{"arxiv_id":"hep-ph/9704452","incoming":{"papers":668,"sentences":1296,"groups":[{"kind":"contests","label":"Contests it","papers":2,"sentences":2,"quotes":[{"arxiv_id":"0804.0869","title":"Triple unification of inflation, dark matter, and dark energy using a single field","url":"/paper/0804.0869","section":"Cosmological evolution","sentence":"This led Kofman, Linde, and Starobinsky [ref] to propose that the residual field could act as dark matter, but in fact detailed calculations [ref] show the relic abundance is far too high under standard assumptions.","intent_p":0.82,"contests_p":0.75},{"arxiv_id":"2202.11650","title":"Inflationary phenomenology of quadratic gravity in the Palatini formulation","url":"/paper/2202.11650","section":"Perturbative reheating","sentence":"For example, the equation should include fluctuations that are present in such systems with dissipation [ref] .","intent_p":0.64,"contests_p":0.72}]},{"kind":"extends","label":"Builds on it","papers":3,"sentences":3,"quotes":[{"arxiv_id":"0810.3913","title":"Constraints on generating the primordial curvature perturbation and non-Gaussianity from instant preheating","url":"/paper/0810.3913","section":"Instant preheating","sentence":"This formula can be extended to the case where the $ψ$ particles have a bare mass, the more general result is then [ref]","intent_p":1.0,"contests_p":null},{"arxiv_id":"1510.08553","title":"Preheating after Multifield Inflation with Nonminimal Couplings, I: Covariant Formalism and Attractor Behavior","url":"/paper/1510.08553","section":"Mode Expansion and Adiabatic Parameters","sentence":"(See also Refs. [ref] .) Within the single-field attractor, the coupled equations of motion in Eq. ([ref]) reduce to","intent_p":0.8,"contests_p":null},{"arxiv_id":"2209.01713","title":"Quantum interference in gravitational particle production","url":"/paper/2209.01713","section":"Introduction","sentence":"Although the quantum nature of the inflaton coherent-oscillation induced GPP has been known (e.g., see [ref] ), the present paper extends the previous ideas to graviton-mediated scattering, and to our knowledge is the first to articulate clearly and to compute analytically the quantum interference effects.","intent_p":0.84,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":70,"sentences":88,"quotes":[{"arxiv_id":"2112.11536","title":"Quintessential inflation and nonlinear effects of the tachyonic trap mechanism","url":"/paper/2112.11536","section":"The Strongly Non-Linear Regime","sentence":"The final particle number density, at large $$ values, can be computed using the equation [ref] [equation] Substituting again $ω_k_*^2(t)≃ω_k=0^2(t)$ in the above expression we can factor out $ω_k$, and write [equation]","intent_p":0.93,"contests_p":null},{"arxiv_id":"2210.16983","title":"Cosmology in theories with spontaneous scalarization of neutron stars","url":"/paper/2210.16983","section":"Introduction","sentence":"However, we will show that implementing the backreaction under the Hartree approximation [ref] leads to $ϕ_max$ significantly smaller than $10^-11$.","intent_p":0.96,"contests_p":null},{"arxiv_id":"1004.3551","title":"A Terminal Velocity on the Landscape: Particle Production near Extra Species Loci in Higher Dimensions","url":"/paper/1004.3551","section":"Particle Production near ESPs and Computation of the Terminal Velocity","sentence":"Ignoring backreaction onto the trajectory while $ϕ⃗$ is close to the ESP, we can compute the number density of $χ$ particles with wave-number $k$ after the encounter, $t>t_$, to [ref] [equation] where we incorporated the subsequent dilution for $t>t_$ due to the expansion of the universe.","intent_p":0.85,"contests_p":null},{"arxiv_id":"2507.13156","title":"Preheated inflation","url":"/paper/2507.13156","section":"Resonant particle production during inflation","sentence":"We saw in the previous section that the theory of Mathieu equations [ref] can be approximately applied to Eq. [ref], so that, from Floquet's theorem, the solution to this equation can be written approximately as the product of a periodic function $P_k(z)$ by an exponential $e^μ_k(z) z$, which we can approximate as $X_k(z) = P_k(z) e^μ_k(z) z ≃(2 ω_k^0)^-1/2 e^±i ω_k γ/2H z e^μ_k(z) z$, where the normalization is chosen so as to ensure a vanishing occupation number for each $k$ mode before it entered the resonance band, with $ω_k^0 ∼2H/γ$ denoting the corresponding frequency.","intent_p":0.89,"contests_p":null},{"arxiv_id":"2311.14273","title":"Gravitational Dark Matter from Minimal Preheating","url":"/paper/2311.14273","section":"Lattice treatment","sentence":"In terms of publicly available lattice code CosmoLattice [ref] we solve eq.