Rescaled Einstein-Hilbert gravity from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> gravity: Inflation, dark energy, and the swampland criteria

Abstract

We consider the scenario that the effective gravitational Lagrangian of a minimally coupled scalar field at large curvatures is described by a rescaled Einstein-Hilbert gravity, with the Ricci scalar being multiplied by a dimensionless parameter $\ensuremath{\alpha}$. Such Lagrangian densities might originate, for example, by a class of exponential models of $f(R)$ gravity, in the presence of a canonical scalar field, for which at early times the effective Lagrangian of the theory becomes that of a rescaled canonical scalar field with the Einstein-Hilbert term becoming $\ensuremath{\sim}\ensuremath{\alpha}R$, with $\ensuremath{\alpha}$ a dimensionless constant, and the resulting theory is an effective theory of a Jordan frame $f(R,\ensuremath{\phi})$ theory. This rescaled Einstein-Hilbert canonical scalar field theory at early times has some interesting features, since it alters the inflationary phenomenology of well-known scalar field models of inflation, but more importantly, in the context of this rescaled theory, the swampland criteria are easily satisfied, assuming that the scalar field is slowly rolling. We consider two models of inflation to exemplify our study, a fiber inflation model and a model that belongs to the general class of supergravity $\ensuremath{\alpha}$-attractor models. The inflationary phenomenology of the models is demonstrated to be viable, and for the same set of values of the free parameters of each model which ensure their inflationary viability, all the known swampland criteria are satisfied too, and we need to note that we assumed that the first swampland criterion is marginally satisfied by the scalar field, so $\ensuremath{\phi}\ensuremath{\sim}{M}_{p}$ during the inflationary era. Finally, we examine the late-time phenomenology of the fiber inflation potential in the presence of the full $f(R)$ gravity, and we demonstrate that the resulting model produces a viable dark energy era, which resembles the $\mathrm{\ensuremath{\Lambda}}$-cold-dark-mater model. Thus, in the modified gravity model we present, the Universe is described by a rescaled Einstein-Hilbert gravity at early times; hence, in some sense, the modified gravity effect is minimal primordially, and the scalar field controls mainly the dynamics with a rescaled Ricci scalar gravity. However, the effect of $f(R)$ gravity becomes stronger at late times, where it controls the dynamics, synergistically with the scalar field.

Topics & Concepts