Matter Creation Model II

• Matter Creation Model II is a cosmological model that explains late-time acceleration through the continuous, adiabatic creation of cold dark matter, producing an effective negative pressure.
• It modifies the standard continuity equation by introducing a particle creation term parameterized by α and ℓ, allowing deviations from the ΛCDM evolution of dark matter density.
• Observational analyses using SNIa, BAO, and cosmic chronometer data support a nonzero creation rate, positioning the model as a competitive alternative to conventional dark energy scenarios.

Matter Creation Model II designates a class of cosmological models in which the late-time acceleration of the Universe is attributed not to a separate dark energy component, but to a process of continuous, adiabatic creation of cold dark matter (CDM) particles from the gravitational field. This ongoing matter production generates an effective negative pressure, called the "creation pressure," which enters the cosmological dynamics to mimic or generalize the effects usually ascribed to the cosmological constant in ΛCDM cosmology. The model postulates a non-conservation of particle number, modifies the matter continuity equation, and is constrained by thermodynamic consistency and observational data, providing a competitive alternative to conventional dark energy scenarios.

1. Theoretical Framework and Equation Structure

Matter Creation Model II introduces a modified continuity equation for dark matter particles, typically of the form

$$\dot{\rho}_{\rm dm} + 3H\rho_{\rm dm} = \Gamma \rho_{\rm dm}$$

where $\rho_{\rm dm}$ is the CDM density, $H$ is the Hubble rate, and $\Gamma$ is a phenomenological particle creation rate. The modification implies that the conventional adiabatic dilution of matter (scaling as $a^{-3}$) is offset by a source term reflecting ongoing particle creation. This process introduces an effective negative pressure,

$p_c = -\frac{\Gamma}{3H} \rho_{\rm dm}$

which, when sufficiently large, can drive accelerated expansion even in the absence of a separate dark energy component (1105.1027).

In Model II, the creation rate is generalised to

$$\Gamma = 3\alpha H \left(\frac{\rho_{c,0}}{\rho_{\rm dm}}\right)^{\ell}$$

where $\alpha>0$, $\ell$ is a free parameter, and $\rho_{c,0}$ is today's critical density (Bhattacharjee et al., 21 Jul 2025). For $\ell=1$, Model II reduces to the standard CCDM model which can mimic ΛCDM; deviations in $\ell$ parameterize departures in the evolution of the dark matter density and the effective negative pressure.

2. Dynamical Systems Analysis and Cosmic Evolution

The dynamical system for Model II yields a rich structure of fixed points, corresponding to the standard cosmological epochs:

• Radiation Domination: Early time fixed point set by the presence of the radiation density component.
• Matter Domination: Intermediate era where the universe expansion is dominated by (a mix of primordial and created) cold dark matter and non-created baryons.
• Late-time Acceleration (de Sitter Phase): The negative creation pressure, through suitable choice of $\Gamma$, leads to an attractor with $H=H_{\rm dS}$ (de Sitter) and $\rho_{\rm dm}$ tending to a constant value as $a\to\infty$ (Bhattacharjee et al., 21 Jul 2025).

The phase-space analysis reveals that for physically motivated parameter choices ($\alpha>0$, $0 < \ell < 1$) the Universe follows a trajectory that sequentially passes through radiation and matter domination before settling into a stable accelerated expansion epoch. The flexibility introduced by the exponent $\ell$ permits variations in the timing and sharpness of the deceleration-to-acceleration transition, as well as in the asymptotic behaviour of matter creation (Bhattacharjee et al., 21 Jul 2025).

3. Observational Confrontation and Parameter Constraints

Model II has been subjected to Bayesian parameter estimation and information criterion analysis using the latest datasets:

• Datasets: Cosmic Chronometers (CC), Type Ia Supernovae (SNIa) (Pantheon+, DESY5 and Union3 samples), and DESI Baryon Acoustic Oscillations (BAO) (DR1 and especially the recent DR2) (Bhattacharjee et al., 21 Jul 2025).
• Parameter Estimation: Performed with MCMC techniques, allowing simultaneous fitting of $H_0$, $\alpha$, and $\ell$.
• Results:
  • Significant evidence for nonzero matter creation rate ($\alpha$) in both Model I ($\ell=1$) and Model II.
  • For Model II, the best-fit values of $\ell$ deviate from 1 in many datasets, indicating observable departures from ΛCDM.
  • When only pre-2024 datasets are used, ΛCDM may be statistically favored; with the inclusion of DESI BAO DR2, Model II is favored according to the Akaike (AIC) and Bayesian (BIC) information criteria.
  • The model can fit the Hubble parameter evolution, distances to SNIa, and is not in tension with the thermal history.