([ref]) with the initial conditions of positive-frequency Bunch-Davies vacuum: [equation] The lattice calculation provides us the PDF of $δϕ$ via occupation number $n_k$ [ref] [equation] Using eq.([ref]) one finds the number density and energy density of the fluctuations [equation]","intent_p":1.0,"contests_p":null}]},{"kind":"data_used","label":"Uses its data or values","papers":3,"sentences":3,"quotes":[{"arxiv_id":"1506.01469","title":"Constraints on variations in inflaton decay rate from modulated preheating","url":"/paper/1506.01469","section":"Dynamics of fields","sentence":"Typical value of $⟨χ^2⟩$ in any Hubble patch is of the order of $10^-14$ at the time of the start of preheating [ref] [ During inflation $χ$ field does not get any super-horizon perturbation.","intent_p":0.96,"contests_p":null},{"arxiv_id":"0904.2778","title":"On the Suppression of Parametric Resonance and the Viability of Tachyonic Preheating after Multi-Field Inflation","url":"/paper/0904.2778","section":"Implementation of LatticeEasy","sentence":"The total potential energy is equally distributed among the $𝒩$ fields and sums up to $m^2 φ_0^2/2$, where $φ_0 = 0.193$ [ref] , in line with single-field models.","intent_p":0.84,"contests_p":null},{"arxiv_id":"1703.07642","title":"Symmetric and Asymmetric Reheating","url":"/paper/1703.07642","section":"Rescattering and other effects","sentence":"Using expressions for $Φ(t_r)$ from [ref] , immediately after preheating ends $m_χ_i∼√(g_i) ×10^15$.","intent_p":0.91,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":20,"sentences":25,"quotes":[{"arxiv_id":"2203.13286","title":"Preheating in Palatini Higgs inflation on the lattice","url":"/paper/2203.13286","section":"Lattice results","sentence":"Furthermore, the relative increase resulting from each zero-crossing is consistent with that obtained using a Bogoliubov transformation [ref] .","intent_p":0.97,"contests_p":null},{"arxiv_id":"2505.03160","title":"Particle decay as asymptotic narrow parametric resonance","url":"/paper/2505.03160","section":"Introduction","sentence":"Following this approach, the growth rate was estimated in Ref. [ref] to be $μ̃=qm_aπ/4$, which differs from $μ̃=q m_a/2$ predicted by NPR [ref] .","intent_p":0.88,"contests_p":null},{"arxiv_id":"0807.0382","title":"Parametric Decay of the Curvaton","url":"/paper/0807.0382","section":"The parametric resonance","sentence":"This however leads only to minor differences as compared to the standard case [ref] as we will discuss below.","intent_p":0.8,"contests_p":null},{"arxiv_id":"2310.16876","title":"Effective Action Approach for Preheating","url":"/paper/2310.16876","section":"Parametric Resonance","sentence":"We have checked that the narrow resonance using the effective action method gives an inflaton background decay rate with the Bose enhancement, consistent with the narrow resonance study in [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1608.08848","title":"Postinflationary vacuum instability and Higgs-inflaton couplings","url":"/paper/1608.08848","section":"Duration of the Resonance","sentence":"[ref] differs from ours by a factor of $1/4$. ] In our parameter range, we find that $δ≃0.1$ gives a good approximation for most cases.","intent_p":0.95,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":11,"sentences":11,"quotes":[{"arxiv_id":"2602.04285","title":"Parametric Resonance and Backreaction Effects in Magnetogenesis from Ultralight Dark Matter","url":"/paper/2602.04285","section":"Stability of the Narrow Band Resonance","sentence":"From work in the context of inflationary reheating [ref] we know that the damping of the oscillations of $ϕ$ due to the expansion of space do not destroy the resonance.","intent_p":0.98,"contests_p":null},{"arxiv_id":"2310.16876","title":"Effective Action Approach for Preheating","url":"/paper/2310.16876","section":"One-loop effective action","sentence":"Since the time duration of preheating is small compared to the Hubble time scale, these assumptions are valid and self-consistent during the preheating process [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"2104.03977","title":"Small Field Polynomial Inflation: Reheating, Radiative Stability and Lower Bound","url":"/paper/2104.03977","section":"Radiative Corrections and Stability","sentence":"Preheating with such small coupling is not efficient [ref] , i.e. reheating has to proceed via perturbative inflaton decay as we analyzed in Sec. [ref].","intent_p":0.98,"contests_p":null},{"arxiv_id":"2210.08407","title":"Heating up Peccei-Quinn scale","url":"/paper/2210.08407","section":"Parametric resonance","sentence":"We observe that the correction [ref] does not exceed other terms in Eq. [ref], i.e., [equation] This means that the effect of the axion field on the frequency of radial field oscillations can be negligible well until the time, when the axion