Gravitational Reheating: Mechanisms & Implications

• Gravitational reheating is defined as energy transfer via gravity-induced particle production from the inflationary phase to matter and radiation.
• The mechanism relies on non-adiabatic evolution of the spacetime metric, where both abrupt and smooth transitions critically influence particle production efficiency and reheating temperature.
• It plays a key role in shaping observables such as gravitational-wave spectra and dark-sector abundances, thereby constraining inflationary and thermal history models.

Gravitational reheating denotes a class of post-inflationary mechanisms in which the energy transfer from the inflationary background to matter and radiation proceeds through gravity, rather than through ad hoc direct inflaton couplings. In the narrow sense used in many kination and quintessential-inflation analyses, particles are created by the non-adiabatic evolution of the spacetime metric at the end of inflation. In a broader sense, the term also includes Planck-suppressed graviton-mediated production from the inflaton condensate, curvature-induced excitation through non-minimal couplings such as $\xi R\phi^2$, and purely geometric reheating in modified-gravity descriptions such as Jordan-frame Starobinsky inflation (Artymowski et al., 2017, Haque et al., 2022, Dorsch et al., 4 Mar 2026). Across these realizations, a persistent distinction is that particle production is not itself reheating; reheating is the later epoch at which the produced radiation actually dominates the cosmic energy density (Artymowski et al., 2017).

1. Conceptual scope and dynamical regimes

The literature uses the same term for several related but technically distinct post-inflationary situations. In one widely studied regime, inflation ends directly into a stiff or kination phase with $w \simeq 1$, there is no coherent inflaton oscillation, and reheating must originate from gravitational particle creation during the transition from de Sitter expansion to the decelerating background (Haro et al., 2022). In another regime, the inflaton oscillates about a potential minimum, and reheating is driven by graviton-mediated processes or by gravitational production of heavy spectator scalars in the oscillatory curvature background (Haque et al., 2022, Haro et al., 2024). Modified-gravity realizations add a third category: in Jordan-frame Starobinsky inflation there is no explicit inflaton in the fundamental action, and reheating is sourced by oscillations of the Ricci scalar itself (Dorsch et al., 4 Mar 2026).

A central organizing variable is the post-inflationary equation of state. In stiff or semi-stiff histories, the background redshifts faster than radiation, so even inefficient gravitationally produced radiation can eventually dominate. This is why analyses of purely gravitational reheating often require $w>1/3$, and in some minimal scenarios the viable region is pushed close to kination (Artymowski et al., 2017, Haque et al., 2022). In oscillatory models with monomial behavior near the minimum, the averaged equation of state is $w=(k-2)/(k+2)$ or, equivalently for $V\sim \varphi^{2n}$, $w_{\rm eff}=(n-1)/(n+1)$; viability of purely gravitational reheating then requires $n>2$, i.e. $w_{\rm eff}>1/3$ (Choi et al., 2024, Haro et al., 2024).

The same breadth of usage explains why “gravitational reheating” is not synonymous with a single microphysical mechanism. Some papers study direct excitation of quantum fields by the time-dependent background, others use $s$-channel graviton exchange from the inflaton condensate, and others rely on curvature-induced tachyonic growth of a reheaton. The common element is that the relevant coupling is fixed by gravity or curvature rather than introduced as an arbitrary inflaton portal (Opferkuch et al., 2019, Mambrini et al., 2021, Haque et al., 2022).

2. Quantum-field-theoretic basis

The core calculation is usually formulated as particle production in a time-dependent FLRW background. For a massive scalar conformally coupled to gravity, the rescaled mode function obeys

$\chi_k''+\left[k^2+a^2(\eta)m^2\right]\chi_k=0,$

and the produced occupation numbers are encoded in the Bogoliubov coefficient $w \simeq 1$0 (Hashiba et al., 2018). In de Sitter-to-kination matching calculations, one defines an adiabatic Bunch–Davies vacuum during inflation and a late-time kination vacuum, then determines $w \simeq 1$1 by matching the mode function and its derivative across the transition (Hashiba et al., 2018).

