A simple $$F(\mathcal{R},\phi )$$ deformation of Starobinsky inflationary model
Dhimiter D. Canko, Ioannis D. Gialamas, George P. Kodaxis
Abstract
Abstract We study a model including a real scalar field $$\phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ϕ</mml:mi></mml:math> non-minimally coupled to $$F(\mathcal{R})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> gravity, which is conformally equivalent to an Einstein–Hilbert theory, involving two real scalar fields. We consider three special cases of the potential of the field $$\phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ϕ</mml:mi></mml:math> in the $$F(\mathcal{R})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> -frame: a vanishing potential, a mass term and a Higgs potential. All these lead to non-trivial two-field potentials in the Einstein-frame which in particular directions resemble the well-known Starobinsky model. We find, that all these cases can yield viable inflationary models in complete agreement with current observational data.