Stability investigations of de Sitter inflationary solutions in power-law extensions of the Starobinsky model

Abstract

In this paper, we would like to examine whether stable de Sitter inflationary solutions appear within power-law extensions of the Starobinsky model. In particular, we will address general constraints for the existence along with the stability of de Sitter inflationary solutions in a general case involving not only the Starobinsky $R^2$ term but also an additional power-law $R^n$ one. According to the obtained results, we will be able to identify which extension is more suitable for an early inflationary phase rather than a late-time cosmic acceleration phase. To be more specific, we will consider several values of $n$ to see whether the corresponding de Sitter inflationary solutions are stable or not.

arXiv comment40 pages, 20 figures. Final version with additional stability analysis using an effective potential method. Matches the published version. All conclusions remain unchanged. Comments are welcome

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