Analysis of the action-based constrained adiabatic particle production model

TL;DR

The paper tackles the lack of a field-action formulation for gravitationally induced adiabatic particle production by deriving a generalized minisuperspace Lagrangian that reproduces the Friedmann and continuity equations with a particle-creation pressure term. It shows that consistency with the Euler–Lagrange equations constrains the particle-creation coupling to depend on the scale factor as $\Gamma = \dot a h(a)$, which further reduces to $\Gamma = 3\beta H$, with a unique action $L = \left( 3 a \dot a^2 - \tfrac{a^3}{2} \dot\phi^2 + a^3 V(\phi) \right) e^{-\\int h(a) da}$. The authors perform a full dynamical-systems analysis including radiation and baryons, finding that higher-order evolution constrains the model to $V(\phi) = c_1$ or $c_1 e^{c_2\phi}$ and $\beta$ in the range $1/3<\beta<2/3$, with a consistent scaling solution that yields late-time acceleration. Finally, they compare the model to observational data, showing good agreement with $H(z)$ measurements and Pantheon supernova distances for $\beta \approx 0.5$ and the tested potentials, supporting an action-based ΛCDM-like alternative based on particle production.

Abstract

The theory of gravitationally induced adiabatic particle production offers an alternative approach to exploring the accelerating expansion of the universe. However, existing models generally lack a well-defined field-action formulation. This article aims to establish a suitable Lagrangian formulation consistent with the framework of particle creation. A general form of action is considered for this purpose. The corresponding field equations in comparison with those commonly used in the particle creation formalism leads to some specific form of the Lagrangian, which further constrains the form of the particle creation models. We perform the phase space stability analysis of the constrained model and compared with observational data. Our result shows that the constrained model is capable of explaining the cosmic evolution from the radiation to the late-time cosmic acceleration if the model parameter lies within the range $1/3 < β< 2/3$.

Figures (4)

• Figure 1: The evolution of cosmological eras have been shown from very past $a(t) = 10^{-8}$ to some future values $a(t)=10^2$. To represent the contribution of matter we considered the total matter density parameter as $\Omega_m = x^2 + \Omega_b$. The late time de - sitter phase is considered due to the domination of scalar field potential term $y^2$. For the above plot, the values of $\beta, \lambda$ are taken to be $1/2$ and $0.2$, respectively. The above plot clearly explains the cosmological eras.
• Figure 2: Once again we have considered the values of $a(t)$ from $10^{-8}$ to $10^2$. For the above plot, the values of $\beta$ is taken to be $1/2$. The above plot clearly explains the cosmological eras similar to the above case.
• Figure 3: Comparison of the model-predicted Hubble parameter $H(z)$ with observational data given in farooq. The solid blue line represents the evolution of $H(z)$ as obtained from solving (\ref{['H-sol']}) for the particle creation rate $\Gamma = 3 \beta H$ with $\beta = 0.5$, whereas $\lambda=0$ and $\lambda = 0.2$ correspond to the constant and exponential potentials, respectively. The red points with error bars correspond to the observational estimates of the Hubble parameter. The above plot shows that the values of Hubble parameter predicted from our model is closely connected to its observed values.
• Figure 4: Comparison of distance modulus $\mu(z)$ as a function of redshift between the particle creation rate $\Gamma = 3 \beta H$ with $\beta = 0.5$ (blue curve) and binned observational data from the Pantheon supernova sample PantheonPlus2022(red points with error bars). As previously, $\lambda=0, \ 0.2$ corresponds to constant and exponential potentials. The plot above shows a very good agreement of the observed distance modulus with the theory.