A major technical issue is that exact $w \simeq 1$2 are rarely available for realistic smooth backgrounds. One analytic strategy is to approximate the scale factor near the end of inflation by

$w \simeq 1$3

which reduces the mode equation to a parabolic-cylinder form with

$w \simeq 1$4

This produces a compact estimate for the energy density of gravitationally produced particles and makes the dependence on transition-time quantities such as $w \simeq 1$5 and $w \simeq 1$6 explicit (Haro et al., 2022).

The treatment of the transition profile is decisive. In an abrupt toy model connecting de Sitter inflation directly to kination, the ultraviolet tail behaves as

$w \simeq 1$7

so the spectrum falls by a power law and superheavy production can remain sizable (Hashiba et al., 2018). In a smooth $w \simeq 1$8 transition with timescale $w \simeq 1$9, numerical solutions instead show that production of superheavy particles is efficient only if $w>1/3$0, while for $w>1/3$1 the spectrum is exponentially suppressed; the energy density is summarized as

$w>1/3$2

in the smooth model (Hashiba et al., 2018). This sharp contrast between discontinuous and smooth transitions is one of the recurring technical subtleties in the subject.

3. Kination, quintessential inflation, and non-oscillating reheating

Quintessential-inflation models provide the cleanest setting for gravitational reheating in the narrow sense. After inflation the universe enters a kination era in which the inflaton kinetic energy dominates and $w>1/3$3; because there is no coherent oscillatory reheating stage, the relevant source is purely gravitational particle production during the inflation-to-kination transition (Haro et al., 2022). For light or massless minimally coupled particles, the produced energy density reproduces the classic estimate

$w>1/3$4

(Haro et al., 2022).

For heavy conformally coupled particles, the controlling parameter is the ratio $w>1/3$5. In smooth non-oscillating backgrounds the reheating temperature is exponentially suppressed for $w>1/3$6, while the maximum occurs around

$w>1/3$7

For a typical inflationary scale $w>1/3$8, the maximum reheating temperature is of order

$w>1/3$9

(Haro et al., 2022). When Big Bang Nucleosynthesis and gravitational-wave overproduction are imposed simultaneously, the viable mass range is

$w=(k-2)/(k+2)$0

with

$w=(k-2)/(k+2)$1

(Haro et al., 2022).

More detailed Boltzmann treatments of kination reheating reach a related conclusion but with a different thermal history. In a model where massive scalars are gravitationally produced during a stiff epoch and later decay into conformally coupled massless scalars, numerical evolution shows that the universe typically passes through a temporary matter-dominated stage before radiation domination, and the reheating temperature lies in the range

$w=(k-2)/(k+2)$2

(Lankinen et al., 2019). This indicates that the effective reheating temperature is sensitive not only to the production event itself but also to the subsequent decay kinetics and redshifting hierarchy.

A distinct but related non-oscillatory variant is Ricci reheating. There the reheaton couples through $w=(k-2)/(k+2)$3, and a post-inflationary kination era flips the sign of the Ricci scalar, generating

$w=(k-2)/(k+2)$4

for $w=(k-2)/(k+2)$5. The resulting tachyonic growth can yield reheating temperatures high enough for thermal leptogenesis; in the special case where the Standard Model Higgs plays the role of the reheaton, the viable regime is restricted to

$w=(k-2)/(k+2)$6

(Opferkuch et al., 2019). This mechanism remains gravitational in origin, but it is conceptually different from perturbative Bogoliubov production because the reheating energy is extracted through curvature-driven instability.

4. Oscillating backgrounds and modified-gravity realizations

When the inflaton oscillates after inflation, gravitational reheating can proceed through production of heavy spectator scalars in the oscillatory curvature background. For potentials behaving as $w=(k-2)/(k+2)$7, one has

$w=(k-2)/(k+2)$8

and the inflaton background redshifts as $w=(k-2)/(k+2)$9. In this class of models the viable purely gravitational regime is again $V\sim \varphi^{2n}$0 (Haro et al., 2024). The reheating formulas separate into two cases: decay of the gravitationally produced heavy particles during inflaton domination, and decay after that phase has ended. The maximum reheating temperature is defined as the temperature reached when decay concludes at the onset of radiation domination (Haro et al., 2024).

