21, no. 01 (2012): 1250003.
[72] Amirhashchi, H., A. Pradhan, and B. Saha. "An interacting two-fluid scenario for dark energy in an FRW universe." Chinese Physics Letters 28, no. 3 (2011): 039801.
[73] Amirhashchi, H., A. Pradhan, and H. Zainuddin. "An interacting and non-interacting two-fluid dark energy models in FRW universe with time dependent deceleration parameter." International Journal of Theoretical Physics 50 (2011): 3529-3543.
[74] Amirhashchi, H., A. Pradhan, and H. Zainuddin. "Interacting two-fluid viscous dark energy models in a non-flat universe." Research in Astronomy and Astrophysics 13, no. 2 (2013): 129.
[75] Pradhan, A., H. Amirhashchi, and B. Saha. "An interacting and non-interacting two-fluid scenario for dark energy in FRW universe with constant deceleration parameter." Astrophysics and Space Science 333, pp.343-350, 2011.
[76] Saha, B., H. Amirhashchi, and A. Pradhan. "Two-fluid scenario for dark energy models in an FRW universe-revisited." Astrophysics and Space Science 342, no. 1, 257-267, 2012.
[77] Adhav, K. S., G. B. Tayade, and A. S. Bansod. "Interacting dark matter and holographic dark energy in an anisotropic universe." Astrophysics and space science 353, pp.249-257, 2014.
[78] Rao, V. U. M., M. Vijaya Santhi, T. Vinutha, and Y. Aditya. "Two-Fluid Scenario for Higher Dimensional Dark Energy Cosmological Model in Saez-Ballester Theory of Gravitation." Prespacetime Journal 7, no. 2, 293-308, 2016.
[79] Reddy, D.R.K., Santikumar, R. and Naidu, R.L. Bianchi Type III Cosmological Models in f(R, T) Theory of Gravity. Astrophysics and Space Science, 342, 249-252, 2012.
[80] Reddy, D. R. K., R. L. Naidu, and B. Satyanarayana. "Kaluza-Klein Cosmological Model in f (R, T) Gravity." International Journal of Theoretical Physics 51, pp.3222-3227, 2012.
[81] Singh, C. P., and V. Singh. "Reconstruction of modified f (R, T) gravity with perfect fluid cosmological models." General Relativity and Gravitation 46, pp.1-14, 2014.
[82] Sahoo, P. K., B. Mishra, and G. Chakradhar Reddy. "Axially symmetric cosmological model in f (R, T) gravity." The European Physical Journal Plus 129, pp.1-8, 2014.
[83] Kumar Yadav, Anil. "Bianchi-V string cosmology with power law expansion in f (R, T) gravity." The European Physical Journal Plus 129, no. 9, 194, 2014.
[84] Brahma, Bishnu Prasad, and Mukunda Dewri. "Bulk Viscous Bianchi Type-V Cosmological Model in f (R, T) Theory of Gravity." Frontiers in Astronomy and Space Sciences 9, 11, 2022.
[85] Zhang, Xin. "An interacting two-fluid scenario for quintom dark energy." Communications in Theoretical Physics 44, no. 4, 762, 2005.