Cosmological Matter Creation

• Cosmological matter creation scenario is a framework where continuous matter production via modified conservation laws and creation pressure replaces the cosmological constant to drive cosmic acceleration.
• It employs revised particle number and energy conservation equations with a creation rate typically linked to the Hubble parameter, effectively mimicking dark energy behavior.
• The approach offers a coherent dynamical systems perspective addressing key issues like the cosmological constant and coincidence problems while satisfying thermodynamic constraints.

The cosmological matter creation scenario encompasses a broad class of models in which the energy-momentum content of the universe evolves via the continuous production of matter—typically cold dark matter, radiation, or both—at the expense of gravitational or vacuum energy. These mechanisms challenge the traditional reliance on a cosmological constant and exotic dark energy fields, offering instead dynamical explanations for late-time cosmic acceleration, the cosmological constant problem, the coincidence problem, and even the initial conditions of the universe. Central to these models is the modification of the conservation laws and the introduction of a creation pressure, sometimes coupled to horizon thermodynamics, generalized entropy laws, or scalar-tensor/modeled gravity frameworks. The scenario is supported by an extensive body of research covering both microphysical and phenomenological perspectives, with observational constraints now testing its viability at precision-cosmology levels.

1. Particle Creation Mechanisms and Fundamental Formulation

A universally encountered feature of cosmological matter creation models is the modification of the particle number and energy conservation equations to incorporate a source term representing matter creation. For a generic fluid component (e.g., dark matter or radiation), the particle number evolution is governed by

$\dot{n} + 3H n = n\Gamma,$

where $n$ is the number density, $H$ is the Hubble parameter, and $\Gamma$ is the particle creation rate, typically a function of $H$ and possibly other background quantities (Carneiro, 2014, 1108.3040, Nunes et al., 2016, Cárdenas et al., 24 Jan 2025).

The corresponding energy conservation law is likewise modified: $\dot{\rho} + 3H(\rho + p) = \Gamma(\rho + p),$ where $\rho$ and $p$ are the energy density and pressure, respectively. In addition, a negative “creation pressure” $p_c$, associated with the irreversible production of particles, naturally arises: $p_c = -\frac{\Gamma}{3H} (\rho + p),$ playing a crucial role in the expansion history and the emergence of cosmic acceleration (Bhattacharjee et al., 21 Jul 2025, Carneiro, 2014, Lobo et al., 2015).

The microphysical motivation for these terms spans a variety of scenarios:

• Gravitational particle creation from vacuum fluctuations, especially for ultra-light dark particles or relativistic quanta during strong curvature epochs (1108.3040).
• Irreversible thermodynamic flow of energy from the gravitational sector to matter, modeled through open system non-equilibrium thermodynamics (Lobo et al., 2015, Gangopadhyay et al., 2014).
• Nonminimal curvature-matter couplings in the gravitational action, recast into scalar-tensor equivalents (Lobo et al., 2015, Montani et al., 17 Jul 2024).
• Holographic and horizon-entropy-driven approaches, exploiting the thermodynamic properties of the cosmic apparent horizon (Cárdenas et al., 2023, Cárdenas et al., 24 Jan 2025, Tu et al., 2019).

2. Early Universe and Inflationary Dynamics

In the primordial universe, high particle creation rates can naturally drive inflation without recourse to an inflaton field or ad hoc potential: $(1/a^4) \frac{d}{dt} (a^4 n) = \gamma H n,$ producing a vacuum energy scaling as $\Lambda \propto H^2$ and leading to non-singular inflation (1108.3040). For $\gamma$ approaching critical values (e.g., $\gamma \to 4$), the solution approaches the de Sitter regime ($H \sim$ const.), with natural exit to radiation domination as particle production shuts off.

The primordial spectrum generated in such scenarios is found to be nearly scale-invariant: $$n_s = 1 - 2\epsilon, \quad \epsilon = -\frac{\dot{H}}{H^2} \ll 1,$$ yielding $n_s \simeq 0.97$ for 60 $e$-folds, consistent with CMB measurements (1108.3040).

Further, in models incorporating holographic equipartition or thermodynamic particle creation with $\Gamma \propto H^2$, an early inflationary (quasi–de Sitter) phase is obtained, transitioning naturally to a radiation-dominated era as $\Gamma$ drops to $\propto H$ (Tu et al., 2019).

