Adiabatic Matter Creation Process

• Adiabatic matter creation is a cosmological process where particle number is not conserved but specific entropy remains constant, generating effective negative pressure.
• The process modifies standard energy–momentum conservation laws by introducing a source term tied to the particle creation rate, influencing cosmic expansion without explicit dark energy.
• Various models—from barotropic fluids to quantum field theoretic approaches—demonstrate its potential to replicate observed cosmic acceleration and impact structure formation.

The adiabatic matter creation process encompasses a range of theoretical frameworks in cosmology where the total number of particles in the universe is not conserved, but the specific entropy per particle remains constant—hence, it is “adiabatic” in the thermodynamic sense. The mechanism is implemented by modifying the standard energy–momentum conservation law and introducing a negative creation pressure in the cosmological fluid equations. This process was originally motivated to dynamically explain the observed accelerated expansion of the universe without invoking an explicit dark energy component or modifying general relativity. Multiple formalisms, ranging from quantum field theory in curved spacetime (where particle creation occurs due to the expansion of the universe) to macroscopic fluid and thermodynamic descriptions, have established the adiabatic matter creation process as a physically viable and observationally relevant paradigm in modern cosmology.

1. Fundamental Principles and Thermodynamic Formalism

The defining feature of adiabatic matter creation is that the universe is treated as an open thermodynamic system. The particle number density $n$ obeys a non-conservation (balance) law: $\dot{n} + 3 H n = n \Gamma$ where $H$ is the Hubble parameter and $\Gamma$ is the particle creation rate, typically parameterized as a function of $H$ and cosmic time. For adiabatic (isentropic) evolution, the specific entropy per particle $\sigma$ is constant, though the total entropy increases due to newly created particles.

Utilizing the Gibbs equation (for comoving observers): $$T d\sigma = d\left( \frac{\rho}{n} \right) + p\,d\left(\frac{1}{n}\right)$$ and the balance equation for $n$, the adiabatic condition $(d\sigma = 0)$ leads to a modified conservation law: $\dot{\rho} + 3 H (\rho + p) = \Gamma (\rho + p)$ The additional source term on the right represents the energy influx from gravitationally-induced matter creation, and can be reinterpreted as an effective “creation pressure”: $p_c = -\frac{\Gamma}{3H} (\rho + p)$ This negative pressure modifies the cosmological dynamics and allows for accelerating expansion even in the absence of a cosmological constant or explicit dark energy.

2. Creation Pressure, Entropy, and Generalized Thermodynamics

Adiabatic matter creation models generalize the traditional (Prigogine-type) approach by relaxing the strict isentropic assumption and allowing for a more general entropy production term. The effective pressure entering the energy–momentum tensor can thus be written as: $$P = -\frac{\Gamma}{3H} (\rho + p) - \frac{n T}{3H} \dot{\sigma}$$ where the second term accounts for entropy production if the specific entropy per particle evolves ($\dot{\sigma} \neq 0$). This formalism enables a precise accounting of both reversible (adiabatic) and irreversible (entropy-producing) processes tied to matter creation (Ivanov et al., 2019).

In models that tie the particle creation rate $\Gamma$ directly to the thermodynamic constraints—including contributions from the cosmic horizon (via the Bekenstein–Hawking or holographic entropy)—the adiabatic expansion condition, in some cases, uniquely fixes $\Gamma$ in terms of cosmological quantities such as the deceleration parameter and the horizon entropy change (Cárdenas et al., 24 Jan 2025).

The generalized second law of thermodynamics is incorporated by stating that the total entropy, which includes both the entropy of the apparent horizon ($S_h$) and the entropy of the matter ($S_m$), is non-decreasing: $\frac{d}{da}(S_h + S_m) \geq 0,$ with further concavity ($d^2/da^2 \leq 0$) required for eventual equilibrium (Nunes et al., 2016, Pan et al., 2016).

