$R^2$ Inflation Revisited and Dark Energy Corrections

Abstract

The vacuum R 2 model is known to generate a quasi-de Sitter evolution for inflation, using solely the slow-roll assumptions. Using standard reconstruction techniques, we demonstrate that the f (R) gravity which actually realizes the quasi-de Sitter evolution is not simply the R 2 model but a deformed R 2 model which contains extra terms in addition to the R 2 model. We analyze in detail the inflationary dynamics of the deformed R 2 model and we demonstrate that the predictions are quite close to the ones of the pure R 2 model, regardless the values of the free parameters. Basically the deformed R 2 model is also a single parameter inflationary model, exactly like the ordinary R 2 model. In contrast to the early-time era, where the deformed R 2 model is quite similar to the R 2 model, at late times, the phenomenological picture is different. The deformed R 2 model describes stronger gravity compared to the ordinary R 2 with an effectively smaller effective Planck mass. We propose the addition of an early dark energy term which does not affect at all the inflationary era, but takes over the control of the late-time dynamics at late times. We study in some detail the predicted dark energy era evolution, and we demonstrate that the dark energy corrected deformed R 2 model can describe a viable dark energy era, compatible with the Planck constraints on cosmological parameters. Furthermore the model is distinct from the Λ-Cold-Dark-Matter model, but shows a qualitatively similar behavior.

Testing scale-invariant inflation against cosmological data

“…One can attempt to define the functional form of f (R) that best accommodates inflationary observables consistent with data, via reconstruction techniques based on the measured spectral indices: the results of such an exercise clearly indicate a preference for a quadratic term in the Ricci scalar [177] (see also refs. [178][179][180][181][182][183][184][185][186][187]). The fundamental reason why the Starobinsky model and models close thereto perform extremely well is, in essence, scale-invariance.…”

Self-tuning inflation

“…Inflationary scenarios have fueled additional interest in f (R) theories, beginning with Starobinsky's seminal paper [5]. This model has remained very successful up to now, and a large number of its generalizations with minor modifications have been built [6][7][8][9][10][11][12]. Nevertheless, in the IR limit, the Starobinsky model implies that the cosmological constant must also be fine-tuned and there is no "natural" expectation for the unique coefficient in front of the R 2 term in the action to be large.…”

Self-tuning inflation

“…Inflationary scenarios have fueled additional interest in f (R) theories [5,6], beginning with Starobinsky's seminal paper [7]. This model has remained very successful up to now, and a large number of its generalizations with minor modifications have been built [8][9][10][11][12][13][14][15][16][17][18]. Nevertheless, in the IR limit, the Starobinsky model implies that the cosmological constant must also be fine-tuned and there is no "natural" expectation for the unique coefficient in front of the R 2 term in the action to be large.…”