Early Universe

Reheating Temperature: How Inflation's Cold Vacuum Refilled the Universe with Hot Particles

At the end of cosmic inflation, the observable universe was a nearly empty, ice-cold vacuum — its temperature effectively driven toward zero as exponential expansion diluted everything by a factor of at least e⁶⁰ (about 10²⁶) in every direction. Within perhaps 10^-32 of a second, that frozen void was refilled with a seething plasma of quarks, gluons, photons, and neutrinos at temperatures that plausibly reached 10⁹ to 10¹⁵ gigaelectronvolts (GeV). The reheating temperature, written T_rh or T_R, is the temperature of that newborn thermal bath at the moment the universe first settled into radiation-dominated thermal equilibrium — the true "start" of the hot Big Bang.

Formally, T_rh is the temperature reached when the energy stored in the oscillating inflaton field has been converted into relativistic particles and the plasma has thermalized, marking the handoff from an inflaton-dominated era to the standard radiation era. It is one of the most important — and least directly measured — numbers in early-universe cosmology.

TypeEarly-universe thermodynamic scale
RegimeEnd of inflation → radiation era
Key equationT_rh ≈ (90/π²g*)^(1/4) √(Γφ M_Pl)
Plausible range~4 MeV (BBN floor) to ~10^15–10^16 GeV
Timescale~10^-36 to 10^-32 s after inflation
Constrained byBBN, CMB, gravitino overproduction

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What the reheating temperature is

Inflation solves the horizon and flatness problems by having a scalar field — the inflaton — dominate the energy density and drive quasi-exponential expansion. But that same expansion is catastrophic for matter: any pre-existing particles are diluted by a³ (number density) or a⁴ (radiation energy density), where the scale factor a grows by at least e⁶⁰. By the end of inflation the universe is essentially a cold, empty condensate storing almost all its energy in the inflaton's potential.

The reheating temperature T_rh is the temperature of the relativistic plasma once that inflaton energy has been transferred to Standard Model (and beyond) particles and the system has reached thermal equilibrium. It is not the peak temperature the universe ever saw — the plasma can transiently reach a higher T_max during the process — but it is the temperature at the onset of the standard radiation-dominated hot Big Bang.

Before reheating: inflaton-dominated, matter-like (w ≈ 0) oscillations.
After reheating: radiation-dominated (w = 1/3), T ∝ 1/a.

The mechanism: from oscillating inflaton to thermal bath

After inflation ends, the inflaton φ rolls to the minimum of its potential and oscillates. Around a quadratic minimum these coherent oscillations redshift like pressureless matter. Energy leaves the inflaton through two broad channels:

Preheating — an explosive, non-perturbative stage. Parametric resonance (Bose enhancement of specific momentum bands) or tachyonic instability pumps energy into daughter fields far faster than any decay rate, producing a highly non-thermal spectrum. Landmark work by Kofman, Linde & Starobinsky (1994–1997) established this stage.
Perturbative reheating — the older Dolgov–Linde / Abbott–Farhi–Wise picture: the inflaton decays quantum-mechanically with a width Γ_φ, and the products scatter and thermalize.

Reheating completes when the decay rate matches the expansion rate, Γ_φ ≈ H. At that moment the inflaton has effectively dumped its energy into radiation, and the plasma's temperature is T_rh. The universe then evolves as ordinary radiation, setting the stage for baryogenesis, the QCD and electroweak transitions, and nucleosynthesis.

Key quantities and a worked estimate

Setting the radiation energy density ρ_r = (π²/30) g_* T⁴ equal to the energy at Γ_φ ≈ H (Friedmann: H² = ρ/3M_Pl²) gives the standard relation:

T_rh ≈ (90 / π² g_*)^1/4 √(Γ_φ M_Pl)

where g_* is the effective relativistic degrees of freedom (106.75 in the full Standard Model), and M_Pl = 2.4 × 10¹⁸ GeV is the reduced Planck mass. Numerically, using g_* ≈ 106.75, this is roughly T_rh ≈ 0.2 √(Γ_φ M_Pl).

Worked example: take an inflaton of mass m_φ = 10¹³ GeV that decays gravitationally-suppressed, Γ_φ ≈ m_φ³/M_Pl² ≈ (10¹³)³/(2.4×10¹⁸)² ≈ 1.7 × 10² GeV. Then √(Γ_φ M_Pl) ≈ √(170 × 2.4×10¹⁸) ≈ 2.0 × 10¹⁰ GeV, giving T_rh ≈ 4.1 × 10⁹ GeV — comfortably in the range that permits thermal leptogenesis while skirting the gravitino ceiling.

How it is constrained and (indirectly) observed

Reheating leaves no photons we can see directly, so T_rh is bounded rather than measured. The main handles are:

Big Bang Nucleosynthesis (BBN): the firmest, most model-independent limit. Neutrinos must thermalize before neutron–proton freeze-out, forcing T_rh ≳ 4 MeV (Kawasaki, Kohri & Sugiyama, 1999–2000). Below this the light-element abundances and N_eff go wrong.
CMB: Planck's measurements of the scalar tilt n_s and the tensor-to-scalar ratio r bound the inflationary energy scale (V^1/4 ≲ 1.6 × 10¹⁶ GeV from r < 0.036, BICEP/Keck 2021), capping the maximum possible T_rh. The number of e-folds N_* depends on the reheating history, so precision CMB data indirectly probe T_rh and the reheating equation of state.
Primordial gravitational waves: the reheating equation of state alters the spectrum of inflationary GWs at high frequencies — a future target for space- and pulsar-timing-based detectors.

