A possible origin of the $\alpha$-vacuum as the initial state of the Universe

Dong-han Yeom; Kuan-Nan Lin; Pisin Chen; Wei-Chen Lin

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A possible origin of the $\alpha$-vacuum as the initial state of the Universe

Pisin Chen, Kuan-Nan Lin, Wei-Chen Lin, Dong-han Yeom

General Relativity and Quantum Cosmology · Submitted 23 Apr 2024

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim This therefore provides the $\alpha$-vacuum a geometrical origin.

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arXiv ID2404.15450 (version 1)

Pith ID74GI6LZS, Pith's permanent record of this paper and its review

CitationDong-han Yeom, Kuan-Nan Lin, Pisin Chen, Wei-Chen Lin. "A possible origin of the $\alpha$-vacuum as the initial state of the Universe." arXiv:2404.15450 (2024). https://pith.science/paper/74GI6LZS

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.63 · human participants 0.01 · controlled comparison 0.11 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.90 · mentions code or data availability 0.02.

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We investigate the cosmological observables using the Euclidean path integral approach. Specifically, we study both the no-boundary compact instantons scenario and the Euclidean wormholes scenario that can induce the creation of two universes from nothing. It is known that perturbations associated with the no-boundary scenario can only be consistent with the Bunch-Davies vacuum. Here we demonstrate that the Euclidean wormholes can allow for a de Sitter invariant vacuum, the so-called $\alpha$-vacuum state, where the Bunch-Davies vacuum is a special case. This therefore provides the $\alpha$-vacuum a geometrical origin. As an aside, we discuss a subtle phase issue when considering the power spectrum related to $\alpha$-vacuum in the closed universe framework.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We investigate the cosmological observables using the Euclidean path integral approach.	method 0.92	0.88	0.02	asserted 0.81
s1	Specifically, we study both the no-boundary compact instantons scenario and the Euclidean wormholes scenario that can induce the creation of two universes from nothing.	contribution 0.74	0.70	0.03	asserted 0.58
s2	It is known that perturbations associated with the no-boundary scenario can only be consistent with the Bunch-Davies vacuum.	background 0.99	0.05	0.03	asserted 0.96
s3	Here we demonstrate that the Euclidean wormholes can allow for a de Sitter invariant vacuum, the so-called $\alpha$-vacuum state, where the Bunch-Davies vacuum is a special case.	result 0.90	0.92	0.80	asserted 0.99
s4	This therefore provides the $\alpha$-vacuum a geometrical origin.	interpretation 0.99	0.78	0.67	asserted 0.91
s5	As an aside, we discuss a subtle phase issue when considering the power spectrum related to $\alpha$-vacuum in the closed universe framework.	contribution 0.57	0.63	0.02	unclear 0.58

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

We investigate the cosmological observables using the Euclidean path integral approach. Specifically, we study both the no-boundary compact instantons scenario and the Euclidean wormholes scenario that can induce the creation of two universes from nothing. It is known that perturbations associated with the no-boundary scenario can only be consistent with the Bunch-Davies vacuum. Here we demonstrate that the Euclidean wormholes can allow for a de Sitter invariant vacuum, the so-called $\alpha$-vacuum state, where the Bunch-Davies vacuum is a special case. This therefore provides the $\alpha$-vacuum a geometrical origin. As an aside, we discuss a subtle phase issue when considering the power spectrum related to $\alpha$-vacuum in the closed universe framework.

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3 arXiv papers cite this in 6 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 3 sentences without a confident label

Cites it as background 2 papers

This topic has been widely explored in the literature, with numerous works investigating scalar correlations with non-BD initial conditions [ref] .

New shape for cross-bispectra in Chern-Simons gravity · A short aside on the initial conditions of inflation · 1.00
However, several alternative choices for the initial state and for Bunch-Davis initial conditions $-$ have been already proposed [ref] .

Bipartite temporal Bell inequality for squeezed coherent state of inflationary perturbations · Conclusion · 0.80

What it cites · 33 sentences without a confident label

Uses the method or tool of 1 paper

In our numerical treatment, we set the Euclidean initial conditions as follows to make the equation of motion regular [ref] : [equation] where $δ_n$ is an arbitrary phase that can be mode-dependent.

Suppression of long-wavelength CMB spectrum from the no-boundary initial condition · Computations from instantons · 0.97

Uses data or values from 1 paper

For instance, the latest CMB anisotropy measurement from Planck [ref] shows a nearly scale-invariant scalar power spectrum with the non-measurements of the primordial non-Gaussianities and of the isocurvature perturbations.

Planck 2018 results. VI. Cosmological parameters · Introduction · 0.80

Compares with 3 papers

This is qualitatively consistent with the conventional suppression that occurs in a flat de Sitter universe with a mode-independent $α$-parameter [ref] .

Observing Trans-Planckian Signatures in the Cosmic Microwave Background · Agreement between analytic and numerical results · 0.97
This is qualitatively consistent with the conventional suppression that occurs in a flat de Sitter universe with a mode-independent $α$-parameter [ref] .

A note on inflation and transplanckian physics · Agreement between analytic and numerical results · 0.97
This is qualitatively consistent with the conventional suppression that occurs in a flat de Sitter universe with a mode-independent $α$-parameter [ref] .

A generic estimate of trans-Planckian modifications to the primordial power spectrum in inflation · Agreement between analytic and numerical results · 0.97

Cites as background 10 papers

Euclidean wormholes In Euclidean gravity, there are several models of Euclidean wormholes [ref] .

Why concave rather than convex inflaton potential? · Background solutions · 1.00
Euclidean wormholes In Euclidean gravity, there are several models of Euclidean wormholes [ref] .

Fuzzy Euclidean wormholes in de Sitter space · Background solutions · 1.00
This continuous class of vacua is known as the $α$-vacuum [ref] , where $α$ is a parameter that describes a specific vacuum and the Bunch-Davies vacuum is just a special case of the $α$-vacuum.

Conformal Vacua and Entropy in de Sitter Space · Introduction · 0.88

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