3. Late-Time Acceleration and Observational Concordance

In late cosmological epochs, the appeal of the matter creation scenario is its ability to mimic a cosmological constant or quintessence field dynamically. The rate $\Gamma$ is generally taken as proportional either to $H$, $H^\alpha$, or inverse powers of the dark matter density. Specific phenomenological forms include: $$\Gamma = 3\alpha H \left(\frac{\rho_{c,0}}{\rho_{\text{dm}}}\right)^l$$ with $\alpha$ and $l$ as free parameters (Bhattacharjee et al., 21 Jul 2025). For $l=1$, the solution for $\rho_{\text{dm}}(a)$ becomes

$$\rho_{\text{dm}}(a) = (\rho_{\text{dm,0}} - \alpha \rho_{c,0})a^{-3} + \alpha \rho_{c,0},$$

so that the creation term reproduces the cosmological constant's role in the background expansion, leading to an asymptotic de Sitter (accelerating) phase. Phase-space analysis confirms a sequence of radiation→matter→acceleration regimes.

In models allowing general forms of $\Gamma(H,z)$, the evolution can deviate in quantifiable ways from $\Lambda$CDM, potentially explaining discrepancies (e.g., the $H_0$ tension). The matter creation pressure is responsible for the negative effective pressure driving acceleration: $p_c = -\frac{\Gamma}{3H}\rho_{\text{dm}},$ with the present acceleration phase realized for sufficiently large $\Gamma/H$ (Bhattacharjee et al., 21 Jul 2025, Cárdenas et al., 2023).

Observational analyses have applied Cosmic Chronometers, SNIa (Pantheon+, DESY5, Union3), and DESI BAO data, finding significant evidence for nonzero matter creation rates (nonzero $\alpha$) and, in some parameter regimes and with recent datasets, a statistical preference for matter creation models over $\Lambda$CDM (Bhattacharjee et al., 21 Jul 2025, Pigozzo et al., 2015).

Comparisons with dark energy models can be facilitated via the $Om$ diagnostic: $Om(z) = \frac{h^2(z) - 1}{(1+z)^3 - 1},$ where $h(z) = H(z)/H_0$. While $Om(z) = \Omega_{m,0}$ for $\Lambda$CDM, matter creation models yield an $Om(z)$ that decreases with $z$, mimicking quintessence (Nunes et al., 2016, Ivanov et al., 2019).

4. Thermodynamics, Entropy, and Horizon Effects

Cosmological matter creation scenarios have a rich thermodynamical structure. The total entropy of the universe is given by

$$S_{\text{total}} = S_{h} + S_{m} = \frac{\pi}{H^2} + \frac{4\pi}{3 H^3} n(t),$$

with $S_h$ the horizon entropy and $S_m$ the matter entropy (Lobo et al., 2015, Cárdenas et al., 2023, Cárdenas et al., 24 Jan 2025). The generalized second law requires $dS/da \geq 0$ and $d^2S/da^2 \leq 0$ at equilibrium, constraining admissible behavior of $\Gamma$ and ensuring the physical viability of matter creation processes.

In frameworks where horizon entropy or entropic forces are explicitly included, e.g.,

$$p_{\text{eff}} = p - [(\rho c^2 + p) \Gamma(t)]/(3H),$$

the departure from $\Lambda$CDM can be subtle. Bayesian evidence and MCMC analyses indicate that models with $\Gamma \propto H$ (and small Hawking temperature parameter $\gamma$) can be statistically preferred over $\Lambda$CDM, albeit with the parameters constrained to small values by data (Gohar et al., 2020). Such results suggest a thermodynamic/holographic origin for at least part of the observed cosmic acceleration.

The inclusion of chemical potential in the matter creation framework further refines the thermodynamic consistency, allowing the scenario to avoid unphysical behaviors (such as negative entropy production or ad hoc phantom regimes), and enabling a natural transition between quintessence and phantom expansion as needed, modulated by the chemical potential $\mu$ (Cárdenas et al., 2023).

5. Modified Gravity and Extended Theoretical Structures

A substantial subset of matter creation models are embedded in modified gravity frameworks, notably $f(R)$ gravity recast in scalar-tensor language. The action is generalized as

$$S = \frac{1}{2\chi} \int d^4x \sqrt{-g} [\phi R - V(\phi)],$$

coupling the Ricci scalar $R$ to a dynamically evolving scalar field $\phi$, with a potential $V(\phi)$ that sets the vacuum energy density (Montani et al., 17 Jul 2024).

