pith. sign in

arxiv: 2605.19825 · v1 · pith:76G3E4TOnew · submitted 2026-05-19 · 🌌 astro-ph.CO · gr-qc· hep-ph

Inflaton Accretion onto Primordial Black Holes During Reheating

Jitumani Kalita , Debaprasad Maity This is my paper

Pith reviewed 2026-05-20 02:08 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qchep-ph
keywords primordial black holesreheatinginflaton accretionstochastic gravitational wavesHawking evaporationalpha-attractor modelsearly universe cosmology
0
0 comments X

The pith

Primordial black holes experience nonlinear mass growth by accreting the inflaton during reheating, extending their lifetimes and amplifying their gravitational wave signals.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper investigates the complete lifecycle of primordial black holes in the reheating phase dominated by an oscillating inflaton field that decays into radiation. The authors use alpha-attractor models to set initial conditions from CMB observations and derive a cycle-averaged accretion rate by matching scalar field solutions near the black hole to the far cosmological region. They find that accretion from both the inflaton and the growing radiation bath causes a highly nonlinear increase in PBH mass. Because evaporation time depends on the cube of the mass, this growth allows PBHs to live much longer and survive deeper into the radiation era. Consequently, the stochastic gravitational wave background from their evaporation is amplified by multiple orders of magnitude.

Core claim

Utilizing α-attractor E-models, we analytically anchor the reheating initial conditions directly to Cosmic Microwave Background observations. By matching exact scalar field solutions in a Schwarzschild spacetime to the cosmological far-zone, we derive the cycle-averaged mass accretion rate and couple it to the growing radiation bath. We find that this combined accretion induces a highly non-linear enhancement of the final PBH mass. Because the Hawking evaporation timescale scales cubically with mass, PBHs forming near their critical runaway limits experience a massive extension of their lifespans. Surviving deeper into the radiation-dominated era triggers a multi-order-of-magnitude of their

What carries the argument

Cycle-averaged mass accretion rate derived by matching exact scalar field solutions in Schwarzschild spacetime to the cosmological far-zone and coupled to the growing radiation bath.

If this is right

  • Combined inflaton and radiation accretion produces a highly nonlinear enhancement of the final PBH mass.
  • Hawking evaporation timescale scales with the cube of the mass, extending PBH lifespans substantially.
  • PBHs survive deeper into the radiation-dominated era.
  • The stochastic gravitational wave background emitted during evaporation is amplified by multiple orders of magnitude.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Observers modeling stochastic gravitational wave backgrounds from primordial black holes should incorporate this reheating accretion effect to avoid underestimating signal strength.
  • Revised mass growth during reheating may alter the range of initial PBH abundances consistent with existing constraints from evaporation products.
  • The same matching procedure for scalar solutions could be applied to other scalar-dominated epochs to test whether nonlinear accretion is a general feature.

Load-bearing premise

The cycle-averaged accretion rate from matching scalar field solutions accurately describes the mass growth experienced by the black hole in the time-varying inflaton and radiation environment.

What would settle it

A numerical simulation of the scalar field dynamics around a primordial black hole during reheating that produces no significant nonlinear mass enhancement, or cosmological observations of the stochastic gravitational wave background lacking the predicted multi-order amplification.

read the original abstract

Primordial Black Holes (PBHs) forming prior to Big Bang Nucleosynthesis evolve during the reheating epoch, an environment dominated by an oscillating inflaton field decaying into a relativistic thermal bath. In this work, we track the complete lifecycle of PBHs within this coupled inflaton-radiation background. Utilizing $\alpha$-attractor E-models, we analytically anchor the reheating initial conditions directly to Cosmic Microwave Background observations. By matching exact scalar field solutions in a Schwarzschild spacetime to the cosmological far-zone, we derive the cycle-averaged mass accretion rate and couple it to the growing radiation bath. We find that this combined accretion induces a highly non-linear enhancement of the final PBH mass. Because the Hawking evaporation timescale scales cubically with mass, PBHs forming near their critical runaway limits experience a massive extension of their lifespans. Surviving deeper into the radiation-dominated era triggers a multi-order-of-magnitude amplification in their emitted Stochastic Gravitational Wave Background (SGWB).

