Quick Navigation

Overview Topics Abstract Importance Paper Tools References Reactions Discussion Publication Related

Topics

Open Quantum Systems Decoherence Quantum Simulation Quantum Foundations

Universe as Klein-Gordon Eigenstates

arXiv

Authors: Marco Matone

Year

2021

Paper ID

61015

Status

Preprint

Abstract Read

~2 min

Abstract Words

175

Citations

N/A

Abstract

We formulate Friedmann's equations as second-order linear differential equations. This is done using techniques related to the Schwarzian derivative that selects the β-times t_β:=int^t a^-2β, where a is the scale factor. In particular, it turns out that Friedmann's equations are equivalent to the eigenvalue problems $O_1/2 Ψ=fracΛ{12}Ψ\ , qquad O₁ a =fracΛ{3} a \ ,which is suggestive of a measurement problem.O_β(ρ,p)are space-independent Klein-Gordon operators, depending only on energy density and pressure, and related to the Klein-Gordon Hamilton-Jacobi equations. TheO_β's are also independent of the spatial curvature, labeled byk, and absorbed inΨ=sqrt a e^{frac{i}{2}sqrt{k}η} \ .The above pair of equations is the unique possible linear form of Friedmann's equations unlessk=0, in which case there are infinitely many pairs of linear equations. Such a uniqueness just selects the conformal timeη\equiv t_{1/2}among thet_β$'s, which is the key to absorb the curvature term. An immediate consequence of the linear form is that it reveals a new symmetry of Friedmann's equations in flat space.

Why This Paper Matters

This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
It adds a 2021 reference point for readers tracking recent quantum research.
We formulate Friedmann's equations as second-order linear differential equations.

Paper Tools

Become a member to use research tools

Sign in to open papers, visit source links, share, cite, compare, copy DOI links, request category corrections, and build your reading list.

Become a member Sign in

Show Paper arXiv Publisher Share Cite This Paper Copy URL Compare Copy DOI Add to Reading List Category Correction Request

References & Citation Signals

[1] DOI https://doi.org/arXiv:2110.01557 [2] arXiv https://arxiv.org/abs/2110.01557 [3] Publisher https://arxiv.org/abs/2110.01557

Local Citation Graph (Related-Paper Links)

External citation index: OpenAlex citation signal

Community Reactions

Quick sentiment from readers on this paper.

Score: 0

Likes: 0 Dislikes: 0

Discussion & Reviews (Moderated)

Average Rating: 0.0 / 5 (0 ratings)

No written reviews yet.