Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T19:32:56.783197Z
Paper Citation Record · LEDGER
The Creation of Particles in an Expanding Universe
As of 13 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 6 inbound Pith citation observations for arXiv:2507.05372.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-02T21:30:42.605866Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-04T11:39:47.031071Z
Reference resolution
35 of 35 outbound references displayed
- verified exact0
- verified fuzzy25
- unresolved10
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation a8914143-c21b-47d6-a0ad-1d61b3e69cd0 · outbound
This paper cites This would lead to high energy divergence difficulties in the total creation rate, summed over all modes, ifaˆk(t)†a⃗k(t) were interpreted as the particle number operator.
The Creation of Particles in an Expanding Universe This would lead to high energy divergence difficulties in the total creation rate, summed over all modes, ifaˆk(t)†a⃗k(t) were interpreted as the particle number operator
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:57.358833Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 6e4d0e0b-900d-4df7-93ad-8b34438d9080 · outbound
This paper cites G(H) is of order H n.
The Creation of Particles in an Expanding Universe G(H) is of order H n
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:57.341679Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation c8324994-2f08-4f67-a074-080019ac8b2b · outbound
This paper cites in the limitH → 0 ), regardless of the relative magnitude of the expansion.
The Creation of Particles in an Expanding Universe in the limitH → 0 ), regardless of the relative magnitude of the expansion
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:57.322348Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 703922b4-6dfc-449c-a531-45fea60cdfe3 · outbound
This paper cites Chapter II).
The Creation of Particles in an Expanding Universe Chapter II)
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:57.305111Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a138d938-2c06-418e-a370-90662c7e73fc · outbound
This paper cites Therefore, we are justified in using the same symbolβc in each case.
The Creation of Particles in an Expanding Universe Therefore, we are justified in using the same symbolβc in each case
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:57.285696Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 890f76d3-a14d-4b8f-949f-bc22bdc32298 · outbound
This paper cites an unresolved cited work.
The Creation of Particles in an Expanding Universe Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:32:57.261376Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation ace90985-7a63-4ee4-8cc5-1d481e2c7904 · outbound
This paper cites an unresolved cited work.
The Creation of Particles in an Expanding Universe Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:32:57.243686Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation c861e3a3-98ef-48a7-ba32-815753592235 · outbound
This paper cites 1 ˙θ (t′) d dt′ n−1 S (t′) ˙θ (t′) [2j, t′]∗ # e−iθ(t′) , (F) or d dt βc = −(−i)n ˙θ(t).
The Creation of Particles in an Expanding Universe 1 ˙θ (t′) d dt′ n−1 S (t′) ˙θ (t′) [2j, t′]∗ # e−iθ(t′) , (F) or d dt βc = −(−i)n ˙θ(t)
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:57.225686Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation c1b9a038-f760-4029-951e-f1cc61358461 · outbound
This paper cites an unresolved cited work.
The Creation of Particles in an Expanding Universe Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:32:57.206737Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation ff7bfdbe-a83c-4854-a9a7-92504bfb8f7f · outbound
This paper cites an unresolved cited work.
The Creation of Particles in an Expanding Universe Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:32:57.178830Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 20dd4512-fc4a-4582-82be-c091a6ea1aee · outbound
This paper cites The proof is in part D.
The Creation of Particles in an Expanding Universe The proof is in part D
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:57.157126Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation e1cfb7df-e01a-4783-b3f5-ccda44f5dfac · outbound
This paper cites an unresolved cited work.
The Creation of Particles in an Expanding Universe Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:32:57.563022Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 60106453-d124-4e06-8ba1-355b09761c80 · outbound
This paper cites Thus, terms likeS(p, t)2 = O (H 2) and d dt S(p, t) = 104 O (H 2) are neglected.
The Creation of Particles in an Expanding Universe Thus, terms likeS(p, t)2 = O (H 2) and d dt S(p, t) = 104 O (H 2) are neglected
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:57.544786Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a478024a-d17d-4df1-b196-182f5e73a76d · outbound
This paper cites (68) The matrices β and γ5 are hermitian, and satisfy βγ 5 = −γ5β , β 2 = 1 , γ5 2 = 1 , and (69) σkβγ 5 = βγ 5σk , (k = 1, 2, 3) where σk = iβγ 5γk.