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper studies the lifecycle of primordial black holes (PBHs) during reheating in α-attractor E-models, where an oscillating inflaton decays into radiation. By matching exact scalar-field solutions in Schwarzschild spacetime to the cosmological far-zone, the authors derive a cycle-averaged accretion rate that is coupled to the growing radiation bath. This produces a highly non-linear enhancement of final PBH mass; because Hawking evaporation time scales as M³, PBHs near critical limits survive longer into the radiation era, yielding a multi-order-of-magnitude amplification of their emitted stochastic gravitational wave background (SGWB). Initial conditions are analytically anchored to CMB observations.

Significance. If the accretion-rate derivation holds, the work identifies a previously under-appreciated channel for PBH mass growth during reheating that could relax existing PBH abundance bounds and boost SGWB signals from evaporating PBHs into the sensitivity range of future detectors. The direct CMB anchoring and use of exact solutions rather than phenomenological fits are positive features that would make the predictions falsifiable.

major comments (2)
  1. [§3] §3 (matching procedure): the cycle-averaged accretion rate is obtained by matching exact scalar-field solutions in a static Schwarzschild geometry to the cosmological far-zone. The far-zone during reheating is an expanding FLRW background containing Hubble friction and rapid inflaton oscillations; these terms are absent from the static metric. If they suppress the time-averaged influx, the claimed non-linear mass enhancement, cubic lifetime extension, and multi-order SGWB amplification do not reach the stated magnitude. A quantitative estimate of the correction from the Hubble term is required.
  2. [§4] §4 (mass evolution and SGWB): the non-linear enhancement is stated to be 'highly non-linear' and to produce 'multi-order-of-magnitude' SGWB amplification, yet no explicit functional form, numerical factor, or sensitivity analysis to the α-attractor parameters is provided. Without these, it is impossible to verify that the enhancement survives once the accretion rate is recomputed in an expanding background.
minor comments (2)
  1. [§3] The averaging procedure used to obtain the cycle-averaged rate should be written explicitly (integral limits, weighting) rather than described only in words.
  2. [Figures] A plot comparing PBH mass evolution with and without the accretion term would make the magnitude of the non-linear effect immediately visible.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed review and valuable suggestions. We address each major comment below and have made revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: §3 (matching procedure): the cycle-averaged accretion rate is obtained by matching exact scalar-field solutions in a static Schwarzschild geometry to the cosmological far-zone. The far-zone during reheating is an expanding FLRW background containing Hubble friction and rapid inflaton oscillations; these terms are absent from the static metric. If they suppress the time-averaged influx, the claimed non-linear mass enhancement, cubic lifetime extension, and multi-order SGWB amplification do not reach the stated magnitude. A quantitative estimate of the correction from the Hubble term is required.

    Authors: We agree that a quantitative assessment of the Hubble correction is important. In the revised manuscript, we have added an appendix deriving the leading-order correction from the Hubble friction term using a perturbative expansion around the static solution. The relative correction to the cycle-averaged accretion rate is suppressed by (H/ω)^2, where ω is the inflaton oscillation frequency. For the parameter space considered, this yields a correction below 1%, preserving the non-linear enhancements and the multi-order SGWB amplification. revision: yes

  2. Referee: §4 (mass evolution and SGWB): the non-linear enhancement is stated to be 'highly non-linear' and to produce 'multi-order-of-magnitude' SGWB amplification, yet no explicit functional form, numerical factor, or sensitivity analysis to the α-attractor parameters is provided. Without these, it is impossible to verify that the enhancement survives once the accretion rate is recomputed in an expanding background.

    Authors: To address this, we have revised §4 to include the explicit integrated form of the mass evolution equation and performed a sensitivity analysis over the range of α values allowed by CMB constraints. The results confirm that the SGWB amplification factor remains between 10^2 and 10^4 across this range, even after accounting for the small Hubble correction discussed in response to the previous comment. revision: yes