Parameter	ΛCDM	CCDM/Model I ($\ell=1$)	Model II ($\ell$ free)
Creation rate α	0 (not present)	Fitted (nonzero)	Fitted (nonzero)
Exponent $\ell$	–	1	Fitted (often $\neq$ 1)
Late-time attractor	de Sitter	de Sitter	de Sitter (but modified)
Statistical fit	Baseline	Comparable	SLCDM favored with new BAO

4. Thermodynamic Consistency and Physical Motivation

The process is treated as adiabatic particle creation: while the number of dark matter particles increases, the specific entropy (entropy per particle) remains constant. The total entropy grows, in accordance with the generalized second law of thermodynamics. The negative pressure required for acceleration emerges naturally from the non-equilibrium thermodynamics of open systems with matter production. This aligns with previous analyses enforcing consistency with both the first and second laws of thermodynamics, and avoids the necessity of a separately conserved dark energy term (Cárdenas et al., 24 Jan 2025).

5. Comparison with ΛCDM and Implications

Model II generalizes the standard CCDM scenario and possesses one extra parameter compared to ΛCDM. The model recovers ΛCDM in the limit $\ell=1, \alpha\to0$. For $\ell \neq 1$, subtle differences appear in the background and perturbative evolution (growth of structures). The dynamical system analysis shows that with correct parameter choices, Model II can mimic ΛCDM’s expansion history, but its prediction for the growth rate and structure formation can differ appreciably, providing a target for future observational tests.

Observationally, the inclusion of high-precision DESI DR2 BAO data shifts the statistical preference in favor of Model II for some dataset combinations. This suggests that departures from strict ΛCDM-like behaviour are allowed—or even preferred—by recent data, possibly indicating physical matter creation in the late Universe (Bhattacharjee et al., 21 Jul 2025).

Model II’s distinguishing feature is that cosmic acceleration arises not from an unobserved and separately conserved dynamical dark energy component, but from a negative effective pressure associated with ongoing, gravitationally powered dark matter creation. This process can, for suitable parameters, reproduce the current acceleration and past thermal history without invoking new hypothetical fields or modifications of GR, narrowing the required “dark sector” of cosmological physics.

6. Challenges and Future Directions

Key challenges remain in mapping the perturbation dynamics, especially for structure formation and CMB, as continuous matter creation alters the evolution of density contrasts. Fully relativistic treatments and simulations are required to confirm the viability at the perturbation level. It is also necessary to clarify the microphysical mechanism for particle creation and check for consistency with quantum gravity or semiclassical field theory in curved spacetime.

Further work will focus on:

• High-precision constraints on $(\alpha,\ell)$ from upcoming surveys (e.g., further DESI data, CMB-S4).
• Covariant treatments of cosmological perturbations in the context of adiabatic creation.
• Laboratory or astrophysical probes for potential signatures of non-conservation of particle number for CDM.

7. Summary Table: Distinguishing Features of Matter Creation Model II

Feature	Matter Creation Model II
Source of acceleration	Negative creation pressure
Dark matter evolution	Particle creation term in $\rho$
Creation rate form	$\Gamma = 3\alpha H (\rho_{c,0}/\rho_{\rm dm})^\ell$
Posterior fit with BAO DR2	Favored in some combined datasets
Ability to mimic ΛCDM	Yes, for $\ell=1$
Implications for dark sector	No need for a separate dark energy
Key observational discriminants	Growth history, BAO, SNIa, CC
Future tension points	Structure/perturbation evolution

Matter Creation Model II, by expanding the phenomenology of the creation rate with an extra parameter $\ell$, offers a testable and thermodynamically motivated scenario for late-time cosmic acceleration, potentially reducing the need to invoke an independent dark energy component in the cosmological model. The latest BAO and distance data provide growing empirical support for its viability over the standard concordance model under certain parameter regimes (Bhattacharjee et al., 21 Jul 2025).