Gravitationally Induced Particle Creation

Updated 27 January 2026

Gravitationally Induced Particle Creation is a process in an expanding universe where a time-dependent gravitational field continuously produces particles, introduces a negative creation pressure, and drives accelerated expansion.
It integrates thermodynamic and kinetic formalisms, applying macroscopic FRW equations and the extended Boltzmann framework to model non-equilibrium cosmic evolution.
This approach unifies dark energy alternatives, cosmic reheating, and dark matter production with observational constraints matching predictions.

Gravitationally induced particle creation is a theoretically motivated, covariant open-system process in which a time-dependent gravitational field triggers the continuous production of particles in an expanding universe. This mechanism, originating in both kinetic-theory and thermodynamic frameworks, is characterized by a non-conservation of particle number and accompanying irreversible entropy production, and can be formulated at both macroscopic and microscopic (kinetic) levels in a Friedmann-Robertson-Walker (FRW) background. The process introduces an effective negative creation pressure, modifies the cosmic expansion history, and offers a unifying approach to late-time acceleration, thermodynamics of cosmology, and quantum-field aspects of curved spacetime (Lima et al., 2014).

1. Covariant Thermodynamics of Gravitational Particle Creation

The open-system thermodynamic formalism treats the expanding universe as a macroscopic system where the number of particles $N$ is not conserved. The key equations in a spatially flat FRW background are:

Particle Number Balance:

$\dot n + 3H n = n\Gamma$

where $n$ is number density, $H\equiv\dot a/a$ is the Hubble parameter, and $\Gamma$ is the particle production rate per particle (Lima et al., 2014, Haro et al., 2015).

Energy Continuity and Creation Pressure:

$\dot\rho + 3H(\rho + P) = (\rho + P)\Gamma \ P_c = -\frac{\rho + P}{3H}\Gamma$

Here $P_c$ is the negative creation pressure, and $\rho$ , $P$ are the energy density and kinetic pressure, respectively.

Second Law and Adiabatic Creation:

For "adiabatic" (specific entropy per particle constant) creation, the entropy flux $S^\mu = s u^\mu$ (with $s$ the entropy density) obeys $S^\mu{}_{;\mu} = s\Gamma$ , implying monotonic entropy growth.

This framework establishes that the process is intrinsically irreversible, always producing entropy, and can drive effective accelerated cosmic expansion even in the absence of a cosmological constant (Haro et al., 2015).

2. Kinetic Theory and the Extended Boltzmann Equation

A covariant and consistent kinetic formulation is obtained by generalizing the Boltzmann equation:

Extended Boltzmann Equation:

$p^\mu \nabla_\mu f = \mathcal{C}[f] + \mathcal{P}_g[f]$

where $f$ is the one-particle distribution function, $\mathcal{C}[f]$ the standard collisional term, and $\mathcal{P}_g[f]$ a non-collisional source term encoding the quantum-gravitational origin of particle production. In an FRW geometry, this reduces to (Lima et al., 2014):

$L(f) = H\left(1-\frac{\Gamma}{3H}\right) p \partial_p f$

with $L(f)$ the Liouville operator for geodesic motion.

The non-equilibrium solution in the "adiabatic" regime retains a functional equilibrium form, $f(t,p) = \exp[\alpha - \beta(t) E(p)]$ , but the time evolution of the temperature is modified:

$\frac{\dot T}{T} = \begin{cases} -H + \frac{1}{3}\Gamma, & m\ll T \ -2H + \frac{2}{3}\Gamma, & m \gg T \end{cases}$

where $m$ is the particle mass.

This establishes the equivalence between the macroscopic thermodynamic and microscopic kinetic treatments and enables modeling of non-equilibrium distribution evolution in gravitational particle creation scenarios.

3. Cosmological Expansion: Dynamical and Observational Consequences

When included in FRW cosmology, gravitationally induced particle creation leads to:

Modified Friedmann-Raychaudhuri Equations:

$\dot{H} = -\frac{3\gamma}{2} \left(1 - \frac{\Gamma}{3H}\right) H^2$

(for fluid equation-of-state parameter $\gamma$ ).

Cosmic Phases:
- For constant $\Gamma$ , solutions interpolate from a Big Bang singularity ( $t\to t_s$ , $H\to\infty$ ) to an asymptotic de Sitter phase ( $H\to \Gamma/3$ ) (Haro et al., 2015).
- The creation pressure mimics a cosmological constant at late times; trajectories naturally reproduce a standard radiation/matter era at early times and approach equilibrium in a final de Sitter state.

Empirically, the magnitude and time-dependence of $\Gamma$ are constrained by CMB, supernova (SN Ia), BAO, and other cosmological probes, with late-time observations allowing for a particle creation rate at the level $\Gamma/(3H_0)\simeq 0.08\pm0.03$ (Safari et al., 2020). Phenomenological models with redshift-dependent or constant $\Gamma$ can fit cosmological data comparably to $\Lambda$ CDM, and can alleviate the Hubble tension at the $2.4\sigma$ – $3\sigma$ level (Schiavone et al., 20 Jan 2026).

