Numerical study of some generalizations of the Starobinsky inflationary model

Abstract In this work, a numerical study of three Starobinsky-type inflationary scenarios has been performed: the $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -Starobinsky inflationary model, the power-law Starobinsky inflationary model, and the power-law $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -Starobinsky inflationary model. For an appropriate choice of parameters, each scenario reproduces the standard Starobinsky limit. For each case, we derive the relevant slow-roll expressions in order to compute numerically the scalar and tensor power spectra over the parameter space in each case and evaluate the associated inflationary observables. Finally, we provide a comparative analysis in the $$(n_\textrm{S},A_\textrm{S})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>n</mml:mi> <mml:mtext>S</mml:mtext> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>A</mml:mi> <mml:mtext>S</mml:mtext> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and $$(r,n_\textrm{S})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>r</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>n</mml:mi> <mml:mtext>S</mml:mtext> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> parameter spaces, presented via contour plots. Our results indicate that, for certain choices of parameters, all the $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -Starobinsky model, the power-law $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -Starobinsky model, and the power-law alpha -Starobinsky models are favored by Planck 2018 observations.