Inflation, the Hubble tension, and early dark energy: An alternative overview
William Giarè
Abstract
I review and discuss the possible implications for inflation resulting from considering new physics in light of the Hubble tension. My study is motivated by a simple argument that the constraints on inflationary parameters, most typically the spectral index <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>n</a:mi><a:mi>s</a:mi></a:msub></a:math>, depend to some extent on the cosmological framework. To avoid broadening the uncertainties resulting from marginalizing over additional parameters (typical in many alternative models), I first adopt the same alternative viewpoint of previous studies and analyze what happens if a physical theory can extra parameters to nonstandard values. Focusing on the dark energy equation of state <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>w</c:mi></c:math> and the effective number of relativistic species <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>N</e:mi><e:mi>eff</e:mi></e:msub></e:math>, I confirm that physical theories able to fix <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mi>w</g:mi><g:mo>≈</g:mo><g:mo>−</g:mo><g:mn>1.2</g:mn></g:mrow></g:math> or <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>N</i:mi><i:mi>eff</i:mi></i:msub><i:mo>≈</i:mo><i:mn>3.9</i:mn></i:math> produce values of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>H</k:mi><k:mn>0</k:mn></k:msub></k:math> from Cosmic Microwave Background and Baryon Acoustic Oscillations in line with the local distance ladder estimate. While in the former case I do not find any relevant implications for inflation, in the latter scenarios, I observe a shift toward <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>n</m:mi><m:mi>s</m:mi></m:msub><m:mo>≈</m:mo><m:mn>1</m:mn></m:math>. From a model-selection perspective, both cases are strongly disfavored compared to <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mrow><o:mi mathvariant="normal">Λ</o:mi></o:mrow></o:math> cold dark matter. However, models with <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mrow><r:msub><r:mrow><r:mi>N</r:mi></r:mrow><r:mrow><r:mi>eff</r:mi></r:mrow></r:msub><r:mo>≈</r:mo><r:mn>3.3</r:mn><r:mi>–</r:mi><r:mn>3.4</r:mn></r:mrow></r:math> could bring the <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:msub><t:mi>H</t:mi><t:mn>0</t:mn></t:msub></t:math> tension down to <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mo>∼</v:mo><v:mn>3</v:mn><v:mi>σ</v:mi></v:math> while being moderately disfavored. Yet, this is enough to change the constraints on inflation so that the most accredited models (e.g., Starobinsky inflation) would no longer be favored by data. I then focus on Early Dark Energy (EDE), arguing that an EDE fraction <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mrow><x:msub><x:mrow><x:mi>f</x:mi></x:mrow><x:mrow><x:mi>EDE</x:mi></x:mrow></x:msub><x:mo>∼</x:mo><x:mn>0.04</x:mn><x:mi>–</x:mi><x:mn>0.06</x:mn></x:mrow></x:math> (only able to mildly reduce the <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:msub><z:mi>H</z:mi><z:mn>0</z:mn></z:msub></z:math> tension down to <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:mo>∼</bb:mo><bb:mn>3</bb:mn><bb:mi>σ</bb:mi></bb:math>) could already require a similar change in perspective on inflation. In fact, performing a full joint analysis of EDE and Starobinsky inflation, I find that the two models can hardly coexist for <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:msub><db:mi>f</db:mi><db:mi>EDE</db:mi></db:msub><db:mo>≳</db:mo><db:mn>0.06</db:mn></db:math>. Published by the American Physical Society 2024