Role of the curvaton after the last Planck dataset

The expected improvements in the precision of inflationary physics observables including the scalar 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> and the tensor-to-scalar ratio <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>r</c:mi></c:math> will reveal more than just the viability of a particular model of inflation. In the presence of a curvaton field <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>χ</e:mi></e:math>, supposedly dead models of inflation can be resurrected, as these observables are affected by curvaton perturbations. For currently successful models, improved constraints will enable us to constrain the properties of extra decaying scalar degrees of freedom produced during inflation. In this work, we demonstrate these diverse uses of a curvaton field with the most recent constraints on (<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>n</g:mi><g:mi>s</g:mi></g:msub><g:mo>,</g:mo><g:mi>r</g:mi></g:math>) and two exemplary inflation models, a Starobinsky-like model and a model of new inflation. The specific models used as examples can be derived in the context of supergravity. Our analysis invokes three free parameters: the curvaton mass <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>m</i:mi><i:mi>χ</i:mi></i:msub></i:math>, its decay rate <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi mathvariant="normal">Γ</k:mi><k:mi>χ</k:mi></k:msub></k:math>, and the reheating temperature <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msub><n:mi>T</n:mi><n:mrow><n:mi>RH</n:mi></n:mrow></n:msub></n:math> produced by inflaton decays. We systematically analyze possible postinflationary era scenarios of a curvaton field. By projecting the most recent cosmic microwave background (CMB) data on (<p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msub><p:mi>n</p:mi><p:mi>s</p:mi></p:msub><p:mo>,</p:mo><p:mi>r</p:mi></p:math>) into this parameter space, we can either set constraints on the curvaton parameters from successful models of inflation (so that the success is not spoiled) or determine the parameters that are able to save a model for which <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msub><r:mi>n</r:mi><r:mi>s</r:mi></r:msub></r:math> is predicted to be below the experimental data. We emphasize that the initial value of <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mo stretchy="false">⟨</t:mo><t:msup><t:mi>χ</t:mi><t:mn>2</t:mn></t:msup><t:mo stretchy="false">⟩</t:mo><t:mo>∝</t:mo><t:msup><t:mi>H</t:mi><t:mn>4</t:mn></t:msup><t:mo>/</t:mo><t:msubsup><t:mi>m</t:mi><t:mi>χ</t:mi><t:mn>2</t:mn></t:msubsup></t:math> produced during inflation is determined from a stochastic approach and thus not a free parameter in our analysis. We also investigate the production of local non-Gaussianity <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:msubsup><x:mi>f</x:mi><x:mrow><x:mi>NL</x:mi></x:mrow><x:mrow><x:mo stretchy="false">(</x:mo><x:mi>loc</x:mi><x:mo stretchy="false">)</x:mo></x:mrow></x:msubsup></x:math> and apply current CMB constraints to the parameter space. Intriguingly, we find that a large value of <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:msubsup><bb:mi>f</bb:mi><bb:mrow><bb:mi>NL</bb:mi></bb:mrow><bb:mrow><bb:mo stretchy="false">(</bb:mo><bb:mi>loc</bb:mi><bb:mo stretchy="false">)</bb:mo></bb:mrow></bb:msubsup></bb:math> of <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:mi mathvariant="script">O</fb:mi><fb:mo stretchy="false">(</fb:mo><fb:mn>1</fb:mn><fb:mo stretchy="false">)</fb:mo></fb:math> can be produced for both of the two representative inflation models.