Matter creation is modeled thermodynamically, e.g., as

$d\ln N/d\ln V = (H/\hat{H})^\beta,$

yielding a radiation–like component with energy density governed by

$\dot{\rho}_r = -4H \rho_r [1 - (H/\hat{H})^\beta].$

The resulting closed dynamical system for $\{H(z),\phi(z),V(\phi),\rho_{m}+\rho_{r}\}$ supports viable cosmologies that interpolate between high–$H_0$, late-time behavior and Planck data–compatible high-redshift evolution, thus offering a resolution to the Hubble tension (Montani et al., 17 Jul 2024).

Additionally, models with nonminimal curvature-matter coupling of the form

$L = \frac{1}{2} f_1(R) + [1 + \lambda f_2(R)] L_m$

naturally lead to generalized continuity equations and irreversible matter creation (Lobo et al., 2015).

6. Dynamical System Analysis and Integrability

The mathematical richness of matter creation models is manifest in their dynamical system structure. For example, when applied to two-component fluids (e.g., van der Waals gas and dust), the system forms an integrable set of autonomous first-order equations for $(n, H, T)$, with globally conserved Hamiltonians and additional invariants ("second integrals") that organize the phase space into domains with distinct physical interpretations—such as regions of standard expansion, inflation, or potential phantom behavior (Ivanov et al., 2019).

The effective phase space can thereby be partitioned depending on the form and strength (parametrized e.g., by $\beta$) of the creation rate, with observable consequences for cosmic evolution, the onset of acceleration, and possible avoidance of singularities.

7. Broader Implications and Observational Signatures

Matter creation scenarios provide natural mechanisms for addressing foundational problems in cosmology:

• The cosmological constant problem is alleviated by vacuum energy dynamically decaying into matter, consistent with low-energy QCD estimates and obviating the requirement for enormous fine tuning (1108.3040, Carneiro, 2014).
• The coincidence problem is resolved since continuous creation maintains commensurate densities of matter and effective dark energy, stabilizing $\Omega_{m}$ and $\Omega_{\Lambda}$ ratios over cosmological timescales (Carneiro, 2014, Pigozzo et al., 2015).
• Observed cosmic acceleration can be entirely attributed to negative creation pressure, with precision dataset combinations now providing significant ($>2\sigma$ in some studies) evidence for nonzero matter creation (Bhattacharjee et al., 21 Jul 2025, Pigozzo et al., 2015).
• Thermodynamic consistency and generalized entropy constraints illustrate that these models are, when carefully constructed, internally robust, preserving the second law and avoiding unphysical regimes (Cárdenas et al., 24 Jan 2025, Cárdenas et al., 2023).
• Phenomena such as emergent universe solutions, cosmological bounces, and even the temporary creation of wormholes (in specific non-singular bounce models) may be supported without requiring exotic matter violating the weak energy condition (Gangopadhyay et al., 2014, Pavlović et al., 2022).

Current and future high-precision surveys (DESI, LSST, Euclid), as well as upcoming CMB missions, will further sharpen the empirical viability of cosmological matter creation scenarios relative to both $\Lambda$CDM and modified gravity/dark sector extensions.

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Summary Table: Generic Key Equations in Matter Creation Cosmology

Feature	Representative Equation	Typical Physical Implication
Modified particle number	$\dot n + 3H n = n\Gamma$	Nonconservation, particle production
Energy conservation (with $p_c$)	$\dot\rho + 3H(\rho + p + p_c) = 0$	Creation pressure modifies expansion
Creation pressure	$p_c = -\frac{\Gamma}{3H}(\rho + p)$	Negative, drives acceleration
Friedmann equation (with creation)	$H^2 = \frac{1}{3}(\rho + \Lambda)$	$\Lambda$ may arise from $p_c$ or $V(\phi)$
Entropy (horizon+matter)	$S_{\text{tot}} = \pi/H^2 + \frac{4\pi}{3H^3}n$	Generalized 2nd law, thermodynamic constraints

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The cosmological matter creation scenario is thus a comprehensive and theoretically flexible framework, distinguished by its interplay of microscopic particle production, non-equilibrium thermodynamics, dynamical effective vacuum energy, and phenomenologically testable implications for the universe's expansion history.