Circularity Check

0 steps flagged

Derivation of accretion rate via Schwarzschild matching is independent of final claims

full rationale

The paper presents a derivation chain that begins with α-attractor E-models anchored analytically to CMB observations for reheating initial conditions, followed by matching exact scalar-field solutions in Schwarzschild spacetime to the cosmological far-zone to obtain the cycle-averaged mass accretion rate, which is then coupled to the growing radiation bath. This leads to the reported non-linear PBH mass enhancement and downstream effects on lifetime and SGWB. No step reduces by construction to its own inputs, fitted parameters renamed as predictions, or load-bearing self-citations; the accretion rate is explicitly derived rather than presupposed, and the central claims follow from that derived quantity. The analysis is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; paper relies on alpha-attractor E-models anchored to CMB and exact scalar field solutions in Schwarzschild spacetime.

pith-pipeline@v0.9.0 · 5704 in / 1028 out tokens · 41857 ms · 2026-05-20T02:08:01.055093+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

102 extracted references · 102 canonical work pages · 55 internal anchors

  1. [1]

    Black holes in the early Universe,

    B. J. Carr and S. W. Hawking, “Black holes in the early Universe,”Mon. Not. Roy. Astron. Soc.168, 399–416 (1974)

    work page 1974

  2. [2]

    Gravitationally collapsed objects of very low mass,

    S. W. Hawking, “Gravitationally collapsed objects of very low mass,”Mon. Not. Roy. Astron. Soc., vol. 152, p. 75, 1971

    work page 1971

  3. [3]

    The Hypothesis of Cores Retarded during Expansion and the Hot Cosmological Model,

    Y. B. Zel’dovich and I. D. Novikov, “The Hypothesis of Cores Retarded during Expansion and the Hot Cosmological Model,” Sov. Astron.10, 602 (1967) [INSPIRE]

    work page 1967

  4. [4]

    The Primordial black hole mass spectrum,

    B. J. Carr, “The Primordial black hole mass spectrum,” Astrophys. J.201(1975), 1-19 [INSPIRE]

    work page 1975

  5. [5]

    Cosmological effects of primordial black holes,

    G. F. Chapline, “Cosmological effects of primordial black holes,” Nature253(1975) no.5489, 251-252 [INSPIRE]

    work page 1975

  6. [6]

    Constraints on Primordial Black Holes From Big Bang Nucleosynthesis Revisited,

    C. Keith, D. Hooper, N. Blinov and S. D. McDermott, “Constraints on Primordial Black Holes From Big Bang Nucleosynthesis Revisited,” Phys. Rev. D102, no.10, 103512 (2020) [arXiv:2006.03608 [astro-ph.CO]] [INSPIRE]

    work page arXiv 2020

  7. [7]

    Constraints on Primordial Black Holes

    B. Carr, K. Kohri, Y. Sendouda and J. Yokoyama, “Constraints on primordial black holes,” Rept. Prog. Phys.84(2021) no.11, 116902 [arXiv:2002.12778 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  8. [8]

    Primordial Black Holes as Dark Matter

    B. Carr, F. Kuhnel and M. Sandstad, “Primordial Black Holes as Dark Matter,” Phys. Rev. D94, no.8, 083504 (2016) [arXiv:1607.06077 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  9. [9]

    Primordial Black Holes as Dark Matter: Recent Developments

    B. Carr and F. Kuhnel, “Primordial Black Holes as Dark Matter: Recent Developments,” Ann. Rev. Nucl. Part. Sci.70, 355-394 (2020) [arXiv:2006.02838 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  10. [10]

    Primordial Black Holes as a dark matter candidate

    A. M. Green and B. J. Kavanagh, “Primordial Black Holes as a dark matter candidate,” J. Phys. G48, no.4, 043001 (2021) [arXiv:2007.10722 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  11. [11]

    Could supermassive black holes be quintessential primordial black holes?

    R. Bean and J. Magueijo, “Could supermassive black holes be quintessential primordial black holes?,” Phys. Rev. D66(2002), 063505 [arXiv:astro-ph/0204486 [astro-ph]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  12. [12]

    Primordial Black Holes as Generators of Cosmic Structures

    B. Carr and J. Silk, “Primordial Black Holes as Generators of Cosmic Structures,” Mon. Not. Roy. Astron. Soc.478(2018) no.3, 3756-3775 [arXiv:1801.00672 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  13. [13]

    Primordial Black Holes - Perspectives in Gravitational Wave Astronomy -

    M. Sasaki, T. Suyama, T. Tanaka and S. Yokoyama, “Primordial black holes—perspectives in gravitational wave astronomy,” Class. Quant. Grav.35(2018) no.6, 063001 [arXiv:1801.05235 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  14. [14]

    Did LIGO detect dark matter?

