Standard non-thermal leptogenesis works at arbitrarily low reheating temperatures above the BBN bound when the inflaton potential has a quartic minimum (k≥4), because the inflaton's evolving mass kinematically shuts off RHN production early.
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How long before the end of inflation were observable perturbations produced?
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We reconsider the issue of the number of e-foldings before the end of inflation at which observable perturbations were generated. We determine a plausible upper limit on that number for the standard cosmology which is around 60, with the expectation that the actual value will be up to 10 below this. We also note a special property of the $\lambda \phi^4$ model which reduces the uncertainties in that case and favours a higher value, giving a fairly definite prediction of 64 e-foldings for that model. We note an extreme (and highly implausible) situation where the number of e-foldings can be even higher, possibly up to 100, and discuss the shortcomings of quantifying inflation by e-foldings rather than by the change in $aH$. Finally, we discuss the impact of non-standard evolution between the end of inflation and the present, showing that again the expected number of e-foldings can be modified, and in some cases significantly increased.
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representative citing papers
Scalar metric perturbations after inflation break conformal invariance and induce quantum production of gravitons, generating a GW spectrum that peaks near GHz frequencies for standard primordial scalar power spectra.
For monomial inflationary potentials with k≥4, the inflaton regenerates from the thermal bath after reheating because its amplitude-dependent mass vanishes asymptotically.
Radiative corrections pull an isolated, long-lived massive graviton out of the gapped linear-dilaton continuum, giving a sub-MeV dark-matter candidate that can coexist with a holographic fluid component.
Negative field-space curvature enhances post-inflationary Ricci scalar oscillations and boosts CGPP dark matter number density by up to an order of magnitude relative to flat field-space cases, with nontrivial relic abundance dependence on spectator mass and reheating temperature.
Switching to 3-torus topology and summing SL(3,Z) geometries via automorphic forms makes the no-boundary wavefunction favor large inflating universes with over 250 e-folds, plus CMB corrections from torus moduli.
Improved end-of-inflation dynamics shift the Starobinsky model's predicted spectral index n_s by up to 1.2×10^{-3} within the allowed reheating range.
Stiff-fluid reheating in Starobinsky inflation fits CMB+BAO at 1 sigma only if excluded by BBN radiation bounds, with remaining 2 sigma space testable by LISA, ET, DECIGO and BBO via blue-tilted GW spectrum.
Inflaton accretion during reheating drives non-linear PBH mass growth that extends lifetimes and amplifies emitted SGWB by multiple orders of magnitude.
Deformed alpha-attractor T-models with a Gaussian feature near the minimum yield more smaller shorter-lived oscillons during self-resonance preheating, suppressing energy in oscillons and altering the high-frequency gravitational wave tail while leaving low frequencies unchanged.
Dark matter freezes in from non-thermal Z' decays before reheating ends in an inflationary model with a secluded U(1)_D gauge sector, Z' reheaton, and lattice treatment of non-perturbative effects, opening viable parameter space with GW probes.
Lattice simulations show that the post-inflationary equation of state with trilinear interactions returns to zero after an initial deviation, substantially lowering stochastic gravitational wave amplitudes relative to prior estimates.
Single-field inflation with ε(N) approaching a constant in (0,1) at early times forms an asymptotic universality class with a Weyl-flat null origin while producing ns and r values compatible with Planck data.
Generalized no-scale models with R=2/(3α) for α≠1 or non-minimal gauge couplings allow unsuppressed inflaton decays, producing calculable reheating temperatures and (n_s,r) predictions.
Two minimal single-parameter extensions of the α-Starobinsky model shift ns into the 1σ ACT DR6 region while keeping r < 0.038 and yielding T_re ~ 10^9 GeV for N_k in [50,65].
Reheating temperature and equation-of-state parameter assumptions in Weyl-invariant Einstein-Cartan gravity models significantly alter predicted inflationary observables.
Multi-field fibre inflation in perturbative LVS uses collective dynamics of several moduli to achieve viable cosmology with sub-Planckian individual field ranges given by total range divided by sqrt(n).
Differences in inflationary energy scales between Einstein and Jordan frames produce distinct reheating e-folding numbers and temperatures, leading to contrasting thermal histories with potential observational signatures.
Updated Planck CMB measurements give ns = 0.9649 ± 0.0042, r < 0.056, confirm flatness at 0.4 percent, and show no evidence for scale-dependent features or non-slow-roll dynamics in the inflaton potential.
Pure natural inflation remains compatible with ACT+DESI constraints on ns and r for small positive and mildly negative p under instantaneous and perturbative reheating.
Assisted multi-fibre inflation distributes the required field range across several moduli in global CY orientifolds, overcoming single-field Kähler cone obstructions to realize viable inflation.
Review classifies QCD axion models extending the standard mass-coupling window and updates bounds from cosmology, astrophysics, and experiments.
Lecture notes providing a generic introduction to reheating after inflation, covering its theoretical, phenomenological, and observational aspects.
citing papers explorer
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Leptogenesis and Low Reheating Temperatures
Standard non-thermal leptogenesis works at arbitrarily low reheating temperatures above the BBN bound when the inflaton potential has a quartic minimum (k≥4), because the inflaton's evolving mass kinematically shuts off RHN production early.
