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Dark Radiation and the Hagedorn Phase
High Energy Physics - Theory · Submitted 6 Aug 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We point out that if the sector associated with the Standard Model degrees of freedom entered an open string Hagedorn phase in the early universe while the dark radiation sector was not part of this plasma, then this can lead to low values of the observable $\Delta N_{\text{eff}}$ (number of additional neutrinolike species) from the dark radiation.
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The abstract, sentence by sentence
We point out that if the sector associated with the Standard Model degrees of freedom entered an open string Hagedorn phase in the early universe while the dark radiation sector was not part of this plasma, then this can lead to low values of the observable $\Delta N_{\text{eff}}$ (number of additional neutrinolike species) from the dark radiation. For explicit analysis, we focus on warped string compactifications with the Standard Model degrees of freedom at the bottom of a warped throat. If the Hubble scale during inflation is above the warped string scale associated with the throat, then the Standard Model sector will enter the Hagedorn phase. In this scenario, bulk axions are no longer dangerous from the point of view of dark radiation. While this article focuses on warped compactifications, the basic idea can be relevant to any scenario where the early universe entered a Hagedorn phase.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We point out that if the sector associated with the Standard Model degrees of freedom entered an open string Hagedorn phase in the early universe while the dark radiation sector was not part of this plasma, then this can lead to low values of the observable $\Delta N_{\text{eff}}$ (number of additional neutrinolike species) from the dark radiation. | contribution 0.48 | 0.64 | 0.85 | hedged possibility 0.95 |
| s1 | For explicit analysis, we focus on warped string compactifications with the Standard Model degrees of freedom at the bottom of a warped throat. | method 0.84 | 0.68 | 0.03 | asserted 0.82 |
| s2 | If the Hubble scale during inflation is above the warped string scale associated with the throat, then the Standard Model sector will enter the Hagedorn phase. | result 0.61 | 0.34 | 0.07 | asserted 0.95 |
| s3 | In this scenario, bulk axions are no longer dangerous from the point of view of dark radiation. | interpretation 0.70 | 0.59 | 0.27 | asserted 0.99 |
| s4 | While this article focuses on warped compactifications, the basic idea can be relevant to any scenario where the early universe entered a Hagedorn phase. | limitation 0.47 | 0.23 | 0.06 | hedged possibility 0.92 |
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The paper
Original abstract
We point out that if the sector associated with the Standard Model degrees of freedom entered an open string Hagedorn phase in the early universe while the dark radiation sector was not part of this plasma, then this can lead to low values of the observable $\Delta N_{\text{eff}}$ (number of additional neutrinolike species) from the dark radiation. For explicit analysis, we focus on warped string compactifications with the Standard Model degrees of freedom at the bottom of a warped throat. If the Hubble scale during inflation is above the warped string scale associated with the throat, then the Standard Model sector will enter the Hagedorn phase. In this scenario, bulk axions are no longer dangerous from the point of view of dark radiation. While this article focuses on warped compactifications, the basic idea can be relevant to any scenario where the early universe entered a Hagedorn phase.
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How the literature uses it
6 arXiv papers cite this in 18 sentences
Papers citing it · 16 sentences without a confident label
Cites it as background 2 papers
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Moreover, there has been a lot of recent progress in understanding Hagedorn phase and it's subsequent gravitational wave production [ref] .
Fire at the Tip of the Throat: Hagedorn Phase after brane-antibrane inflation? · Introduction · 0.92
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Introduction.– Many scenarios of string [ref] or supersymmetric theories [ref] , (see, e.g., [ref] for discussions in light of current data or in the context of axions [ref] ) predict relatively low temperatures for the final reheating before the start of standard cosmology.
High Energy Sphalerons for Baryogenesis at Low Temperatures · Introduction · 0.91
What it cites · 29 sentences without a confident label
Builds on 1 paper
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While the original string gas cosmology exclusively discusses closed string degrees of freedom, there is a natural extension involving branes [ref] ; since a dilute gas of D-branes converts closed strings to open strings efficiently, it is reasonable to expect that the energy density in a brane-supported SM would dominate over closed string dark radiation in a variation of the mechanism described here.
Brane Gases in the Early Universe · Conclusion and Discussions · 0.83
Uses data or values from 2 papers
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The latest results from the Planck collaboration [ref] give $< 0.3$, and big bang nucleosynthesis studies give similar constraints [ref] .
Big Bang Nucleosynthesis: 2015 · Introduction · 0.95
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The latest results from the Planck collaboration [ref] give $< 0.3$, and big bang nucleosynthesis studies give similar constraints [ref] .
Planck 2018 results. I. Overview and the cosmological legacy of Planck · Introduction · 0.95
Cites as support 1 paper
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It is also important to note that the energy density of the open strings is much greater than that in the closed strings in the Hagedorn phase [ref] .
Strings and D-Branes at High Temperature · The Hagedorn Phase of Open Strings · 0.97
Cites as background 8 papers
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Here, the SM is supported on branes localized at the tip of a warped throat (or other highly warped region), and the warp factor provides a large hierarchy through the Randall-Sundrum mechanism [ref] .
A Large Mass Hierarchy from a Small Extra Dimension · Introduction · 0.84
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Our analysis will be in the context of warped string compactifications [ref] , specifically in the setting of [ref] , although the basic features of the arguments could well be relevant for cosmologies where the early universe went through a Hagedorn phase.
Hierarchies from Fluxes in String Compactifications · Introduction · 0.94
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Generically, one also expects a multitude of axions with a wide range of masses and decay constants [ref] (see e.g [ref] for explicit statistical analysis).
On String Theory Expectations for Photon Couplings to Axion-Like Particles · Introduction · 0.85
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