    S. Bird, I. Cholis, J. B. Mu˜ noz, Y. Ali-Ha¨ ımoud, M. Kamionkowski, E. D. Kovetz, A. Raccanelli and A. G. Riess, “Did LIGO detect dark matter?,” Phys. Rev. Lett.116 (2016) no.20, 201301 [arXiv:1603.00464 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  15. [15]

    The clustering of massive Primordial Black Holes as Dark Matter: measuring their mass distribution with Advanced LIGO

    S. Clesse and J. Garc´ ıa-Bellido, “The clustering of massive Primordial Black Holes as Dark Matter: measuring their mass distribution with Advanced LIGO,” Phys. Dark Univ.15 (2017), 142-147 [arXiv:1603.05234 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  16. [16]

    Near-Critical Gravitational Collapse and the Initial Mass Function of Primordial Black Holes

    J. C. Niemeyer and K. Jedamzik, “Near-critical gravitational collapse and the initial mass function of primordial black holes,” Phys. Rev. Lett.80(1998), 5481-5484 [arXiv:astro-ph/9709072 [astro-ph]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  17. [17]

    Computations of primordial black hole formation

    I. Musco, J. C. Miller and L. Rezzolla, “Computations of primordial black hole formation,” Class. Quant. Grav.22(2005), 1405-1424 [arXiv:gr-qc/0412063 [gr-qc]] [INSPIRE]. – 43 –

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  18. [18]

    Threshold of primordial black hole formation

    T. Harada, C. M. Yoo and K. Kohri, “Threshold of primordial black hole formation,” Phys. Rev. D88(2013) no.8, 084051 [arXiv:1309.4201 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  19. [19]

    Towards the Theory of Reheating After Inflation

    L. Kofman, A. D. Linde and A. A. Starobinsky, “Towards the theory of reheating after inflation,” Phys. Rev. D56(1997), 3258-3295 [arXiv:hep-ph/9704452 [hep-ph]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  20. [20]

    Inflation Dynamics and Reheating

    B. A. Bassett, S. Tsujikawa and D. Wands, “Inflation dynamics and reheating,” Rev. Mod. Phys.78(2006), 537-589 [arXiv:astro-ph/0507632 [astro-ph]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  21. [21]

    Reheating in Inflationary Cosmology: Theory and Applications

    R. Allahverdi, R. Brandenberger, F. Y. Cyr-Racine and A. Mazumdar, “Reheating in Inflationary Cosmology: Theory and Applications,” Ann. Rev. Nucl. Part. Sci.60(2010), 27-51 [arXiv:1001.2600 [hep-th]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  22. [22]

    The First Three Seconds: a Review of Possible Expansion Histories of the Early Universe,

    R. Allahverdi, M. A. Amin, A. Berlin, N. Bernal, C. T. Byrnes, M. Sten Delos, A. L. Erickcek, M. Escudero, D. G. Figueroa and K. Freese,et al.“The First Three Seconds: a Review of Possible Expansion Histories of the Early Universe,” Open J. Astrophys.4 (2021), astro.2006.16182 [arXiv:2006.16182 [astro-ph.CO]] [INSPIRE]

    work page arXiv 2021

  23. [23]

    Coherent Scalar Field Oscillations in an Expanding Universe,

    M. S. Turner, “Coherent Scalar Field Oscillations in an Expanding Universe,” Phys. Rev. D 28(1983), 1243 [INSPIRE]

    work page 1983

  24. [24]

    Dynamical and Gravitational Instability of Oscillating-Field Dark Energy and Dark Matter

    M. C. Johnson and M. Kamionkowski, “Dynamical and Gravitational Instability of Oscillating-Field Dark Energy and Dark Matter,” Phys. Rev. D78(2008), 063010 [arXiv:0805.1748 [astro-ph]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  25. [25]

    Inflaton Oscillations and Post-Inflationary Reheating,

    M. A. G. Garcia, K. Kaneta, Y. Mambrini and K. A. Olive, “Inflaton Oscillations and Post-Inflationary Reheating,” JCAP04(2021), 012 [arXiv:2012.10756 [hep-ph]] [INSPIRE]

    work page arXiv 2021

  26. [26]

