Thermodynamic analysis for Non-linear system (Van-der-Waals EOS) with viscous cosmology

Abstract

The following paper is motivated by the recent works of Kremer [Gen Relativ Gravit 36(6):1423–1432, 2004; Phys Rev D 68(12):123507, 2003], Vardiashvili (Inflationary constraints on the van Der Waals equation of state, arXiv:1701.00748, 2017), Jantsch (Int J Mod Phys D 25(03):1650031, 2016), Capozziello (Phys Lett A 299(5–6):494–498, 2002) on Van-Der-Waals EOS cosmology. The main aim of this paper is to analyze the thermodynamics of a Non-linear system which in this case is Van-Der-Waals fluid EOS (Capozziello et al., Quintessence without scalar fields, arXiv:astro-ph/0303041, 2003). We have investigated the Van-Der-Waals fluid system with the generalized EOS as p=wleft( rho ,t right) rho +fleft( rho right) -3eta left( H,t right) H (Brevik et al., Int J Geom Methods Mod Phys 15(09):1850150, 2018). The third term signifies viscosity which has been considered as an external parameter that only modifies pressure but not the density of the liquid. The w(rho ,t) and f(rho )are the two functions of energy density and time that are different for the 3 types of Vander Waal models namely one parameter model, two parameters model and three parameters model (Ivanov and Prodanov, Eur Phys J C 79(2):118, 2019; Elizalde and Khurshudyan, Int J Mod Phys D 27(04):1850037, 2018). The value of EOS parameter (w_{EOS}) (Capozziello et al., Quintessence without scalar fields, arXiv:astro-ph/0303041, 2003; Obukhov and Timoshkin, Russ Phys J 60(10):1705–1711, 2018) will showdifferent values for different models. We have studied the changes in the parameters for different cosmic phases [Kremer, Phys Rev D 68(12):123507, 2003; Capozziello et al., Phys Lett A 299(5–6):494–498, 2002; Capozziello et al., Quintessence without scalar fields, arXiv:astro-ph/0303041, 2003]. We have also studied the thermodynamics and the stability conditions for the three models in viscous condition [Obukhov and Timoshkin, Russ Phys J 60(10):1705–1711, 2018; Panigrahi and Chatterjee, Gen Relativ Gravit 49(3):35, 2017; Panigrahi and Chatterjee, J Cosmol Astropart Phys 2016(05):052, 2016; Chakraborty et al., Evolution of FRW Universe in Variable Modified Chaplygin Gas Model, arXiv:1906.12185, 2019]. We have discussed the importance of viscosity (Brevik and Grøn, Astrophys Space Sci 347(2):399–404, 2013) in explaining accelerating universe with negative pressure (Panigrahi and Chatterjee, Gen Relativ Gravit 49(3):35, 2017).Finally, we have resolved the finite time future singularity problems [Brevik et al., The effect of thermal radiation on singularities in the Dark Universe, arXiv:2103.08430, 2021; Odintsov and Oikonomou, Phys Rev D 98(2):024013, 2018; Odintsov and Oikonomou, Int J Mod Phys D 26(08):1750085, 2017; Frampton et al., Phys Rev D 85(8):083001, 2012; Frampton et al., Phys Lett B 708(1–2):204–211, 2012; Frampton et al., Phys Rev D 84(6):063003, 2011] and discussed the thermodynamics energy conditions [Visser and Barcelo, Energy conditions and their cosmological implications. In: Cosmo-99, pp 98–112, 2000; Chattopadhyay et al., Eur Phys J C 74(9):1–13, 2014; Arora et al., Phys. Dark Universe 31:100790, 2021; Sharma and Pradhan, Int J Geom Methods Mod Phys 15(01):1850014, 2018; Sahoo et al., AstronomischeNachrichten 342(1–2):89–95, 2021; Yadav et al., Mod Phys Lett A 34(19):1950145, 2019; Sharma et al., Int J Geom Methods Mod Phys 17(07):2050111, 2020, Moraes and Sahoo, Eur Phys J C 77(7):1–8, 2017; Hulke et al., New Astron 77:101357, 2020; Singla et al., Gravit Cosmol 26(2):144–152, 2020; Sharif et al., Eur Phys J Plus 128(10):1–11, 2013] with those models.