Reheating After Inflation
Inflation ends with the universe in a strange and unusable state. A single scalar field, the inflaton φ, holds essentially all the energy, stored as potential rather than motion; sixty or more e-folds of near-exponential expansion have swept the cosmos clean of every particle that came before, leaving it cold, smooth, and empty. Yet every success of the hot Big Bang — the light-element yields of nucleosynthesis, the acoustic peaks of the microwave background, the very existence of matter over antimatter — presupposes a dense, thermal, radiation-dominated plasma. Reheating is the bridge between these two worlds: the epoch in which the inflaton's frozen energy is converted into a hot bath of relativistic particles, igniting the radiation era. The mechanism is at heart a story of an oscillating field. Once slow roll fails, the inflaton stops crawling and swings about the minimum of its potential, and each swing shakes the fields it couples to, radiating quanta the way an accelerating charge radiates light. In the simplest picture the field carries a decay width Γφ; reheating completes when the decay clock overtakes the expansion clock, Γφ ≃ H, fixing a reheating temperature T_reh ∼ √(Γφ M_Pl). But the coherent inflaton is a condensate of astronomical occupation number, and Bose enhancement can make the first stage explosive and non-perturbative — preheating by parametric resonance, draining the field in a few dozen oscillations into a wildly non-thermal spectrum. Reheating sets the initial data for everything downstream: the maximum temperature, the entropy, and the abundances that baryogenesis and nucleosynthesis inherit.
- Reheating is the epoch at the end of inflation when the coherently oscillating inflaton transfers its stored energy into a hot plasma of relativistic particles, launching the radiation-dominated hot Big Bang.
- After slow roll ends the inflaton oscillates about its potential minimum; for a quadratic minimum these oscillations redshift as pressureless matter, ρφ ∝ a⁻³, until decay takes over.
- In the perturbative picture the inflaton decays with rate Γφ and reheating completes when Γφ ≃ H, fixing T_reh = (90/π²g⋆)^(1/4)√(Γφ M_Pl) ≈ 0.54 √(Γφ M_Pl) for g⋆ ≈ 107.
- Preheating — explosive, non-perturbative production through parametric resonance or tachyonic instability — usually precedes and dominates the first burst of energy transfer, far out of equilibrium.
- The universe must reheat above the temperatures demanded by baryogenesis and above T ∼ few MeV so that nucleosynthesis proceeds; T_reh is unobserved directly but bracketed between that floor and the inflationary scale.
- Reheating fixes the initial conditions — thermalization, entropy, effective degrees of freedom — for the entire standard thermal history that follows.
- Key idea: Reheating converts the coherent oscillation energy of the inflaton into a thermal plasma; equating the decay rate to the Hubble rate, Γφ ≃ H, gives the reheating temperature T_reh ∼ √(Γφ M_Pl) that seeds the hot Big Bang.
Where this lives today
Reheating is now a quantitative frontier. Because the number of e-folds between horizon exit and the end of inflation depends on the expansion history afterward, the duration and averaged equation of state ⟨w⟩ of the reheating epoch shift the predicted n_s and tensor-to-scalar ratio r; Planck and the coming CMB-S4 and LiteBIRD experiments therefore constrain reheating indirectly, and analyses now report the allowed reheating temperature and e-fold number N_reh alongside n_s and r. Preheating is itself a source: the violent, inhomogeneous field dynamics radiates a stochastic gravitational-wave background at frequencies set by the inflaton mass and resonance scale — typically above the bands of LISA or pulsar-timing arrays, but a target for proposed high-frequency detectors, and its nonlinear fragmentation into oscillons is followed on classical lattices (CosmoLattice, LATTICEEASY). And the reheating temperature remains the phenomenological hinge connecting inflation to physics beyond the Standard Model: too high and thermal gravitinos or moduli overclose the universe or spoil BBN; too low and baryogenesis or dark-matter production has no thermal window. Pinning T_reh ties early-universe theory to laboratory particle physics.