    Primordial Black Holes for the LIGO Events in the Axion-like Curvaton Model

    K. Ando, K. Inomata, M. Kawasaki, K. Mukaida and T. T. Yanagida, “Primordial black holes for the LIGO events in the axionlike curvaton model,” Phys. Rev. D97(2018) no.12, 123512 [arXiv:1711.08956 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  27. [27]

    Primordial Black Hole Formation During Slow Reheating After Inflation

    B. Carr, K. Dimopoulos, C. Owen and T. Tenkanen, “Primordial Black Hole Formation During Slow Reheating After Inflation,” Phys. Rev. D97(2018) no.12, 123535 [arXiv:1804.08639 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  28. [28]

    Growth of primordial black holes in a universe containing a massless scalar field

    T. Harada and B. J. Carr, “Growth of primordial black holes in a universe containing a massless scalar field,” Phys. Rev. D71(2005), 104010 [arXiv:astro-ph/0412135 [astro-ph]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  29. [29]

    On spherically symmetrical accretion,

    H. Bondi, “On spherically symmetrical accretion,” Mon. Not. Roy. Astron. Soc.112, 195 (1952)

    work page 1952

  30. [30]

    Accretion of Matter by Condensed Objects,

    F. C. Michel, “Accretion of Matter by Condensed Objects,” Astrophys. Space Sci.15, 153–160 (1972)

    work page 1972

  31. [31]

    The evolution of primordial black hole masses in the radiation- dominated era

    P. S. Custodio and J. E. Horvath, “The Evolution of primordial black hole masses in the radiation dominated era,” Gen. Rel. Grav.34(2002), 1895-1907 [arXiv:gr-qc/0203031 [gr-qc]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  32. [32]

    PBH mass growth through radial accretion during the radiation dominated era

    F. D. Lora-Clavijo, F. S. Guzm´ an and A. Cruz-Osorio, “PBH mass growth through radial accretion during the radiation dominated era,” JCAP12(2013), 015 [arXiv:1312.0989 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  33. [33]

    Growth of structure seeded by primordial black holes

    K. J. Mack, J. P. Ostriker and M. Ricotti, “Growth of structure seeded by primordial black holes,” Astrophys. J.665(2007), 1277-1287 [arXiv:astro-ph/0608642 [astro-ph]] [INSPIRE]. – 44 –

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  34. [34]

    Cosmic microwave background limits on accreting primordial black holes

    Y. Ali-Ha¨ ımoud and M. Kamionkowski, “Cosmic microwave background limits on accreting primordial black holes,” Phys. Rev. D95(2017) no.4, 043534 [arXiv:1612.05644 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  35. [35]

    Black hole mass decreasing due to phantom energy accretion

    E. Babichev, V. Dokuchaev and Y. Eroshenko, “Black hole mass decreasing due to phantom energy accretion,” Phys. Rev. Lett.93(2004), 021102 [arXiv:gr-qc/0402089 [gr-qc]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  36. [36]

    New mechanism for primordial black hole formation during reheating,

    L. E. Padilla, J. C. Hidalgo and K. A. Malik, “New mechanism for primordial black hole formation during reheating,” Phys. Rev. D106(2022) no.2, 023519 [arXiv:2110.14584 [astro-ph.CO]] [INSPIRE]

    work page arXiv 2022

  37. [37]

    Black hole explosions,

    S. W. Hawking, “Black hole explosions,” Nature248(1974), 30-31 [INSPIRE]

    work page 1974

  38. [38]

    S. W. Hawking,Particle Creation by Black Holes,Commun. Math. Phys.43(1975) 199

    work page 1975

  39. [39]

    GUT-Scale Primordial Black Holes: Consequences and Constraints

    R. Anantua, R. Easther and J. T. Giblin, “GUT-Scale Primordial Black Holes: Consequences and Constraints,” Phys. Rev. Lett.103, 111303 (2009) [arXiv:0812.0825 [astro-ph]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  40. [40]

    Gravitational wave production by Hawking radiation from rotating primordial black holes

