Selected Honorable Mention EssaysNo Access

A simple all-time model for the birth, big bang, and death of the universe

Department of Mathematics, University of California, Santa Cruz, California 95064, USA

https://doi.org/10.1142/S0218271817430143Cited by:3 (Source: Crossref)

Abstract

We model the standard $Λ$ $Λ$ CDM model of the universe by the spatially flat FLRW line element

ds2ΛCDM=−c2dt2+(8πGρm,0Λc2)2/3(sinh(12√3Λct))4/3dσ2Euclidds2ΛCDM=−c2dt2+(8πGρm,0Λc2)2/3(sinh(12√3Λct))4/3dσ2Euclid<math display="block" altimg="eq-00002.gif"><mrow><mi>d</mi><msubsup><mrow><mi>s</mi></mrow><mrow><mi mathvariant="normal">Λ</mi><mstyle><mtext class="textrm" mathvariant="normal">CDM</mtext></mstyle></mrow><mrow><mn>2</mn></mrow></msubsup><mo class="MathClass-rel">=</mo><mo stretchy="false" class="MathClass-bin">−</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><msup><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy="false" class="MathClass-bin">+</mo><msup><mrow><mfenced separators="" open="(" close=")"><mrow><mfrac><mrow><mn>8</mn><mi>π</mi><mi>G</mi><msub><mrow><mi>ρ</mi></mrow><mrow><mi>m</mi><mo class="MathClass-punc">,</mo><mn>0</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">Λ</mi><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mrow></mfenced></mrow><mrow><mn>2</mn><mo stretchy="false" class="MathClass-bin">/</mo><mn>3</mn></mrow></msup><msup><mrow><mfenced separators="" open="(" close=")"><mrow><mo class="qopname">sinh</mo><mfenced separators="" open="(" close=")"><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><msqrt><mrow><mn>3</mn><mi mathvariant="normal">Λ</mi></mrow></msqrt><mspace width=".17em" class="thinspace"></mspace><mi>c</mi><mi>t</mi></mrow></mfenced><mspace width="-.17em" class="negativethinspace"></mspace></mrow></mfenced></mrow><mrow><mn>4</mn><mo stretchy="false" class="MathClass-bin">/</mo><mn>3</mn></mrow></msup><mi>d</mi><msubsup><mrow><mi>σ</mi></mrow><mrow><mstyle><mtext class="textrm" mathvariant="normal"> Euclid</mtext></mstyle></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></math>

which we extend for all time

$t \in (- \infty, \infty)$ . Although there is a cosmological singularity at the big bang

$t = 0$ , since the spatial part of the metric collapses to zero, nevertheless, this line element is defined for all time

$t \in (- \infty, \infty)$ , is

$C^{\infty}$ for all

$t \neq 0$ , is

$C^{1}$ differentiable at

$t = 0$ , and is non-degenerate and solves Friedmann’s equation for all

$t \neq 0$ . Thus, we can use this extended line element to model the universe from its past-asymptotic initial state

$d S_{4}^{-}$ at

$t = - \infty$ , through the big bang at

$t = 0$ , and onward to its future-asymptotic final state

$d S_{4}^{+}$ at

$t = \infty$ . Since in this model the universe existed before the big bang, we conclude that (1) the universe was not created de novo at the big bang and (2) cosmological singularities such as black holes or the big bang itself need not be an end to spacetime. Our model shows that the universe was asymptotically created de novo out of nothing at

$t = - \infty$ from an unstable vacuum negative half de Sitter

$d s_{d S_{4}^{-}}^{2}$ initial state and then dies asymptotically at

$t = \infty$ as the stable positive half de Sitter

$d s_{d S_{4}^{+}}^{2}$ final state. Since the de Sitter states are vacuum matter states, our model shows that the universe was created from nothing at

$t = - \infty$ and dies at

$t = \infty$ to nothing.

This essay received an Honorable Mention in the 2017 Essay Competition of the Gravity Research Foundation.

Keywords:

PACS: 98.80.Bp, 98.80.Jk, 98.80.−k, 95.30.Sf, 04.20.−q

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