The physical picture
Picture the inflaton at the end of inflation as a single, universe-spanning pendulum displaced far from the bottom of its potential well. During inflation the Hubble drag term 3Hφ̇ is so strong that the field is overdamped — it barely moves, and its potential energy drives the exponential expansion. As the field nears the minimum the potential steepens, the slow-roll parameter ε climbs to one, and the drag can no longer hold it back. The pendulum is released: it swings through the minimum, overshoots, and settles into rapid oscillation at the curvature frequency m = √V″. Each oscillation is a coherent, zero-momentum condensate of φ quanta, the whole cosmos oscillating in lockstep. Two clocks now compete. The expansion clock 1/H dilutes everything and, for a quadratic well, drains the amplitude so that ρφ ∝ a⁻³ — the field redshifts exactly like a gas of massive, pressureless dust. The decay clock 1/Γφ drains the same energy into whatever light fields φ couples to, feeding a radiation bath. Early on H ≫ Γφ, expansion wins and the inflaton simply redshifts while dribbling out radiation that is immediately diluted; reheating is the moment the decay clock catches up.
Preheating is the twist the pendulum picture misses. Because the inflaton is a coherent field of enormous occupation number, any boson it couples to sees a periodically varying effective mass and can be produced by Bose-stimulated parametric resonance: quanta pile into the same low-momentum modes and stimulate ever more production, so occupation numbers grow exponentially in resonance bands rather than linearly. For broad resonance the transfer is explosive — a large fraction of the inflaton energy floods out in tens of oscillations, long before the perturbative width Γφ would finish, and into a violently non-thermal spectrum of a few excited bands. A separate, generally longer, thermalization stage must then redistribute this energy into a genuine Bose-Einstein and Fermi-Dirac plasma before the word "temperature" means anything at all.
The core equations
The whole story starts from the homogeneous inflaton's equation of motion in an expanding universe — a driven oscillator in which the Hubble rate plays the role of friction. It follows from the scalar-field action in a Friedmann–Robertson–Walker background and governs both the slow-roll and the oscillatory regimes.
where: φ — homogeneous inflaton field; H = ȧ/a — Hubble expansion rate; V′(φ) = dV/dφ — slope of the potential. During slow roll φ̈ is negligible and friction balances the slope; once V″ ≫ H² the field oscillates many times per Hubble time. Treating the coherent oscillations as a fluid, the inflaton's energy density obeys a continuity equation with an extra sink that models the decay of φ quanta into light particles at rate Γφ. This is the perturbative, Boltzmann-level description of energy transfer, valid when the coupling is weak enough that produced quanta escape without stimulating more.
where: ρφ — inflaton energy density; 3Hρφ — dilution by expansion (oscillations averaged to dust); Γφρφ — energy drained by decay, adding an exponential e^(−Γφt) once decay dominates. The energy lost by the inflaton reappears as radiation, so the radiation density is sourced by exactly the term that drains φ, while itself redshifting as the fourth power of the scale factor.
where: ρr — energy density of the relativistic plasma; 4Hρr — redshifting of radiation, ρr ∝ a⁻⁴; Γφρφ — the source. Equations (2) and (3) are integrated together to follow reheating. Once the decay products scatter into equilibrium, the radiation density takes its thermal blackbody form, which is what lets us assign a temperature at all. This relation defines the reheating temperature in terms of the density at the onset of radiation domination.
where: g⋆(T) — effective number of relativistic degrees of freedom (106.75 in the full Standard Model above the electroweak scale); T — plasma temperature; π²/30 is the Stefan–Boltzmann constant in natural units summed over species. Combining the completion condition Γφ ≃ H with the Friedmann equation and (4) yields the central result of the field: the reheating temperature as a geometric-mean-like combination of the decay rate and the Planck scale.
where: T_reh — temperature at the onset of radiation domination; M_Pl = (8πG)^(−1/2) ≈ 2.4×10¹⁸ GeV — reduced Planck mass; Γφ — inflaton decay rate. Numerically the prefactor (90/π²)^(1/4) ≈ 1.74, so T_reh ≈ 1.74 g⋆^(−1/4)√(Γφ M_Pl) ≈ 0.54 √(Γφ M_Pl) for g⋆ ≈ 107. The averaged pressure of the oscillating field — and hence how fast ρφ redshifts — depends only on the shape of the potential near its minimum, through a virial average that generalizes the dust result of the quadratic case.
