Viability of Variable Generalised Chaplygin gas - a thermodynamical approach

Abstract

The viability of the variable generalised Chaplygin gas (VGCG) model is analysed from the standpoint of its thermodynamical stability criteria with the help of an equation of state, $P=-\frac{B}{{\rho }^{\alpha }}$, where $B=B_0{V}^{-\frac{n}{3}}$. Here $B_0$ is assumed to be a positive universal constant, $n$ is a constant parameter and $V$ is the volume of the cosmic fluid. We get the interesting result that if the well-known stability conditions of a fluid is adhered to, the values of $n$ are constrained to be negative definite to make ${\left(\frac{\partial P}{\partial V}\right)}_S<0$ \& ${\left(\frac{\partial P}{\partial V}\right)}_T<0$ throughout the evolution. Moreover the positivity of thermal capacity at constant volume $c_V$ as also the validity of the third law of thermodynamics are ensured in this case. For the particular case $n=0$ the effective equation of state reduces to $\Lambda$CDM model in the late stage of the universe while for $n<0$ it mimics a phantom-like cosmology which is in broad agreement with the present SNe Ia constraints like VGCG model. The thermal equation of state is discussed and the EoS parameter is found to be an explicit function of temperature only. Further for large volume the thermal equation of state parameter is identical with the caloric equation of state parameter when $T\to 0$. It may also be mentioned that like Santos et al our model does not admit of any critical points. We also observe that although the earlier model of Lu explains many of the current observational findings of different probes it fails to explain the crucial tests of thermodynamical stability.

arXiv comment16 Pages, 6 figures. arXiv admin note: text overlap with arXiv:0902.1532 by other authors

References in corpus (18)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Type Ia Supernova Discoveries at z>1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution
• Thermodynamics of Spacetime: The Einstein Equation of State
• An alternative to quintessence
• Generalized Chaplygin Gas, Accelerated Expansion and Dark Energy-Matter Unification
• New Constraints on ${\Omega }_M$, ${\Omega }_{\Lambda }$, and w from an Independent Set of Eleven High-Redshift Supernovae Observed with HST
• Spectra and Light Curves of Six Type Ia Supernovae at 0.511 < z < 1.12 and the Union2 Compilation
• Constraints on dark energy from Chandra observations of the largest relaxed galaxy clusters
• Reconstructing Dark Energy
• Constructing Phantom Cosmologies from Standard Scalar Field Universes
• Instability of holographic dark energy models
• Cosmology with a Variable Chaplygin Gas
• Thermodynamics and dark energy
• Thermodynamics of the Variable Modified Chaplygin gas
• Variable Chaplygin Gas: Constraints from CMBR and SNe Ia
• Spherically symmetric inhomogeneous model with Chaplygin gas
• Thermodynamical behaviour of the Variable Chaplygin gas

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