Escher in the Sky

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• 作者：Renata Kallosh ; ^{kallosh@stanford.edu" class="auth_mail" title="E-mail the corresponding author} ; Andrei Linde ^{alinde@stanford.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Inflation ; Supergravity ; Geometry
• 刊名：Comptes Rendus Physique
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：16
• 期：10
• 页码：914-927
• 全文大小：2558 K

文摘

We give a brief review of the history of inflationary theory and then concentrate on the recently discovered set of inflationary models called cosmological α  -attractors. These models provide an excellent fit to the latest observational data. Their predictions class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1631070515001309&_mathId=si1.gif&_user=111111111&_pii=S1631070515001309&_rdoc=1&_issn=16310705&md5=891ae4ca5ce070c0eb8623c027ca33f5" title="Click to view the MathML source">nb>sb>≈1−2/Nclass="mathContainer hidden">class="mathCode"> and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1631070515001309&_mathId=si2.gif&_user=111111111&_pii=S1631070515001309&_rdoc=1&_issn=16310705&md5=77943b0b502a8557a69e8427e2b40c3b" title="Click to view the MathML source">r≈12α/N²class="mathContainer hidden">class="mathCode">$r\approx 12\alpha /N^2$ are very robust with respect to the modifications of the inflaton potential. An intriguing interpretation of α  -attractors is based on a geometric moduli space with a boundary: a Poincaré disk model of a hyperbolic geometry with the radius class="mathmlsrc">class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1631070515001309&_mathId=si3.gif&_user=111111111&_pii=S1631070515001309&_rdoc=1&_issn=16310705&md5=24af599f2493d42f8eb3b86764aea226">class="imgLazyJSB inlineImage" height="15" width="34" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S1631070515001309-si3.gif">class="mathContainer hidden">class="mathCode">$\sqrt{3\alpha }$, beautifully represented by the Escher's picture Circle Limit IV. In such models, the amplitude of the gravitational waves is proportional to the square of the radius of the Poincaré disk.