field fluctuation reaches the maximum value, cf. Ref. [ref] .","intent_p":0.97,"contests_p":null},{"arxiv_id":"2011.02489","title":"Gravitational origin of dark matter and Majorana neutrino mass with non-minimal quartic inflation","url":"/paper/2011.02489","section":"Inflation","sentence":"But as we know the maximum particle production in perturbative decay mode dominantly takes place near the minimum of the inflaton potential [ref] where $Ω(S)^2→1$, we can safely use the bare masses of the inflaton and the other fields as originally introduced in the Lagrangian.","intent_p":0.97,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":343,"sentences":430,"quotes":[{"arxiv_id":"1105.4286","title":"Preheating a bouncing universe","url":"/paper/1105.4286","section":"Broad Resonance with Weak Coupling","sentence":"Studies of reheating in inflationary cosmology [ref] have taught us that in a dynamical space-time only the broad resonance regime with $q>1$ can lead to a significant enhancement of the generation of the $χ$ particles and of the corresponding fluctuations on super-Hubble scales.","intent_p":0.84,"contests_p":null},{"arxiv_id":"0809.3455","title":"Preheating after Multi-field Inflation","url":"/paper/0809.3455","section":"Introduction","sentence":"Particle production can occur whenever the effective mass $m_eff$ of $χ$ becomes light [ref] , given that the coupling constant is chosen appropriately.","intent_p":0.86,"contests_p":null},{"arxiv_id":"0812.4624","title":"Preheating in the Standard Model with the Higgs-Inflaton coupled to gravity","url":"/paper/0812.4624","section":"Reheating in the Standard Model of particle physics","sentence":"Given the shape of the potential ([ref]), very different (p)reheating mechanisms could in principle take place, from a tachyonic production in the region between the end of inflation and the inflection point [ref] , an instant preheating mechanism [ref] and a parametric resonance effect around the minimum of the potential [ref] .","intent_p":0.8,"contests_p":null},{"arxiv_id":"2202.12140","title":"Studying Aspects of the Early Universe with Primordial Black Holes","url":"/paper/2202.12140","section":"The Thermal History of the Universe","sentence":"This inflationary period is supposed to be driven by one (inflaton field) or more scalar fields which at the end of inflation decay to relativistic particles which thermalise by reaching a common temperature, quoted as the reheating temperature [For more details on reheating see [ref] ].[After inflation, the inflaton or/and the other scalar fields oscillates at the bottom of his/their potential, a fact which sources a parametric instability in the equation of motion of the metric perturbations, that are enhanced on small scales.","intent_p":0.96,"contests_p":null},{"arxiv_id":"2102.08394","title":"Challenging the Stability of Light Millicharged Dark Matter","url":"/paper/2102.08394","section":"Including the expansion of the Universe","sentence":"For a detailed discussion of the phenomenon of a stochastic resonance in an expanding Universe, we refer the reader to [ref] .","intent_p":0.97,"contests_p":null}]}],"unlabelled_sentences":734},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":{"arxiv_id":"hep-ph/9704452","kind":"model","paper_version":2,"prompt_version":"held-up-v3.5","generated_at":"2026-10-27T10:13:01+00:00","loaded_at":"2026-10-28T01:01:42.669327+00:00","evidence":"substantial","account":[],"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":12,"entries":[{"p":1.0,"quote":null,"citing":[{"self":false,"year":2018,"title":"Despicable Dark Relics: generated by gravity with unconstrained masses","arxiv_id":"1808.08236"}],"verified":true,"paraphrase":"Solved its equation numerically using the leading order adiabatic expansion with modes expressed as this paper's Ansatz."},{"p":1.0,"quote":{"text":"In order to find $a^3 n_k$ we will adopt the parametrization of Ref. [ref] ,","citing":"2404.06530","section":"CGPP for spin-0 particles"},"citing":[{"self":false,"year":2024,"title":"On the Role of Cosmological Gravitational Particle Production in Baryogenesis","arxiv_id":"2404.06530"}],"verified":true,"paraphrase":"Adopted this paper's parametrization to find the quantity."},{"p":1.0,"quote":null,"citing":[{"self":false,"year":2020,"title":"Analytic study of dark photon and gravitational wave production from axion","arxiv_id":"2007.08148"}],"verified":true,"paraphrase":"Used this paper's method of successive scattering matrices from preheating scenarios to find an analytic expression for the number of dark photons."