3. Macro-Cosmological Implementation and Model Classes

Adiabatic matter creation mechanisms have been studied in a wide variety of cosmological scenarios:

• Simple barotropic models: Here, matter creation modifies the standard continuity equation for pressureless dark matter (or a single barotropic fluid). Typical choices for the creation rate are $\Gamma = 3\beta H$ (with $\beta \ll 1$ to ensure near-standard matter dilution at early times), or more general forms $\Gamma(H)$ (Nunes et al., 2016, Pan et al., 2016).
• Chaplygin/fluid-unified models: When coupled to exotic fluids like Modified or Umami Chaplygin gases, the creation pressure enables unified descriptions that interpolate between inflation, intermediate matter/radiation eras, and late-time acceleration while reproducing observational constraints (Bhattacharya et al., 2017, Mandal et al., 19 Mar 2024).
• Interacting dark sector: Generalizations include models where the created particles are assigned to dark matter, and an explicit interaction with a holographic or other dark energy component is introduced, producing scaling solutions or late-time attractors necessary for cosmic acceleration (Mandal et al., 16 Aug 2024).
• Van der Waals/fluid kinetic theory: In more complex models, the matter creation rate can depend on arbitrary integer powers of $H$, and the thermodynamic sector includes non-ideal (e.g., Van der Waals) gas equations of state. These frameworks can yield temporary inflationary regimes and detailed phase-space structures (Ivanov et al., 2019).
• Observationally constrained models: Models with $\Gamma = 3\alpha H (\rho_{c,0}/\rho_{dm})^l$ produce evolution equations in which the late-time expansion history can closely mimic $\Lambda$CDM, enabling direct confrontation with SNIa, BAO, and cosmic chronometer data (Bhattacharjee et al., 21 Jul 2025).

4. Cosmological and Observational Consequences

The principal observational consequence of adiabatic matter creation is that the effective negative pressure generated can produce cosmic acceleration at late times, allowing these scenarios to serve as alternatives to dark energy or modified gravity (Bhattacharjee et al., 21 Jul 2025, Nunes et al., 2016, Mandal et al., 16 Aug 2024). Key features include:

• Acceleration without explicit dark energy: The creation pressure $p_c < 0$ can yield $w_{\text{eff}} < -1/3$ (or even $w_{\text{eff}} < -1$ for appropriate $\Gamma$), leading to de Sitter–like or even phantom expansion, without invoking a cosmological constant (Cárdenas et al., 24 Jan 2025, Haro et al., 2015). In some models, the entire observed expansion history from early deceleration to late acceleration can be reproduced with only matter/radiation and a time-varying $\Gamma$ (Bhattacharya et al., 2017, Pan et al., 2016).
• Structure formation and CMB: The presence of matter creation modifies both the background expansion and cosmic perturbation evolution; signatures may manifest in deviations of the CMB temperature/polarization power spectra and the growth rate of structure—offering constraints on the parameter space (e.g., via the “creation equation of state” $w_c = -\Gamma/3H$) (Nunes et al., 2016).
• Om diagnostic and model independence: Model-independent diagnostics such as the Om function

$Om(z) = \frac{h^2(z) - 1}{(1+z)^3 - 1}$

reveal that, in matter creation models, Om$(z)$ typically evolves with redshift (unlike in flat $\Lambda$CDM where it remains constant), tending to values lower than $\Omega_{m,0}$ and thus mimicking quintessence or effective phantom behavior (Nunes et al., 2016, Pan et al., 2016, Ivanov et al., 2019).

• Bouncing and singularity avoidance: When the creation rate is appropriately designed (e.g., made dependent on the total energy density), the resulting cosmological evolution can feature nonsingular bounces, avoiding the initial big bang singularity and enabling a smooth transition from contraction to expansion (Mandal et al., 19 Mar 2024, Haro et al., 2015).