The Creation of Particles in an Expanding Universe (68) The matrices β and γ5 are hermitian, and satisfy βγ 5 = −γ5β , β 2 = 1 , γ5 2 = 1 , and (69) σkβγ 5 = βγ 5σk , (k = 1, 2, 3) where σk = iβγ 5γk
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:57.528242Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 892379c4-c4cb-4233-89a9-568a2b06e6aa · outbound
This paper cites (79) Equation (78) is an immediate consequence of eqs.
The Creation of Particles in an Expanding Universe (79) Equation (78) is an immediate consequence of eqs
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:57.511571Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation ee2906cb-5c2f-426c-9fef-825985b3fc53 · outbound
This paper cites an unresolved cited work.
The Creation of Particles in an Expanding Universe Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:32:57.493743Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 315ef5ea-5f2d-4dd3-976c-ac765630cc96 · outbound
This paper cites Thus we consider the D(a) (b) (p)c = D(a) (b) (p, t)c as functions of time.
The Creation of Particles in an Expanding Universe Thus we consider the D(a) (b) (p)c = D(a) (b) (p, t)c as functions of time
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:57.476119Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation c0820f6e-ad79-4778-b7c5-745f66e3b804 · outbound
This paper cites Using (81) and (65) we find that the expectation value of the observable number of fermions at timet in the mode ⃗ p, in the volume(LR(t))3 is ⟨Np(t)⟩ = D(1) (−1)(p, t)c 2.
The Creation of Particles in an Expanding Universe Using (81) and (65) we find that the expectation value of the observable number of fermions at timet in the mode ⃗ p, in the volume(LR(t))3 is ⟨Np(t)⟩ = D(1) (−1)(p, t)c 2
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:57.455956Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation f0b36d4d-0530-4641-a873-3d0b99c4cf5e · outbound
This paper cites (86), or from (83) and (57).
The Creation of Particles in an Expanding Universe (86), or from (83) and (57)
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:57.438278Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 1455b98b-98bc-42a9-8753-6c098f096932 · outbound
This paper cites We have ¯DtN ≤ L3 π2 Z ∞ 0 dpp2 ¯DtNp.
The Creation of Particles in an Expanding Universe We have ¯DtN ≤ L3 π2 Z ∞ 0 dpp2 ¯DtNp
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:57.419074Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d130da11-d3aa-4e92-8e7b-3474cbe033f5 · outbound
This paper cites According to (60) S(p, t) = 1 2 µ p˙R(t)/R(t) p2 R(t)2 + µ2.
The Creation of Particles in an Expanding Universe According to (60) S(p, t) = 1 2 µ p˙R(t)/R(t) p2 R(t)2 + µ2
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:57.402776Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 4c30c1eb-f627-4f46-9f44-c05d7661f6bc · outbound
This paper cites an unresolved cited work.
The Creation of Particles in an Expanding Universe Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:32:57.380812Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a4374dee-f7f3-4505-9fcc-45348c1d566e · outbound
This paper cites an unresolved cited work.
The Creation of Particles in an Expanding Universe Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:32:57.109022Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 2b4fcf29-855d-4d11-9c89-c342162df71b · outbound
This paper cites Bender and C.
The Creation of Particles in an Expanding Universe Bender and C
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:57.084422Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 44d8aa4e-ec16-4186-9329-e9a26c37c6c3 · outbound
This paper cites First let us review the case of special relativity.
The Creation of Particles in an Expanding Universe First let us review the case of special relativity
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:57.054350Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 78461e3a-8481-44a8-843a-8aed83289dbe · outbound
This paper cites vierbein field.
The Creation of Particles in an Expanding Universe vierbein field
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:57.034619Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 1c32e84a-47b0-45ab-b086-4c0070024c30 · outbound
This paper cites (14) In order to form observable numbers, the generalized Pauli adjoint must be introduced.
The Creation of Particles in an Expanding Universe (14) In order to form observable numbers, the generalized Pauli adjoint must be introduced
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:57.004612Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 7bab55bc-407b-4ab9-9732-d4df983d335c · outbound
This paper cites (9) at each point has been chosen such that theγ-matrices form a differentiable matrix-field.