Several closely related quantities are easily confused with T_rh:

Preheating vs. reheating: preheating is the initial non-thermal, resonant energy transfer; reheating is the subsequent thermalization and completion. Preheating alone does not define a temperature because the distribution is not thermal.
T_max vs. T_rh: the plasma temperature actually rises to a peak T_max early in the decay, then falls as T ∝ a^-3/8 until reheating completes at the lower T_rh. T_max can exceed T_rh by an order of magnitude or more, which matters for producing heavy relics.
Warm inflation: a distinct scenario where dissipation keeps a thermal bath alive during inflation, so no separate reheating epoch is needed.
Instant vs. gradual reheating: "instantaneous" reheating assumes ρ_end converts immediately, giving the maximal T_rh for a given inflation model; realistic Γ_φ yields lower values.

The equation-of-state parameter w during reheating (between 0 for a quadratic minimum and up to 1/3) directly shifts N_* and therefore the predicted (n_s, r).

Significance, the gravitino problem, and open questions

The reheating temperature is a linchpin because nearly every early-universe process has a temperature threshold. Baryogenesis requires T_rh above its relevant scale (≳ 100 GeV for electroweak baryogenesis, ≳ 10⁹ GeV for standard thermal leptogenesis via right-handed neutrinos). Thermal WIMP dark matter needs T_rh above the freeze-out temperature, while freeze-in and gravitational production can work at very low T_rh.

The famous tension is the gravitino problem in supersymmetric cosmology. Gravitinos are produced thermally with abundance roughly Y_3/2 ∝ T_rh; an unstable gravitino with mass ~0.1–1 TeV decays after BBN (Γ_3/2 ≈ m_3/2³/M_Pl²) and its energetic products photodissociate light nuclei. Avoiding this forces T_rh ≲ 10⁶–10⁹ GeV — in direct conflict with thermal leptogenesis, a still-unresolved cosmological tension.

Open: the true reheating mechanism and Γ_φ for the real inflaton are unknown.
Open: can gravitational-wave observatories ever pin down w and T_rh directly?

Reheating temperature: physical bounds and the constraints that set them
Bound / regime	Value of T_rh	Physical constraint
Absolute BBN floor	≳ 4 MeV	Neutrinos must thermalize before n/p freeze-out; too-low T_rh spoils light-element abundances
Weak-scale / EW baryogenesis	≳ 100 GeV–1 TeV	Electroweak sphalerons and any weak-scale baryogenesis need T > EW scale
Thermal leptogenesis floor	≳ 10^9 GeV	Right-handed neutrinos (M_R ~ 10^9–10^10 GeV) must be thermally produced
Gravitino problem ceiling	≲ 10^6–10^9 GeV	In SUSY, high T_rh overproduces gravitinos that ruin BBN or overclose the universe
Inflationary energy ceiling	≲ ~10^15–10^16 GeV	Set by the inflationary energy scale; ρ_end limits the maximum possible T_rh

Frequently asked questions

What is the reheating temperature in cosmology?

It is the temperature of the hot plasma produced when the inflaton field's energy is converted into Standard Model particles and thermalizes at the end of cosmic inflation. It marks the onset of the standard radiation-dominated hot Big Bang. Formally it is defined when the inflaton decay rate equals the Hubble rate, Γφ ≈ H.

What is the formula for the reheating temperature?

The standard estimate is T_rh ≈ (90/π²g*)^(1/4) √(Γφ M_Pl), where Γφ is the inflaton decay width, M_Pl = 2.4 × 10^18 GeV is the reduced Planck mass, and g* is the effective relativistic degrees of freedom (about 106.75 for the full Standard Model). It follows from equating the radiation energy density to the Friedmann energy density at Γφ ≈ H.

What is the lowest possible reheating temperature?

The firmest lower bound is about 4 MeV, set by Big Bang Nucleosynthesis. If reheating finished below this, neutrinos would not fully thermalize before neutron–proton freeze-out, spoiling the observed light-element abundances and the effective neutrino number N_eff. This bound is remarkably model-independent.

How is reheating different from preheating?

Preheating is the initial, explosive, non-perturbative energy transfer out of the inflaton, driven by parametric resonance or tachyonic instability, producing a highly non-thermal particle spectrum. Reheating is the subsequent stage in which those particles scatter, thermalize, and reach the equilibrium temperature T_rh. Preheating alone does not define a temperature because the distribution is not yet thermal.

Why does the reheating temperature matter for dark matter and baryogenesis?

Almost every early-universe process has a temperature threshold. Thermal leptogenesis needs T_rh ≳ 10^9 GeV, electroweak baryogenesis needs T_rh above ~100 GeV, and thermal WIMP dark matter must have T_rh above its freeze-out temperature. If T_rh is too low, these mechanisms shut off, while alternatives like freeze-in dark matter can instead operate at very low reheating temperatures.

What is the gravitino problem and how does it limit the reheating temperature?

In supersymmetric cosmology, gravitinos are produced thermally in proportion to T_rh. An unstable gravitino of mass ~0.1–1 TeV decays long after BBN, and its energetic decay products break apart light nuclei, ruining nucleosynthesis. Avoiding this overproduction typically forces T_rh below about 10^6 to 10^9 GeV, which is in tension with thermal leptogenesis.