5. Dynamical Systems and Stability Analysis

A key methodological advance in recent work is the use of dynamical systems analysis to characterize the global behavior of these models:

• Critical points and attractors: By casting the cosmological equations into autonomous ODEs (with dimensionless variables $x, y$ representing energy density fractions or normalized pressures), one determines attractors corresponding to matter-dominated, scaling, and dark energy–dominated eras. Stability of these points determines whether late-time acceleration is generic or contingent on tuned parameters (Mandal et al., 19 Mar 2024, Mandal et al., 16 Aug 2024).
• Classical and Lyapunov stability: Classical stability is assessed via the adiabatic sound speed squared $C_s^2 = \partial p/\partial\rho$, which must be positive. Lyapunov functions are also used to guarantee global attractor behavior of solutions—e.g., $L = \frac{1}{2}(1 - y)^2$ decreasing along trajectories (Mandal et al., 16 Aug 2024).
• Parameter dependence: The detailed phase-space portrait (including transient inflation, scaling, or bouncing solutions) depends on the creation rate form ($\Gamma(H)$), interaction parameters, and the equation of state of the fluid or fluids considered.

6. Quantum Field Theory and Particle Creation

In the context of quantum field theory in curved spacetime, adiabatic matter creation is rigorously modeled as the spontaneous creation of particles from the vacuum due to the time-dependence of the cosmic background (1205.5616, Landete et al., 2013):

• Adiabatic invariance and regularization: The number of particles in each mode is an adiabatic invariant under infinitely slow expansion, and this property underlies the adiabatic regularization technique for UV divergences (1205.5616). This framework is extended to spin-1/2 fields by a generalized WKB-like ansatz (Landete et al., 2013).
• Bogoliubov transformations and particle number: The mixing of positive- and negative-frequency components leads to a time-dependent Bogoliubov coefficient $\beta_k$, with $|\beta_k|^2$ quantifying created particle number density. Observables such as the renormalized stress-energy tensor and spectra of quantum perturbations (e.g., during inflation) are computed within this formalism.
• Conformal invariance and suppression: Fields obeying conformally invariant equations (e.g., massless scalars with conformal coupling, Maxwell field, massless Dirac spinors) experience no gravitational particle creation in a spatially flat FLRW background (1205.5616, Landete et al., 2013).

7. Observational Viability and Statistical Evidence

Recent studies include systematic comparisons between matter creation models and observational datasets:

• Background expansion fits: Many choices of $\Gamma(H)$, including $\Gamma = 3\alpha H(\rho_{c,0}/\rho_{dm})^l$, yield analytic backgrounds nearly indistinguishable from flat $\Lambda$CDM for suitably chosen parameters (Bhattacharjee et al., 21 Jul 2025).
• Information criteria and likelihood ratios: Statistical tests using Akaike and Bayesian information criteria (AIC, BIC), as well as direct likelihood-ratio analysis, evaluate whether such models are statistically preferred over $\Lambda$CDM in light of the latest SNIa, BAO (DESI DR1/DR2), and CC data (Bhattacharjee et al., 21 Jul 2025). In several cases, especially when incorporating the most current BAO datasets, mild to strong evidence for matter creation (as opposed to or alongside $\Lambda$) is found at multiple standard deviations.
• Limitations and ongoing challenges: Although many adiabatic matter creation models match background observables and pass key thermodynamic equilibrium tests, issues remain regarding their predictions for cosmic microwave background structure, large-scale structure formation, and microphysical justification of the particle creation rate. The absence (in most models) of a full perturbation analysis and detailed scrutiny of entropy production and conservation laws at the microscopic level are active areas of inquiry.

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In summary, the adiabatic matter creation process provides a framework where gravitationally induced particle creation (with negative creation pressure) modifies the cosmological evolution, reproducing the observed late-time acceleration without invoking a separate dark energy component or modified gravity. This mechanism integrates thermodynamic, fluid, and quantum-field-theoretic insights, admits various model parameterizations, and is supported by both analytic and numerical methods—while ongoing and future observational probes continue to test its cosmological viability.