where: w — equation-of-state parameter p/ρ; n — power of the potential V ∝ φⁿ near its minimum. A quadratic well (n = 2) gives w = 0 and a⁻³ (dust); a quartic well (n = 4) gives w = 1/3 and a⁻⁴ (radiation-like). When the perturbative width is inadequate, the daughter field's mode functions obey a Mathieu equation whose instability bands are the mathematical signature of preheating: exponentially growing solutions that correspond to explosive particle production.
where: χk — Fourier mode of the field coupled to φ; z = mt — dimensionless time; q — resonance parameter (q ≫ 1 is broad resonance); Φ — inflaton oscillation amplitude; g — coupling. Inside an instability band the mode grows as χk ∝ e^(μk z), so the occupation number nk ∝ e^(2μk mt).
The goal is to prove that a scalar field oscillating in a quadratic minimum behaves, when averaged over an oscillation, exactly like a gas of pressureless dust — so that its energy density dilutes as ρφ ∝ a⁻³ and the universe passes through a transient matter-dominated phase before reheating completes. We start from the equation of motion in the oscillation regime m ≫ H and use a virial average to show the mean pressure vanishes.
Step 1. Multiply the equation of motion (1) by φ̇ to build an energy equation: φ̇φ̈ + 3Hφ̇² + φ̇V′ = 0, which regroups into d/dt(½φ̇² + V) = −3Hφ̇². Why: multiplying by the velocity is the standard trick that turns Newton's equation into a work–energy theorem, exposing the total field energy ρφ = ½φ̇² + V on the left.
Step 2. Recognize the left side as ρ̇φ and the right as a loss, giving ρ̇φ = −3Hφ̇². Using the field pressure pφ = ½φ̇² − V together with ρφ = ½φ̇² + V, note that φ̇² = ρφ + pφ, so ρ̇φ = −3H(ρφ + pφ) — precisely the fluid continuity equation. Why: this shows the abstract field obeys the same continuity law as any cosmological fluid, so all that remains is to find its effective pressure.
Step 3. Average over one oscillation. For V = ½m²φ², the virial theorem for a harmonic oscillator gives equal mean kinetic and potential energies, ⟨½φ̇²⟩ = ⟨½m²φ²⟩ = ⟨V⟩. Therefore ⟨pφ⟩ = ⟨½φ̇²⟩ − ⟨V⟩ = 0. Why: over a full swing the field spends as much energy in motion as in the potential, so the oscillation-averaged pressure cancels exactly — the hallmark of pressureless dust.
Step 4. Insert ⟨pφ⟩ = 0 into the averaged continuity equation: ρ̇φ + 3Hρφ = 0, which integrates to ρφ ∝ a⁻³. Why: a zero-pressure (w = 0) fluid always dilutes as the inverse volume, so the coherent condensate is, on average, indistinguishable from a non-relativistic gas of φ particles of mass m. The result ⟨ρφ⟩ ∝ a⁻³ underlies the transient matter era after inflation and, through equation (6), generalizes to ρφ ∝ a^(−6n/(n+2)) for a V ∝ φⁿ minimum (Ryden Ch. 11; Kolb and Turner).
Go deeper · Derivation B · 1 minThe reheating temperature from balancing the two clocks
The goal is to derive the reheating temperature, equation (5), including its numerical prefactor, under the sudden-decay approximation: assume the inflaton converts essentially all its energy into a thermalized radiation bath at the instant its decay rate equals the Hubble rate. We combine the completion condition, the Friedmann equation written with the reduced Planck mass, and the thermal density of relativistic species.
Step 1. Set the completion condition H(t_reh) = Γφ. Before this the inflaton dominates and expansion outpaces decay; after it, radiation dominates. Why: reheating is not instantaneous, but the crossover Γφ = H is the natural marker of the transition to radiation domination and cleanly defines T_reh.
Step 2. Write the Friedmann equation at that instant with the reduced Planck mass, H² = ρr/(3M_Pl²), taking ρ ≃ ρr because the inflaton has by now dumped its energy. Why: using M_Pl = (8πG)^(−1/2) ≈ 2.4×10¹⁸ GeV absorbs the 8π and keeps the algebra free of stray numerical factors.