4. Quantum-Field Origin and Boltzmann-Bogoliubov Connection

The microphysical underpinning of gravitationally induced particle creation originates from quantum field theory in curved spacetime, where the time dependence of the background induces a nonvanishing Bogoliubov coefficient $\beta_k$ for mode functions, corresponding to particle production (Kolb et al., 2023). The extended Boltzmann source term $\mathcal{P}_g[f]$ in kinetic theory is conjectured to encapsulate this effect at the semiclassical level, but a rigorous derivation including back-reaction remains an open task.

Analytic results for spectra and number densities (e.g., in a stiff-matter era (Lankinen et al., 2016) or inflationary backgrounds (Kolb et al., 2023)) show that the rate is substantial for very massive species and during rapid expansion epochs, and that the reheating, dark matter production, and entropy generation in the early universe can be governed purely by gravitational effects (Hashiba et al., 2018).

5. Generalizations in Modified Gravity and Geometry-Matter Coupling

A wide array of modified gravity theories with explicit curvature-matter or torsion-matter couplings predict nonconservation of the matter energy-momentum tensor and thus gravitationally induced particle production (Lobo et al., 28 Oct 2025):

Nonminimal Curvature-Matter Couplings:

Modified actions of the form $S = \int \sqrt{-g}[f_1(R) + (1 + \lambda f_2(R))\mathcal{L}_m]$ (or their scalar-tensor equivalents) yield $\nabla^\mu T_{\mu\nu} \neq 0$ and a geometric source for open-system thermodynamics.

Interpretation in Thermodynamic Formalism:

The matter creation rate $\Gamma$ is explicitly related to the exchange current induced by the nonminimal coupling, and a negative creation pressure $p_c$ naturally drives late-time acceleration and entropy production.

Consistency with Thermodynamics:

The total (horizon plus fluid) entropy increases monotonically and saturates in the de Sitter phase, consistent with the generalized second law (Lobo et al., 28 Oct 2025, Saha et al., 2016).

Similar structure appears in torsion-matter couplings, $f(R,T_{\mu\nu}T^{\mu\nu})$ , and scalar-tensor $f(R,T)$ extensions, with the particle creation source term controlled by the geometric coupling and defining modified Friedmann equations with built-in negative creation pressure, entropy production, and late-time acceleration (Cipriano et al., 2023, Pinto et al., 2022).

6. Thermodynamic and Statistical Constraints

The thermodynamic consistency of gravitationally induced particle creation is well-established:

First and Second Laws:

The generalized first law at the apparent horizon must be modified, with non-vanishing entropy production balancing the energy flow (Saha et al., 2016, Jawad et al., 2018). The generalized second law holds provided $\Gamma/(3H) \leq 1$ , encompassing both standard and accelerating regimes.

Equilibrium and Stability:

Thermodynamic equilibrium is generally attained only for $1/2 < \Gamma/(3H) < 1$ (constant $\Gamma$ ) or for specific ranges of $\Gamma(t)$ , with equilibrium corresponding physically to the final de Sitter phase (Haro et al., 2015, Saha et al., 2016).

Cosmological data analysis constrains the functional form and allowed magnitude of $\Gamma$ using SNe Ia, BAO, CMB, and other standard probes, placing tight limits on the departure from equilibrium and from standard $\Lambda$ CDM evolution (Safari et al., 2020, Schiavone et al., 20 Jan 2026, Pan et al., 2016).

7. Applications and Phenomenological Implications

Gravitationally induced particle creation impacts a wide range of cosmological phenomena:

Dark Matter and Relic Abundance:

The extended Boltzmann equation with a gravitational creation term modifies the freeze-out dynamics and suppression of thermal relic (e.g., WIMP) abundances, directly altering inferred cross sections and the relic density (Baranov et al., 2015). Purely gravitational production during inflation–kination transitions can account for present-day dark matter and reheating, even in the absence of couplings to standard matter (Hashiba et al., 2018).

Structure Formation and Large-Scale Observables:

The modification of the matter continuity equation and associated negative creation pressure influence the evolution of density perturbations, the linear and nonlinear matter power spectrum, and observable quantities such as cosmic shear and the CMB lensing–Rees–Sciama bispectrum. In viable scenarios, suppression in $P(k)$ and shifts in characteristic bispectrum features provide testable signatures, potentially constraining $\Gamma/H$ at the percent level with future surveys (Nunes, 2016).

Unification and Model Equivalence:

Dynamically, the particle-creation cosmology can be made equivalent to $\Lambda(t)$ models or to specific scalar-field models, establishing its role as a one-component unification mechanism for the dark sector (Graef et al., 2013).

Thermodynamic, kinetic, and quantum-field descriptions collectively provide a coherent and testable framework for gravitationally induced particle creation, offering alternatives to traditional dark energy scenarios and enabling novel cosmological model-building and phenomenology.