For the representative case $V\sim \varphi^{2n}$1, numerical evolution gives

$V\sim \varphi^{2n}$2

and

$V\sim \varphi^{2n}$3

(Haro et al., 2024). A subsequent extension connects the allowed reheating-temperature interval to the scalar spectral index. For $V\sim \varphi^{2n}$4, the quoted allowed $V\sim \varphi^{2n}$5 windows are narrower than the Planck 2018 $V\sim \varphi^{2n}$6 interval and shift further when one imposes the maximal-reheating condition (Haro et al., 2024). This makes gravitational reheating not only a thermal-history mechanism but also a nontrivial constraint on inflationary parameter inference.

Starobinsky inflation has become a second major laboratory for gravitational reheating. In the Einstein-frame perturbative treatment with a scalar reheaton $V\sim \varphi^{2n}$7, purely gravitational interactions are sufficient to complete reheating even for minimal coupling $V\sim \varphi^{2n}$8. The quoted results are

$V\sim \varphi^{2n}$9

with non-perturbative gravitational preheating yielding

$w_{\rm eff}=(n-1)/(n+1)$0

for $w_{\rm eff}=(n-1)/(n+1)$1 and

$w_{\rm eff}=(n-1)/(n+1)$2

for $w_{\rm eff}=(n-1)/(n+1)$3 (Dorsch et al., 2024). The final reheating temperature remains controlled by the later perturbative stage, while the maximum temperature is relevant for relic production.

In the Jordan frame, the same model admits a fully geometric description with no explicit inflaton field. The Ricci scalar oscillates after inflation, acts as the non-adiabatic source in the reheaton mode equation, and acquires exponential damping once the backreaction of the produced particles is included. Solving the coupled background and Boltzmann system gives

$w_{\rm eff}=(n-1)/(n+1)$4

(Dorsch et al., 4 Mar 2026). The same work compares this with the Einstein-frame perturbative value

$w_{\rm eff}=(n-1)/(n+1)$5

and argues that, although the two frames are classically equivalent, quantum reheating calculations can lead to distinct microphysical interpretations and quantitative predictions (Dorsch et al., 4 Mar 2026). This is one of the few explicit frame-equivalence issues that arises directly within gravitational reheating.

5. Minimal gravitational portals, dark sectors, and neutrino sectors

A separate line of work formulates gravitational reheating as a minimal portal scenario in which the inflaton couples to radiation and dark matter only through gravity. In this approach the relevant processes are $w_{\rm eff}=(n-1)/(n+1)$6-channel graviton exchange from the inflaton condensate, with Boltzmann equations for $w_{\rm eff}=(n-1)/(n+1)$7, $w_{\rm eff}=(n-1)/(n+1)$8, and the dark-sector abundance (Haque et al., 2022). In a model-independent analysis, successful reheating together with the BBN lower bound implies roughly

$w_{\rm eff}=(n-1)/(n+1)$9

and

$n>2$0

with $n>2$1 (Haque et al., 2022). The same framework yields strongly mass-dependent dark-matter predictions because gravitational widths for fermions are helicity suppressed, whereas scalar and vector production is comparatively easier (Haque et al., 2022).

During a conventional oscillatory reheating era, direct gravitational production of dark matter from inflaton scattering also depends sensitively on the non-instantaneous temperature history. The key scaling is that the relic abundance depends primarily on

$n>2$2

and the mechanism can generate the observed dark-matter density over a mass range from a GeV to a ZeV (Mambrini et al., 2021). This result highlights an important theme: gravitational reheating and gravitational relic production depend on the full reheating trajectory, not only on the final $n>2$3.

Heavier hidden-sector states can be incorporated as well. A gravitational-portal construction with right-handed neutrinos and a Higgs non-minimal coupling $n>2$4 shows that purely gravitational interactions can simultaneously generate the thermal bath, dark matter, and a lepton asymmetry, but the minimal case $n>2$5 is excluded because it overproduces gravitational waves; viable regions require $n>2$6, with the allowed parameter space extending up to about $n>2$7 (Cléry, 2023).