Step 3. Substitute the thermal density (4), ρr = (π²/30)g⋆T_reh⁴, and the condition H = Γφ, to get Γφ² = (π²g⋆/90)(T_reh⁴/M_Pl²). Why: this single equation ties the microphysical decay rate Γφ to the macroscopic temperature through gravity and thermodynamics.
Step 4. Solve for the temperature: T_reh = (90/π²g⋆)^(1/4)√(Γφ M_Pl). Evaluating the prefactor, (90/π²)^(1/4) = 1.74, so with g⋆ = 106.75 one finds T_reh ≈ 0.54√(Γφ M_Pl). Why: the quarter-power dependence on g⋆ makes T_reh insensitive to the exact particle content — a factor of two in g⋆ shifts it by only 20% — while the square-root ties it to the geometric mean of the decay rate and the Planck scale. The formula is the workhorse relation of reheating, matching Kolb and Turner and Dodelson; the alternative prefactor 0.2(200/g⋆)^(1/4) quoted in some texts uses the non-reduced Planck mass 1.22×10¹⁹ GeV and is numerically the same result.
Go deeper · Derivation C · 2 minParametric resonance and the Mathieu equation
The goal is to show how coupling a light daughter field χ to the oscillating inflaton produces the exponential, non-perturbative particle production that defines preheating, and to identify the resonance parameter q that separates narrow from broad resonance. We take ℒ_int = −½g²φ²χ² with φ(t) = Φ sin(mt), cast the χ mode equation into canonical Mathieu form, and read off the instability from Floquet theory.
Step 1. The interaction gives χ a time-dependent effective mass, m_χ²(t) = g²φ²(t) = g²Φ² sin²(mt). Why: as the inflaton swings through its oscillation, the mass it induces on χ pulses twice per period, and it is this periodic pumping — not a fixed decay width — that drives resonance.
Step 2. Expand χ in comoving Fourier modes and, neglecting expansion over a few oscillations, each mode obeys χk″ + (k² + g²Φ² sin²(mt))χk = 0. Why: dropping the Hubble term is legitimate because broad resonance completes in far fewer than one Hubble time, so the flat-space mode equation captures the essential physics.
Step 3. Use sin²(mt) = ½(1 − cos 2mt) and rescale time to z = mt, which brings the mode equation to the canonical Mathieu form χk″ + [Ak − 2q cos(2z)]χk = 0 with Ak = k²/m² + 2q and q = g²Φ²/4m². Why: the Mathieu equation is the textbook oscillator with a periodically modulated frequency, and its solutions are completely classified by the point (Ak, q) in its stability chart.
Step 4. Apply Floquet's theorem: within an instability band the solution is χk ∝ e^(μk z)P(z) with a positive Floquet exponent μk and a periodic P, so the occupation number nk ∝ |χk|² ∝ e^(2μk mt) grows exponentially. Why: exponential growth of nk is Bose-stimulated emission — each quantum already in a mode enhances the production of the next — and it has no perturbative counterpart in a single decay width.
Step 5. For broad resonance, q ≫ 1, many bands overlap and the effective μ is large (order 0.1–0.3), so the inflaton drains in only tens of oscillations. Why: the broad-resonance regime, generic when g²Φ² greatly exceeds m², makes preheating far faster than perturbative decay and is why thermalization, not production, is the rate-limiting step. The Mathieu structure and its exponential Floquet growth are the defining features of preheating (Kofman, Linde and Starobinsky, 1997).
Limiting cases
The character of reheating is controlled by the shape of the potential near its minimum and by the strength of the inflaton's couplings.
| Case | Result | Meaning |
|---|---|---|
| Quadratic minimum, V = ½m²φ² | ⟨w⟩ = 0, ρφ ∝ a⁻³ | Oscillations behave as pressureless matter; a transient matter era precedes reheating, and parametric resonance is generic. |
| Quartic minimum, V = ¼λφ⁴ | ⟨w⟩ = 1/3, ρφ ∝ a⁻⁴ | Oscillations redshift like radiation; the expansion history is radiation-like even before thermalization completes. |
| General power law, V ∝ φⁿ | ⟨w⟩ = (n−2)/(n+2), ρφ ∝ a^(−6n/(n+2)) | The averaged equation of state interpolates from dust (n = 2) toward stiff fluid (large n). |
| Perturbative (weak coupling) | Γφ ≪ m, T_reh ∼ √(Γφ M_Pl) | The single-width Boltzmann treatment is valid; reheating is slow and gradual, with T_reh set by equation (5). |
| Broad parametric resonance | q = g²Φ²/4m² ≫ 1 | Non-perturbative: nk ∝ e^(2μk mt), energy transfer is explosive and non-thermal, and no single decay width applies. |
Worked examples
1 · The reheating temperature of a GUT-scale inflaton (fully worked)
An inflaton of mass m = 10¹³ GeV decays only through gravitational-strength interactions, with rate Γφ ∼ m³/M_Pl². Estimate the reheating temperature, taking g⋆ = 106.75 and M_Pl = 2.4×10¹⁸ GeV.