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Quantum production of gravitational waves after inflation
Scalar metric perturbations after inflation break conformal invariance and induce quantum production of gravitons, generating a GW spectrum that peaks near GHz frequencies for standard primordial scalar power spectra.
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Inflaton Regeneration via Scalar Couplings: Generic Models and the Higgs Portal
For monomial inflationary potentials with k≥4, the inflaton regenerates from the thermal bath after reheating because its amplitude-dependent mass vanishes asymptotically.
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Massive Graviton Dark Matter from a Gapped Continuum
Radiative corrections pull an isolated, long-lived massive graviton out of the gapped linear-dilaton continuum, giving a sub-MeV dark-matter candidate that can coexist with a holographic fluid component.
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Cosmological gravitational particle production in multifield inflation
Negative field-space curvature enhances post-inflationary Ricci scalar oscillations and boosts CGPP dark matter number density by up to an order of magnitude relative to flat field-space cases, with nontrivial relic abundance dependence on spectator mass and reheating temperature.
-
Inflation and topology from the no-boundary state
Switching to 3-torus topology and summing SL(3,Z) geometries via automorphic forms makes the no-boundary wavefunction favor large inflating universes with over 250 e-folds, plus CMB corrections from torus moduli.
-
Precision Inflationary Predictions: Impact of Accurate End-of-Inflation Dynamics
Improved end-of-inflation dynamics shift the Starobinsky model's predicted spectral index n_s by up to 1.2×10^{-3} within the allowed reheating range.
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Reheating matters: Starobinsky inflation in light of joint CMB+BAO results and gravitational-wave forecasts
Stiff-fluid reheating in Starobinsky inflation fits CMB+BAO at 1 sigma only if excluded by BBN radiation bounds, with remaining 2 sigma space testable by LISA, ET, DECIGO and BBO via blue-tilted GW spectrum.
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Inflaton Accretion onto Primordial Black Holes During Reheating
Inflaton accretion during reheating drives non-linear PBH mass growth that extends lifetimes and amplifies emitted SGWB by multiple orders of magnitude.
-
Self-resonance preheating in deformed attractor models: oscillon formation and evolution
Deformed alpha-attractor T-models with a Gaussian feature near the minimum yield more smaller shorter-lived oscillons during self-resonance preheating, suppressing energy in oscillons and altering the high-frequency gravitational wave tail while leaving low frequencies unchanged.
-
Dark Matter Freeze-in from a $Z^\prime$ Reheaton
Dark matter freezes in from non-thermal Z' decays before reheating ends in an inflationary model with a secluded U(1)_D gauge sector, Z' reheaton, and lattice treatment of non-perturbative effects, opening viable parameter space with GW probes.
-
Equation of state during (p)reheating with trilinear interactions
Lattice simulations show that the post-inflationary equation of state with trilinear interactions returns to zero after an initial deviation, substantially lowering stochastic gravitational wave amplitudes relative to prior estimates.
-
Inflation from a Weyl-flat null origin
Single-field inflation with ε(N) approaching a constant in (0,1) at early times forms an asymptotic universality class with a Weyl-flat null origin while producing ns and r values compatible with Planck data.
-
Reheating in No-Scale Models of Inflation
Generalized no-scale models with R=2/(3α) for α≠1 or non-minimal gauge couplings allow unsuppressed inflaton decays, producing calculable reheating temperatures and (n_s,r) predictions.
-
Minimal Extensions of the $\alpha$-Starobinsky Model: Reconciling ACT DR6 and Reheating Constraints
Two minimal single-parameter extensions of the α-Starobinsky model shift ns into the 1σ ACT DR6 region while keeping r < 0.038 and yielding T_re ~ 10^9 GeV for N_k in [50,65].
-
Reheating in geometric Weyl-invariant Einstein-Cartan gravity
Reheating temperature and equation-of-state parameter assumptions in Weyl-invariant Einstein-Cartan gravity models significantly alter predicted inflationary observables.
-
Assisted Fibre Inflation in Perturbative LVS
Multi-field fibre inflation in perturbative LVS uses collective dynamics of several moduli to achieve viable cosmology with sub-Planckian individual field ranges given by total range divided by sqrt(n).
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Einstein or Jordan: seeking answers from the reheating constraints
Differences in inflationary energy scales between Einstein and Jordan frames produce distinct reheating e-folding numbers and temperatures, leading to contrasting thermal histories with potential observational signatures.
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Planck 2018 results. X. Constraints on inflation
Updated Planck CMB measurements give ns = 0.9649 ± 0.0042, r < 0.056, confirm flatness at 0.4 percent, and show no evidence for scale-dependent features or non-slow-roll dynamics in the inflaton potential.
-
Pure Natural Inflation Passes the ACT
Pure natural inflation remains compatible with ACT+DESI constraints on ns and r for small positive and mildly negative p under instantaneous and perturbative reheating.
-
On Global Embedding of Assisted Fibre Inflation
Assisted multi-fibre inflation distributes the required field range across several moduli in global CY orientifolds, overcoming single-field Kähler cone obstructions to realize viable inflation.
-
The landscape of QCD axion models
Review classifies QCD axion models extending the standard mass-coupling window and updates bounds from cosmology, astrophysics, and experiments.
-
Lectures on Reheating after Inflation
Lecture notes providing a generic introduction to reheating after inflation, covering its theoretical, phenomenological, and observational aspects.