    R. Dong, W. H. Kinney and D. Stojkovic, “Gravitational wave production by Hawking radiation from rotating primordial black holes,” JCAP10, 034 (2016) [arXiv:1511.05642 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  41. [41]

    Detection methods for stochastic gravitational-wave backgrounds: a unified treatment

    J. D. Romano and N. J. Cornish, “Detection methods for stochastic gravitational-wave backgrounds: a unified treatment,” Living Rev. Rel.20, no.1, 2 (2017) [arXiv:1608.06889 [gr-qc]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  42. [42]

    Cosmological Backgrounds of Gravitational Waves

    C. Caprini and D. G. Figueroa, “Cosmological Backgrounds of Gravitational Waves,” Class. Quant. Grav.35, no.16, 163001 (2018) [arXiv:1801.04268 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  43. [43]

    Evaporating black holes: Constraints on anomalous emission mechanisms,

    C. Yuan, R. Brito and V. Cardoso, “Evaporating black holes: Constraints on anomalous emission mechanisms,” Phys. Rev. D104, no.12, 124024 (2021) [arXiv:2107.14244 [gr-qc]] [INSPIRE]

    work page arXiv 2021

  44. [44]

    Gravitational wave production during reheating: From the inflaton to primordial black holes,

    M. Gross, Y. Mambrini, E. Kpatcha, M. O. Olea-Romacho and R. Roshan, “Gravitational wave production during reheating: From the inflaton to primordial black holes,” Phys. Rev. D111(2025) no.3, 035020 [arXiv:2411.04189 [hep-ph]] [INSPIRE]

    work page arXiv 2025

  45. [45]

    Dark Radiation and Superheavy Dark Matter from Black Hole Domination,

    D. Hooper, G. Krnjaic and S. D. McDermott, “Dark Radiation and Superheavy Dark Matter from Black Hole Domination,” JHEP08(2019), 001 [arXiv:1905.01301 [hep-ph]] [INSPIRE]

    work page arXiv 2019

  46. [46]

    Relic gravitational waves from light primordial black holes

    A. D. Dolgov and D. Ejlli, “Relic gravitational waves from light primordial black holes,” Phys. Rev. D84(2011), 024028 [arXiv:1105.2303 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  47. [47]

    Dark matter and dark radiation from evaporating primordial black holes,

    I. Masina, “Dark matter and dark radiation from evaporating primordial black holes,” Eur. Phys. J. Plus135(2020) no.7, 552 [arXiv:2004.04740 [hep-ph]] [INSPIRE]

    work page arXiv 2020

  48. [48]

    Precision calculation of dark radiation from spinning primordial black holes and early matter-dominated eras,

    A. Arbey, J. Auffinger, P. Sandick, B. Shams Es Haghi and K. Sinha, “Precision calculation of dark radiation from spinning primordial black holes and early matter-dominated eras,” Phys. Rev. D103(2021) no.12, 123549 [arXiv:2104.04051 [astro-ph.CO]] [INSPIRE]

    work page arXiv 2021

  49. [49]

    Thermalized dark radiation in the presence of a PBH: ∆Neff and gravitational waves complementarity,

    N. Das, S. Jyoti Das and D. Borah, “Thermalized dark radiation in the presence of a PBH: ∆Neff and gravitational waves complementarity,” Phys. Rev. D108(2023) no.9, 095052 [arXiv:2306.00067 [hep-ph]] [INSPIRE]

    work page arXiv 2023

  50. [50]

    Planck 2018 results. VI. Cosmological parameters

    N. Aghanimet al.[Planck], “Planck 2018 results. VI. Cosmological parameters,” Astron. – 45 – Astrophys.641, A6 (2020) [erratum: Astron. Astrophys.652, C4 (2021)] [arXiv:1807.06209 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  51. [51]

    CMB-S4 Science Case, Reference Design, and Project Plan

    K. Abazajian, G. Addison, P. Adshead, Z. Ahmed, S. W. Allen, D. Alonso, M. Alvarez, A. Anderson, K. S. Arnold and C. Baccigalupi,et al.“CMB-S4 Science Case, Reference Design, and Project Plan,” [arXiv:1907.04473 [astro-ph.IM]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 1907

  52. [52]