Step 1. Compute the decay rate. A gravitational-strength coupling gives Γφ = m³/M_Pl² = (10¹³)³/(2.4×10¹⁸)² = 10³⁹/(5.76×10³⁶) = 174 GeV — a tiny width for so heavy a field, which is why T_reh lands well below the inflaton mass.
Step 2. Form the geometric combination √(Γφ M_Pl) = √(174 × 2.4×10¹⁸) = √(4.17×10²⁰) = 2.04×10¹⁰ GeV — the natural scale of T_reh before the order-unity thermodynamic prefactor.
Step 3. Apply the prefactor from equation (5): (90/π²g⋆)^(1/4) = 1.74/106.75^(1/4) = 1.74/3.21 = 0.541. Hence T_reh = 0.541 × 2.04×10¹⁰ = 1.1×10¹⁰ GeV.
Step 4. Interpret. A GUT-scale inflaton that can only decay gravitationally reheats to about 10¹⁰ GeV — above the ∼10⁹ GeV needed for thermal leptogenesis but far below the 10¹⁵–10¹⁶ GeV that GUT baryogenesis would demand. Note the hierarchy: the inflaton mass is 10¹³ GeV, yet T_reh is a thousand times smaller, because it scales as √Γφ, not as the energy stored. T_reh ≈ 1×10¹⁰ GeV.
2 · The BBN floor as an inflaton lifetime bound
Big Bang Nucleosynthesis requires a standard thermal bath, including neutrinos, by T ∼ 1 MeV. Translate this into a bound on the inflaton decay rate and lifetime, and confirm the reheating-temperature floor.
Step 1. Find the Hubble rate at T = 1 MeV with g⋆ = 10.75 (photons, neutrinos, electrons): H = √(π²g⋆/90) T²/M_Pl = √(1.18) × (10⁻³)²/(2.4×10¹⁸) = 4.5×10⁻²⁵ GeV.
Step 2. Convert to ordinary units using 1 GeV = 1.52×10²⁴ s⁻¹: H ≈ 4.5×10⁻²⁵ × 1.52×10²⁴ ≈ 0.7 s⁻¹, so the corresponding age is t ∼ 1/(2H) ∼ 1 s. The inflaton must have completed its decay, Γφ ≳ H, before the universe is about one second old.
Step 3. The lifetime bound is τφ = 1/Γφ ≲ 1/H ≈ 1.5 s. An inflaton that lives longer than a second would still be dumping entropy during nucleosynthesis, spoiling the neutron-to-proton ratio and the light-element yields.
Step 4. Confirm the temperature floor by putting Γφ = H(1 MeV) into equation (5) with g⋆ = 10.75: the prefactor is 1.74/10.75^(1/4) = 0.96, and √(Γφ M_Pl) = √(4.5×10⁻²⁵ × 2.4×10¹⁸) = 1.04×10⁻³ GeV, giving T_reh ≈ 0.96 × 1.04 MeV ≈ 1 MeV. Allowing for the full neutrino-thermalization calculation raises the robust floor to a few MeV. T_reh ≳ few MeV, τφ ≲ 1 s.
3 · How broad is the resonance?
For chaotic inflation the inflaton ends inflation with amplitude Φ ∼ 0.1 M_Pl ≈ 2.4×10¹⁷ GeV and mass m ≈ 10¹³ GeV. With an order-one coupling g ∼ 1, estimate the resonance parameter q and comment.
Step 1. Insert into q = g²Φ²/4m² = (2.4×10¹⁷)²/(4 × (10¹³)²) = 5.76×10³⁴/(4×10²⁶) = 1.4×10⁸.