A more specialized realization is gravitational neutrino reheating. There the inflaton still couples only gravitationally, but the long-lived reheating agent is a right-handed neutrino from a Type-I seesaw sector. The heavy neutrino abundance scales as $n>2$8, so it can overtake the faster-redshifting inflaton background and later reheat the universe when it decays. In the neutrino-dominating regime the reheating temperature scales as

$n>2$9

while successful reheating requires $w_{\rm eff}>1/3$0, and the scenario predicts a nonzero lightest active neutrino mass because $w_{\rm eff}>1/3$1 (Haque et al., 2023). This unifies reheating, neutrino mass generation, baryogenesis, and gravitational-wave phenomenology within a single gravitationally coupled sector.

6. Gravitational-wave signals, bounds, and broader extensions

Gravitational reheating is strongly constrained by primordial gravitational waves because stiff or kination-like post-inflationary eras blue-tilt the tensor spectrum. For a background with barotropic parameter $w_{\rm eff}>1/3$2, the high-frequency part of the spectrum is enhanced by

$w_{\rm eff}>1/3$3

so the enhancement is positive for $w_{\rm eff}>1/3$4 and strongest at $w_{\rm eff}>1/3$5 (Artymowski et al., 2017). The same analysis shows that viable purely gravitational reheating must satisfy CMB and BBN constraints, including extra-radiation bounds, and that the resulting high-frequency gravitational-wave background may in favorable cases be accessible to LIGO, LISA, BBO, or DECIGO depending on $w_{\rm eff}>1/3$6 and the effective post-inflationary dynamics (Artymowski et al., 2017).

Other gravitational-wave channels probe reheating microphysics more directly. Prompt graviton production from the oscillating inflaton condensate yields model-dependent spectra whose morphology reflects the shape of the potential near its minimum. In Starobinsky inflation and $w_{\rm eff}>1/3$7 T-models the prompt spectrum is broad and decreases with frequency, whereas $w_{\rm eff}>1/3$8 leads to a nearly monochromatic signal around

$w_{\rm eff}>1/3$9

and $s$0 gives rising spectra with multiple harmonics; the cutoff frequency can be used to determine the reheating temperature (Choi et al., 2024). Graviton Bremsstrahlung from perturbative inflaton decay produces a stochastic background peaking in the GHz–THz range, with a relic contribution constrained through $s$1 and relevant mainly for high-frequency detectors such as microwave cavities (Barman et al., 2023). Thermal graviton production in the reheating plasma is also enhanced because the temperature during reheating can exceed $s$2; in the radiation-only treatment the peak lies near $s$3 GHz, while reheating can boost the amplitude, shift the peak, or generate plateau-like features depending on $s$4, $s$5, and $s$6 (Bernal et al., 2024).

Reheating can also modify phase-transition gravitational-wave signals. A first-order transition occurring while the universe heats up during reheating is dynamically distinct from an ordinary cooling transition because plasma friction becomes antifriction, often driving the bubble wall into a runaway regime and enhancing the bubble-collision signal (Buen-Abad et al., 2023). In weakly coupled post-fragmentation reheating, nonlinear inflaton fragmentation can dominate over the stiff-era tensor transfer in part of the spectrum, producing signals from Hz to GHz that are independent of the reheating temperature provided reheating occurs after fragmentation (Garcia et al., 2024). These results indicate that “gravitational-wave signature of reheating” is not a single observable but a superposition of background-history effects, direct graviton emission, and source-specific nonlinear processes.

Finally, the subject extends beyond inflationary expansion. In a matter-ekpyrotic bounce within Loop Quantum Cosmology, a sudden transition in the contracting phase can gravitationally produce massive conformally coupled particles, whose later dominance after the bounce yields a reheating temperature compatible with cosmological observations (Haro et al., 2015). This suggests that the operative principle of gravitational reheating is broader than inflation alone: whenever the background undergoes a sufficiently non-adiabatic transition and matter couples only through gravity, the geometry itself can act as the reheating agent.

Overall, the literature converges on several robust points. Gravitational reheating is viable but highly model-dependent in efficiency; smooth transitions usually suppress heavy production relative to abrupt toy models; stiff or kination phases are often required when no direct couplings are present; and gravitational-wave bounds are among the most powerful constraints on the scenario (Hashiba et al., 2018, Haro et al., 2022, Artymowski et al., 2017). A plausible implication is that the topic is best regarded not as a single mechanism but as a family of gravitationally controlled thermalization pathways whose common observables are the reheating temperature, the duration of the nonstandard post-inflationary era, and the associated gravitational-wave spectrum.