Abstract
We present a unified evolution of the universe from very early times until the present epoch by including both the leading local correction R^2 and the leading non-local term Rfrac{1}{square ^2}R to the classical gravitational action. We find that the inflationary phase driven by R^2 term gracefully exits in a transitory regime characterized by coherent oscillations of the Hubble parameter. The universe then naturally enters into a radiation dominated epoch followed by a matter dominated era. At sufficiently late times after radiation–matter equality, the non-local term starts to dominate inducing an accelerated expansion of the universe at the present epoch. We further exhibit the fact that both the leading local and non-local terms can be obtained within the covariant effective field theory of gravity. This scenario thus provides a unified picture of inflation and dark energy in a single framework by means of a purely gravitational action without the usual need of a scalar field.
Highlights
In addition to scalar fields, an inflationary epoch in the early universe can be driven by higher order curvature corrections to the Einstein– Hilbert (EH) action, notably by a R2 term – a scenario first proposed by Starobinsky [13] and further discussed in [14–16]
We find that the inflationary phase driven by R2 term gracefully exits in a transitory regime characterized by coherent oscillations of the Hubble parameter
In addition to scalar fields, an inflationary epoch in the early universe can be driven by higher order curvature corrections to the EH action, notably by a R2 term – a scenario first proposed by Starobinsky [13] and further discussed in [14–16]
Summary
In addition to scalar fields, an inflationary epoch in the early universe can be driven by higher order curvature corrections to the EH action, notably by a R2 term – a scenario first proposed by Starobinsky [13] and further discussed in [14–16]. In the covariant EFT of gravity, we found that a R2 term naturally arises as a leading local correction to the EH action and becomes responsible for driving inflation at early times without the need of additional matter fields. The non-local term becomes dominant and leads to a dark energy dominated universe with equation of state w ≤ −1 This setup provides a unified picture of our universe from earliest epochs until today thereby unifying both inflation and dark energy in a single framework by means of purely gravitational corrections to the EH action. Later we will show that these corrections are naturally present in the covariant EFT of gravity
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