Step 2. Interpret. Since q ≈ 10⁸ is vastly greater than one, the system sits deep in the broad-resonance regime: many Mathieu bands overlap and production proceeds in violent bursts at each inflaton zero crossing. q ≈ 10⁸ ≫ 1 — broad resonance, so preheating drains the inflaton in tens of oscillations, long before perturbative decay could act.
Physics of the portrait
Reheating is where inflationary cosmology touches particle physics, and no one shaped both sides of that meeting more than Andrei Linde — architect of the new and chaotic inflationary scenarios and, with Lev Kofman and Alexei Starobinsky, of the modern theory of reheating and preheating.
Origins · 1 minAndrei Linde and how this was discovered
Andrei Linde is one of the founders of inflationary cosmology and a central figure in the theory of how inflation ends. After Alan Guth's 1981 proposal exposed the "graceful exit" problem — old inflation could not reheat because its bubbles never percolated — Linde (and independently Albrecht and Steinhardt) introduced new inflation in 1982, in which the inflaton rolls slowly off a plateau and then oscillates about its minimum, reheating the universe as it decays. The same year, Dolgov and Linde, and Abbott, Farhi and Wise, wrote down the perturbative theory of reheating: attach a decay width Γφ to the oscillating inflaton and let its energy leak into radiation until Γφ ≃ H. Linde's 1983 chaotic inflation made the oscillating-inflaton picture generic. The decisive advance came in the 1990s: Kofman, Linde and Starobinsky showed in 1994, and developed fully in 1997, that the coherent inflaton does not merely decay particle by particle but pumps its daughter fields through parametric resonance, producing quanta explosively and non-perturbatively — the phenomenon they named preheating. That insight reframed the end of inflation as a problem in non-equilibrium field theory, and it underlies every modern treatment, from gravitational-wave signatures of preheating to the reheating constraints now folded into CMB parameter analyses.
Going further
Texts. Ryden, Introduction to Cosmology, 2nd ed., Ch. 11 (inflation and reheating) · Dodelson, Modern Cosmology, 2nd ed., Ch. 6 · Mo, van den Bosch and White, Galaxy Formation and Evolution, Ch. 3 (thermal history) · Kolb and Turner, The Early Universe, Ch. 8 (inflaton decay and reheating) · Carroll and Ostlie, An Introduction to Modern Astrophysics, 2nd ed., Ch. 30 · Kofman, Linde and Starobinsky, Phys. Rev. D 56, 3258 (1997), "Towards the Theory of Reheating After Inflation".
Provenance. The inflaton equation of motion, the decay-sourced energy budget, the averaged equation of state ⟨w⟩ = (n−2)/(n+2), and the reheating temperature T_reh = (90/π²g⋆)^(1/4)√(Γφ M_Pl) follow Kolb and Turner, Dodelson, and Ryden. The Mathieu-equation analysis of parametric resonance follows Kofman, Linde and Starobinsky (1997). A verifier should recompute: (1) the virial average giving w = 0 for n = 2 and w = (n−2)/(n+2) in general; (2) the algebra from Γφ = H and ρr = (π²/30)g⋆T⁴ to equation (5), including the prefactor (90/π²)^(1/4) = 1.74 and the value 0.54 at g⋆ = 106.75; (3) the reduction of the χ mode equation to canonical Mathieu form with q = g²Φ²/4m²; (4) the worked numbers T_reh ≈ 1.1×10¹⁰ GeV for Γφ = m³/M_Pl² with m = 10¹³ GeV, the BBN floor H(1 MeV) ≈ 0.7 s⁻¹ giving τ ≲ 1 s and T_reh ≈ 1 MeV, and q ≈ 1.4×10⁸ for Φ = 2.4×10¹⁷ GeV. Standard values used (M_Pl ≈ 2.4×10¹⁸ GeV, g⋆ ≈ 106.75, η ≈ 6×10⁻¹⁰, BBN floor ∼ few MeV) are textbook.
Prerequisites. Equilibrium Thermodynamics of the Early Universe · Effective Number of Relativistic Degrees of Freedom · Thermal History of the Universe · Entropy Conservation and Comoving Entropy. Leads to. Baryon Asymmetry and Baryogenesis · Big Bang Nucleosynthesis · Neutrino Decoupling and the Cosmic Neutrino Background · Decoupling and Freeze-Out.
