Singularity resolution and inflation from an infinite tower of regularized curvature corrections

Abstract

We explore four-dimensional scalar-tensor theories obtained from well-defined dimensional regularizations of Lovelock invariants. When an infinite tower of corrections is considered, these theories allow for cosmological models in which the Big Bang singularity is replaced by an inflationary phase in the early-universe, and they also admit a specific class of regular black hole solutions.

Figures (2)

• Figure 1: (Left) Time evolution of $a$ and $H^2$ (in units $\ell=1$) for the modified Friedmann equation in Eq. \ref{['eq:FriedmannExample']}, and in GR, assuming a radiation dominated universe with initial value for the energy density $\rho = 3/(32\pi)$ and scale factor $a=1$ at time $t=1$. In GR, a Big Bang singularity occurs at $t=0$, whereas when an infinite tower of corrections is considered, the singularity is replaced by an inflationary phase. (Right) Slow-roll parameter $-\dot H/H^2$ as a function of the number of e-folds $N$ (defined such that $N=0$ at the end of inflation, i.e., evolution proceeds from right to left), for the theories with couplings given by $c_n = (1-(-1)^n)/(2n)$, and $c_n=1/n!$. The curves are shown up to $N=50$, but they continue all the way to $N\to \infty$.
• Figure 2: Carter-Penrose diagram of the black hole solution in Eq. \ref{['eq:BHsol1']}. Region $\rm I$ corresponds to an asymptotically AdS region; Region $\rm II$ corresponds to the interior of the black hole; Region $\rm III$ corresponds to an asymptotically AdS region in a parallel universe.