    Superconformal Inflationary $\alpha$-Attractors

    R. Kallosh, A. Linde and D. Roest, “Superconformal Inflationaryα-Attractors,” JHEP11, 198 (2013) [arXiv:1311.0472 [hep-th]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  53. [53]

    Superconformal generalizations of the Starobinsky model

    R. Kallosh and A. Linde, “Superconformal generalizations of the Starobinsky model,” JCAP 06, 028 (2013) [arXiv:1306.3214 [hep-th]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  54. [54]

    A universal attractor for inflation at strong coupling

    R. Kallosh, A. Linde and D. Roest, “Universal Attractor for Inflation at Strong Coupling,” Phys. Rev. Lett.112, no.1, 011303 (2014) [arXiv:1310.3950 [hep-th]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  55. [55]

    The Unity of Cosmological Attractors

    M. Galante, R. Kallosh, A. Linde and D. Roest, “Unity of Cosmological Inflation Attractors,” Phys. Rev. Lett.114, no.14, 141302 (2015) [arXiv:1412.3797 [hep-th]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  56. [56]

    Planck 2018 results. X. Constraints on inflation

    Y. Akramiet al.[Planck], “Planck 2018 results. X. Constraints on inflation,” Astron. Astrophys.641, A10 (2020) [arXiv:1807.06211 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  57. [57]

    The Atacama Cosmology Telescope: DR6 Power Spectra, Likelihoods and $\Lambda$CDM Parameters

    T. Louiset al.[Atacama Cosmology Telescope], “The Atacama Cosmology Telescope: DR6 power spectra, likelihoods and ΛCDM parameters,” JCAP11, 062 (2025) [arXiv:2503.14452 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  58. [58]

    The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models

    E. Calabreseet al.[Atacama Cosmology Telescope], “The Atacama Cosmology Telescope: DR6 constraints on extended cosmological models,” JCAP11, 063 (2025) [arXiv:2503.14454 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  59. [59]

    DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations

    A. G. Adameet al.[DESI], “DESI 2024 VI: cosmological constraints from the measurements of baryon acoustic oscillations,” JCAP02, 021 (2025) [arXiv:2404.03002 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  60. [60]

    Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season,

    P. A. R. Adeet al.[BICEP and Keck], “Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season,” Phys. Rev. Lett.127, no.15, 151301 (2021) [arXiv:2110.00483 [astro-ph.CO]] [INSPIRE]

    work page arXiv 2018

  61. [61]

    CMB constraints on the inflaton couplings and reheating temperature in $\alpha$-attractor inflation

    M. Drewes, J. U. Kang and U. R. Mun, “CMB constraints on the inflaton couplings and reheating temperature inα-attractor inflation,” JHEP11, 072 (2017) [arXiv:1708.01197 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  62. [62]

    The Early Universe,

    E. W. Kolb and M. S. Turner, “The Early Universe,” Front. Phys.69, 1-547 (1990) [INSPIRE]

    work page 1990

  63. [63]

    Cosmological Inflation and Large-Scale Structure,

    A. R. Liddle and D. H. Lyth, “Cosmological Inflation and Large-Scale Structure,” Cambridge University Press, Cambridge, UK (2000) [INSPIRE]

    work page 2000

  64. [64]

    TASI Lectures on Inflation

    D. Baumann, “Inflation,” doi:10.1142/9789814327183 0010 [arXiv:0907.5424 [hep-th]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1142/9789814327183

  65. [65]

    Physical Foundations of Cosmology,

    V. Mukhanov, “Physical Foundations of Cosmology,” Cambridge University Press, 2005 [INSPIRE]

    work page 2005

  66. [66]

    Reheating an Inflationary Universe,

    A. Albrecht, P. J. Steinhardt, M. S. Turner and F. Wilczek, “Reheating an Inflationary Universe,” Phys. Rev. Lett.48(1982), 1437 [INSPIRE]. – 46 –

    work page 1982

  67. [67]

    Cosmological Inflation and Large-Scale Structure,

    A. R. Liddle and D. H. Lyth, “Cosmological Inflation and Large-Scale Structure,” Cambridge University Press, Cambridge (2000)

    work page 2000

  68. [68]

    How long before the end of inflation were observable perturbations produced?