Ask the tutor: Ask me to integrate the coupled ρφ–ρr equations and watch T_max overshoot T_reh, or to walk the Mathieu stability chart to see where broad resonance switches on.
Is reheating the same event as the Big Bang?
In the modern picture, reheating is the hot Big Bang's ignition. The classical "Big Bang" — a hot, dense, radiation-dominated plasma expanding and cooling — does not begin at a singularity in inflationary cosmology; it begins when reheating converts the inflaton's energy into that plasma. Everything the textbook hot Big Bang describes (nucleosynthesis, recombination, the CMB) unfolds afterward, using the temperature, entropy and abundances reheating sets. What preceded it was not hotter matter but a cold, inflaton-dominated, near-de Sitter phase.
What is the difference between reheating and preheating?
Perturbative reheating models inflaton decay as independent, single-particle decays with a fixed width Γφ; energy leaks out slowly and reheating completes when Γφ ≃ H. Preheating is the non-perturbative first stage that often precedes it: because the inflaton is a coherent condensate, it pumps its daughter fields through parametric resonance (or, for some potentials, tachyonic instability), and Bose enhancement makes occupation numbers grow exponentially, nk ∝ e^(2μk mt). It transfers a large fraction of the energy in only tens of oscillations, into a few narrow momentum bands, producing a violently non-thermal spectrum that a separate thermalization stage must equilibrate before a temperature exists. Perturbative decay usually mops up whatever the resonance leaves behind.
Why is the reheating temperature not simply the inflationary energy scale?
Because reheating is a race between decay and expansion, not an instantaneous conversion. The inflationary scale is set by the energy stored in the potential, roughly V^(1/4), but that energy is only released as fast as the inflaton decays, at rate Γφ. If the coupling is weak, the inflaton spends many Hubble times redshifting as matter while dribbling out radiation, reaching thermal domination only at Γφ ≃ H — by which point much of the original energy has been diluted away. The resulting T_reh scales as √Γφ and can be many orders of magnitude below the inflationary scale, as the GUT-inflaton example shows.
Can we ever observe the reheating temperature directly?
Not directly — no relic carries a clean imprint of T_reh the way the CMB carries the recombination temperature. But it is bounded and indirectly probed. From below, BBN demands T_reh ≳ a few MeV, and any successful baryogenesis mechanism sets its own higher floor. From above, T_reh cannot exceed the inflationary energy scale, itself limited by the non-detection of primordial B-modes (the tensor-to-scalar ratio r). In between, the reheating epoch's duration and equation of state shift the mapping between CMB scales and the end of inflation, so precision n_s and r constrain the combination of T_reh and the reheating e-fold number. Future gravitational-wave searches for a preheating background offer another, more speculative, handle.
What is the gravitino problem, and how does it constrain reheating?
In supersymmetric theories the gravitino — the spin-3/2 partner of the graviton — is produced thermally in the reheated plasma at a rate proportional to T_reh. If gravitinos are heavy and unstable, they decay late, during or after BBN, and their energetic decay products photodissociate the freshly made light nuclei, ruining the predicted abundances. Avoiding this caps the reheating temperature, typically T_reh ≲ 10⁶–10⁹ GeV depending on the gravitino mass; if instead the gravitino is a stable relic, too high a T_reh overproduces it as dark matter and overcloses the universe. Either way, T_reh becomes a sharp constraint linking inflation to the supersymmetry-breaking scale, and it has driven much model building toward low-scale reheating.
How does reheating affect predictions for the CMB spectral index n_s?
The observable CMB scales left the horizon a certain number of e-folds N before inflation ended, and n_s and r are evaluated at that point on the inflaton potential. But N depends on the entire expansion history between horizon exit and today — including reheating: a longer reheating, or one with a stiffer ⟨w⟩, slides the point where n_s is read off. For a given model this typically shifts n_s by order 0.005–0.01 — comparable to Planck's error bars. That is why modern analyses no longer treat reheating as irrelevant bookkeeping: it is a genuine uncertainty in the n_s–r plane, and conversely a measured n_s constrains the reheating history.