The Creation of Particles in an Expanding Universe (9) at each point has been chosen such that theγ-matrices form a differentiable matrix-field
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:56.980052Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation b93c2eb1-0cfc-4c21-ba42-8e5d8e11d7f9 · outbound
This paper cites When S is coordinate-dependent then ∂lψ no longer has simple properties underS-transformation.
The Creation of Particles in an Expanding Universe When S is coordinate-dependent then ∂lψ no longer has simple properties underS-transformation
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:56.950661Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 1cf60886-3fe0-4666-83aa-5f018c632ab1 · outbound
This paper cites (9) served as the starting point of the entire development, in much the same way as thegij are fundamental to the mathematics involving only tensors.
The Creation of Particles in an Expanding Universe (9) served as the starting point of the entire development, in much the same way as thegij are fundamental to the mathematics involving only tensors
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:56.927140Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation c4bd2f01-2887-46db-8dd9-c729955069b6 · outbound
This paper cites an unresolved cited work.
The Creation of Particles in an Expanding Universe Unresolved cited work
Reference 33
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:32:56.905129Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 2119df0a-cd47-4509-8b5b-37e88aa59cc9 · outbound
This paper cites (45) In special relativity this reduces to eq.
The Creation of Particles in an Expanding Universe (45) In special relativity this reduces to eq
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:56.879657Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation ce146d61-3bb0-449a-adea-c85237cbaabe · outbound
This paper cites an unresolved cited work.
The Creation of Particles in an Expanding Universe Unresolved cited work
Reference 35
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:32:56.857279Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 4e226975-8713-41ea-bb95-c39461dd426b · outbound
This paper cites Hence Max (|βc(0, t)| |αc(0, t)|) < 1.
The Creation of Particles in an Expanding Universe Hence Max (|βc(0, t)| |αc(0, t)|) < 1
Reference 36
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:56.836529Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation ca7d3455-96d6-47e3-8f14-491dc39bf06a · outbound
This paper cites 79, 80, 81, and 86.
The Creation of Particles in an Expanding Universe 79, 80, 81, and 86
Reference 1956
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:32:57.131167Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Pith citing papers
Observation 147525ed-a1ea-4a25-bbb9-96fdf88fe92e · inbound
Gravitational particle production, the cosmological tensions and fast radio bursts cites this paper.
Gravitational particle production, the cosmological tensions and fast radio bursts The Creation of Particles in an Expanding Universe
Reference 28
- Resolution
- verified exact
- arxiv_id, observed 2026-05-18T20:51:50.673225Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 3c4247cc-ab26-4c33-8060-fbe137d7b8e7 · inbound
Spontaneous particle creation by oscillating compact stars cites this paper.
Spontaneous particle creation by oscillating compact stars The Creation of Particles in an Expanding Universe
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T21:30:42.605866Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 93beb916-5264-472f-9cc1-a4b8d880525b · inbound
The effects of non Bunch-Davies initial conditions on gravitationally produced relics cites this paper.
The effects of non Bunch-Davies initial conditions on gravitationally produced relics The Creation of Particles in an Expanding Universe
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T19:15:14.646392Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9fbc95fa-add4-4d88-bbfe-81abfbfa19ec · inbound
What spectators do during inflation cites this paper.
What spectators do during inflation The Creation of Particles in an Expanding Universe
Reference 41
- Resolution
- verified exact
- arxiv_id, observed 2026-05-13T16:52:59.920450Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 3c8e591b-85ec-44ac-971c-5b46b1c45173 · inbound
What spectators do during inflation cites this paper.
What spectators do during inflation The Creation of Particles in an Expanding Universe
Reference 41
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T16:52:32.586161Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 65253ff2-068f-48fb-ad39-d2b8acb6ebf4 · inbound
Scattered wave functions and worldline instantons for particle production in curved spacetime cites this paper.
Scattered wave functions and worldline instantons for particle production in curved spacetime The Creation of Particles in an Expanding Universe
Reference 6
- Resolution
- metadata mismatch
- arxiv_id, observed 2026-07-04T11:39:47.032766Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.