Independent connection in action during inflation

The Atacama Cosmology Telescope (ACT) has recently released new measurements and constraints on inflationary observables. In this paper, it is shown that a component of a dynamical affine connection, which is independent of the metric, can easily drive inflation in agreement with these observations. Such geometrical explanation of inflation is analyzed in detail here in the minimal model, including the predictions for the scalar spectral index <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>n</a:mi></a:mrow><a:mrow><a:mi>s</a:mi></a:mrow></a:msub></a:mrow></a:math> and its running <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msub><c:mrow><c:mi>α</c:mi></c:mrow><c:mrow><c:mi>s</c:mi></c:mrow></c:msub></c:mrow></c:math>, the amplitude of the scalar perturbations, and the tensor-to-scalar ratio <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mi>r</e:mi></e:mrow></e:math>. Furthermore, this minimal model is shown to provide an inflationary attractor: arbitrary initial values of the kinetic energy density are dynamically attracted down to negligible values compared to the potential energy density in homogeneous and isotropic metrics. Also, the role of the Higgs boson during and after inflation is briefly discussed.

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