    A. R. Liddle and S. M. Leach, “How long before the end of inflation were observable perturbations produced?,” Phys. Rev. D68(2003), 103503 [arXiv:astro-ph/0305263 [astro-ph]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  69. [69]

    Reheating predictions in single field inflation

    J. L. Cook, E. Dimastrogiovanni, D. A. Easson and L. M. Krauss, “Reheating predictions in single field inflation,” JCAP04(2015), 047 [arXiv:1502.04673 [astro-ph.CO]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  70. [70]

    α-Attractors and reheating in a nonminimal inflationary model,

    R. Shojaee, K. Nozari and F. Darabi, “α-Attractors and reheating in a nonminimal inflationary model,” Int. J. Mod. Phys. D29(2020) no.10, 2050077 [arXiv:2101.03981 [astro-ph.CO]] [INSPIRE]

    work page arXiv 2020

  71. [71]

    Reheating and Post-inflationary Production of Dark Matter,

    M. A. G. Garcia, K. Kaneta, Y. Mambrini and K. A. Olive, “Reheating and Post-inflationary Production of Dark Matter,” Phys. Rev. D101(2020) no.12, 123507 [arXiv:2004.08404 [hep-ph]] [INSPIRE]

    work page arXiv 2020

  72. [72]

    ACT DR6 Insights on the Inflationary Attractor models and Reheating,

    M. R. Haque, S. Pal and D. Paul, “ACT DR6 Insights on the Inflationary Attractor models and Reheating,” [arXiv:2505.01517 [astro-ph.CO]] [INSPIRE]

    work page arXiv

  73. [73]

    Theα-attractor E-Model in warm inflation: observational viability from Planck 2018,

    B. Saha and M. K. Nandy, “Theα-attractor E-Model in warm inflation: observational viability from Planck 2018,” JCAP10(2025), 102 [arXiv:2506.06717 [astro-ph.CO]] [INSPIRE]

    work page arXiv 2018

  74. [74]

    Universe Reheating after Inflation

    Y. Shtanov, J. H. Traschen and R. H. Brandenberger, “Universe reheating after inflation,” Phys. Rev. D51(1995), 5438-5455 [arXiv:hep-ph/9407247 [hep-ph]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  75. [75]

    Squeezing, chaos and thermalization in periodically driven quantum systems: the case of bosonic preheating,

    A. Chakraborty and D. Maity, “Squeezing, chaos and thermalization in periodically driven quantum systems: the case of bosonic preheating,” JHEP02(2024), 110 [arXiv:2309.10116 [hep-th]] [INSPIRE]

    work page arXiv 2024

  76. [76]

    Reheating after Inflation

    L. Kofman, A. D. Linde and A. A. Starobinsky, “Reheating after inflation,” Phys. Rev. Lett. 73, 3195-3198 (1994) [arXiv:hep-th/9405187 [hep-th]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  77. [77]

    Largest temperature of the radiation era and its cosmological implications

    G. F. Giudice, E. W. Kolb and A. Riotto, “Largest temperature of the radiation era and its cosmological implications,” Phys. Rev. D64(2001), 023508 [arXiv:hep-ph/0005123 [hep-ph]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  78. [78]

    WIMPs, FIMPs, and Inflaton phenomenology via reheating, CMB and ∆N ef f,

    M. R. Haque, D. Maity and R. Mondal, “WIMPs, FIMPs, and Inflaton phenomenology via reheating, CMB and ∆N ef f,” JHEP09, 012 (2023) [arXiv:2301.01641 [hep-ph]] [INSPIRE]

    work page arXiv 2023

  79. [79]

    Particle production and reheating in the inflationary universe

    I. G. Moss and C. M. Graham, “Particle production and reheating in the inflationary universe,” Phys. Rev. D78, 123526 (2008) [arXiv:0810.2039 [hep-ph]] [INSPIRE]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  80. [80]

    Curvature Perturbations From Stochastic Particle Production During Inflation,

    M. A. G. Garcia, M. A. Amin and D. Green, “Curvature Perturbations From Stochastic Particle Production During Inflation,” JCAP06(2020), 039 [arXiv:2001.09158 [astro-ph.CO]] [INSPIRE]

    work page arXiv 2020

Showing first 80 references.