Abstract
We study two homogeneous supersymmetric extensions for the f(R) modified gravity model of Starobinsky with the FLRW metric. The actions are defined in terms of a superfield R that contains the FLRW scalar curvature. One model has N = 1 local supersymmetry, and its bosonic sector is the Starobinsky action; the other action has N = 2, its bosonic sector contains, in additional to Starobinsky, a massive scalar field without self-interaction. As expected, the bosonic sectors of these models are consistent with cosmic inflation, as we show by solving numerically the classical dynamics. Inflation is driven by the R2 term during the large curvature regime. In the N = 2 case, the additional scalar field remains in a low energy state during inflation. Further, by means of an additional superfield, we write equivalent tensor-scalar-like actions from which we can give the Hamiltonian formulation.
Highlights
The model of Starobinsky is formulated as a string-inspired effective action, with higherorder curvature terms arising from corrections due to quantized conformally covariant matter fields [1,2]. of the model, withThe relevant action for FLRW cosmology only quadratic scalar curvature [3], LS =√is given −g(R by the + α 6R2 simplest )
We present numerical solutions to the pure bosonic equations of motion, which exhibit inflation driven by the quadratic curvature term, whereas the scalar field is pushed to the minimum energy state
In order to do it, we derive the Ostrogradsky– Hamiltonian formulation, and show that it is related through canonical transformations to two well-known scalar–tensor formulations: one of the BF type, with the scalar playing the role of the scalar curvature, and the other the standard Hamiltonian obtained by means of a Weyl transformation
Summary
The model of Starobinsky is formulated as a string-inspired effective action, with higherorder curvature terms arising from corrections due to quantized conformally covariant matter fields [1,2]. of the model, with. We construct supersymmetric generalizations for the FLRW model of Starobinsky in its modified gravity form, using the ‘new’ superspace formulation [14,42] for homogeneous supergravity [43], i.e., depending only on time. In order to substantiate the following sections, we discuss the Ostrogradsky formulation, and show the canonical transformations that relate its Hamiltonian to the two Hamiltonians of the scalar–tensor formulations usually related to the Starobinsky model One of these scalar– tensor formulations is the one in standard form, which is manifestly stable, and has a Universe 2021, 7, 449 large-field inflationary potential. In higher-derivative models it becomes a dynamical field on its own In this case, the curvature superfield is of even parity and the action can, in principle, be generalized to the superspace of 4D supergravity. In Appendix A, we summarize the basic results about the superspace formalism following references [14,42,43], and in Appendix B, we provide some lengthy equations
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