$Λ$vCF: Extending $Λ$CDM into a Unified Model with Particle Creation

TL;DR

This work extends the standard $\Lambda$CDM model by introducing bulk viscosity from an isentropic particle-creation mechanism to unify the universe’s expansion history from inflation to late-time acceleration. It derives an analytical Hubble parameter $H(a)$ within a flat FLRW framework, with a viscosity coefficient $\zeta \propto \rho H/H_p^2$ and an evolving equation of state controlled by a swiftness parameter $\gamma$, yielding exact transition points between epochs. A Cosmic Mode Index constraint $N_c=4\pi$ fixes the early-universe viscosity and implies an inflationary scale $H_I \approx 6.10\times10^{13}$ GeV, while an equivalent Hilltop scalar-field description indicates ultra-slow-roll inflation with a graceful exit. The model further provides a causally consistent Israel-Stewart evolution for bulk viscosity, showing a transition from viscoelastic to pseudoplastic behavior as the universe moves from inflation to radiation domination, thereby linking inflationary dynamics to late-time acceleration within a single dissipative-fluid framework.

Abstract

We present a novel extended version of the $Λ$CDM model that provides analytical solution for Hubble parameter uniting all epochs of cosmic evolution starting from inflation to late-acceleration, with intermediate radiation and matter-dominated epochs. This is achieved by relaxing the perfect fluid assumption in the standard model and considering a general viscous cosmic fluid (vCF) with non-zero particle creation rate and evolving adiabatic equation of state. Transition points of the Universe and the finite boundary connecting them is exactly determined. We then propose a novel method to determine the early-time viscous coefficient and inflation energy scale using the Cosmic Mode Index value postulated by Padmanabhan. Considering the data from the Planck 2018 analysis, this yields an inflationary Hubble parameter of $H_{I}\approx10^{13}$\,GeV. An equivalent scalar-field description for the inflationary epoch is then constructed and inferences are made regarding the nature of inflation. Notably, we find that the model describes an ultra-slow-roll hilltop inflation scenario with a graceful exit to radiation-dominated epoch. Subsequently, we show that bulk viscosity in this model can be expressed as Israel-Stewart equation in relativistic dissipative hydrodynamics with an appropriate underlying viscous coefficient and relaxation time that satisfy the causality constraint in its extreme limit. Finally, by comparing the evolution of this causal relation and its Navier-Stokes counterpart, we infer that the evolution from inflation to radiation era signifies a fluid transitioning from viscoelastic to pseudoplastic behavior.

Figures (4)

• Figure 1: Evolution of deceleration parameter with $x=\ln a$, for different values of model parameters. For plotting, we consider the values; $\Omega^0_{\Lambda}=0.68$aghanim2020planck and $\Omega^0_{\zeta}=10^{-108}$. Also, $\omega_e=-(1+2\dot{H}/3H^2)$ denotes effective equation of state.
• Figure 2: Evolution of logarithm of Hubble radius with $\ln(a)$. In this plot, arrowed lines represents the crossing of perturbation modes, and thick dashed black lines are tangent lines drawn at transition points of the Universe.
• Figure 3: Evolution of scalar potential and slowroll parameters with scalar field, considering $N_{t}=60$.
• Figure 4: Figure on the left shows evolution of viscous coefficient and relaxation time with number of e-folds, and the figure on the right depicts the evolution of ratio of viscous coefficients with number of e-folds. For plotting both these figures we have considered the prior values; $\Omega^0_{\zeta}=10^{-108}$, $\Omega^0_{\gamma}=10^{4}$, $\gamma=1$ and $N_t=60$.