},{"p":0.98,"quote":{"text":"Returning to our discussion, in order to compute $⟨χ^2 ⟩$, we write the solution of equation [ref] in terms of Bogoliubov coefficients $α_k = α_k(t)$ and $β_k = β_k(t)$ [ref] , yielding","citing":"2507.13156","section":"Background dynamics"},"citing":[{"self":false,"year":2025,"title":"Preheated inflation","arxiv_id":"2507.13156"}],"verified":true,"paraphrase":"Wrote the solution of this paper's equation in terms of Bogoliubov coefficients to compute the field expectation value."},{"p":0.98,"quote":null,"citing":[{"self":false,"year":2021,"title":"Hidden Photon and Axion Dark Matter from Symmetry Breaking","arxiv_id":"2105.14549"}],"verified":true,"paraphrase":"Following this paper, wrote down the equation of motion of the field."},{"p":0.98,"quote":null,"citing":[{"self":false,"year":2014,"title":"Gravitational-Wave Mediated Preheating","arxiv_id":"1405.4288"}],"verified":true,"paraphrase":"Following this paper, gave the occupation number in a given mode function."},{"p":0.98,"quote":null,"citing":[{"self":false,"year":2019,"title":"The running curvaton","arxiv_id":"1911.10542"}],"verified":true,"paraphrase":"Following this paper's standard procedure, obtained the equation of motion of the curvaton field."},{"p":0.98,"quote":null,"citing":[{"self":false,"year":2023,"title":"Shrinking the Warm Little Inflaton","arxiv_id":"2308.00564"}],"verified":true,"paraphrase":"Computed the occupation number of each comoving momentum mode as given by this paper to validate its analytical estimate."},{"p":0.98,"quote":null,"citing":[{"self":false,"year":2014,"title":"Irruption of massive particle species during inflation","arxiv_id":"1409.1584"}],"verified":true,"paraphrase":"Based its appendix on ideas and methods found in Section VII B of this paper."},{"p":0.94,"quote":null,"citing":[{"self":false,"year":2008,"title":"Preheating in the Standard Model with the Higgs-Inflaton coupled to gravity","arxiv_id":"0812.4624"}],"verified":true,"paraphrase":"Following this paper, wrote an expression accounting for unknown accumulated phases of the Bogoliubov coefficients."},{"p":0.89,"quote":null,"citing":[{"self":false,"year":2018,"title":"Moduli Oscillation Induced by Reheating","arxiv_id":"1811.05002"}],"verified":true,"paraphrase":"Presented the formulation of particle production by following this paper."}],"papers_all":76,"self_papers":1,"self_entries":[{"p":0.99,"quote":null,"citing":[{"self":true,"year":2009,"title":"Cosmological Fluctuations from Infra-Red Cascading During Inflation","arxiv_id":"0902.0615"}],"verified":true,"paraphrase":"Used this paper's approximation to solve the equation analytically and obtain the occupation number of created particles."}]}],"counts":{"by_kind":{"extends":3,"contests":2,"data_used":4,"comparison":23,"method_or_tool":76,"supports_this_paper":13},"dropped":{"relied_on":0,"unknown_ids":0,"account_lines":0,"contest_vetoed":0,"below_threshold":0,"contest_drawback":0,"contest_without_basis":0,"contest_not_one_sentence":0,"contest_on_group_citation":0},"papers_read":40,"self_papers":7,"citing_papers":755,"sentences_read":40,"citing_sentences":1465,"unambiguous_read":40,"typed_independent":110,"independent_papers":748,"by_kind_independent":{"extends":3,"contests":2,"data_used":4,"comparison":23,"method_or_tool":74,"supports_this_paper":13}},"input_sha256":"583b014cd0ad2c41c27075cfa6f1739b6c9550885c5f020421523be2f64c73bd","method":"For a paper with five or more citing arXiv papers, Pith selected up to 40 citing sentences its citation classifier typed, read those whose citation markers point at this paper alone, and wrote one paraphrase for each later paper in each group, each resting on one sentence. A later paper is listed under a label only when the classifier gives one of its sentences that label at intent probability 0.8 or more (0.95 for support), Pith's reading of the sentence finds that the citing paper itself did it, and a second check of the paraphrase against the sentence passes. The section lists uses only: building on the paper, using its method, tool, data or values, comparing with it and citing it as support. It does not list criticism or disagreement, so their absence says nothing about how the paper has been received. Code counted the papers, wrote the summary from the listed entries, set the evidence level and linked each entry to its citing paper. Quotes are copied from the citing sentence and shown only when the citing paper's licence is CC BY, CC BY-SA or CC0; otherwise the paraphrase is shown. Papers that share an author with this one are listed apart. A paper with fewer citing papers gets a line counted by code, which names uses only: a later paper whose only label is a contest is counted as not described.","line":null,"summary":"11 later papers by other authors are listed below: 11 used its method or tool. 1 more paper by the same authors is listed: 1 used its method or tool."},"_links":{"html":"https://pith.science/paper/hep-ph/9704452"}}