<p>We give a brief review of the basic principles of inflationary theory and discuss the present status of the simplest inflationary models which can describe Planck/BICEP/Keck observational data by choice of a single model parameter. In particular, we discuss the Starobinsky model, Higgs inflation, and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3470_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-attractors, including the recently developed<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3470_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-attractor models with <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3470_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="63" /> </InlineMediaObject> <EquationSource Format="TEX">$SL(2,\mathbb {Z})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>L</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mi mathvariant="double-struck">Z</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> invariant potentials. We also describe inflationary models providing a good fit to the recent ACT data, as well as the polynomial chaotic inflation models with three parameters, which can account for any values of the three main CMB-related inflationary parameters <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3470_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">$A_{s}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mi>s</mi> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3470_Article_IEq5.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$n_{s}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>n</mi> <mi>s</mi> </msub> </math></EquationSource> </InlineEquation> and <i>r</i>.</p>

On the present status of inflationary cosmology

期刊论文
发表日期：

2025年9月26日

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Renata Kallosh,
Andrei Linde

摘要

We give a brief review of the basic principles of inflationary theory and discuss the present status of the simplest inflationary models which can describe Planck/BICEP/Keck observational data by choice of a single model parameter. In particular, we discuss the Starobinsky model, Higgs inflation, and $\alpha $ $α$ -attractors, including the recently developed $\alpha $ $α$ -attractor models with $SL(2,\mathbb {Z})$ $S L (2, Z)$ invariant potentials. We also describe inflationary models providing a good fit to the recent ACT data, as well as the polynomial chaotic inflation models with three parameters, which can account for any values of the three main CMB-related inflationary parameters $A_{s}$ $A_{s}$ , $n_{s}$ $n_{s}$ and r.