Inflation in asymptotically safe gravity

Abstract

In Chapter 1, we examine the inflationary modes in the cubic curvature theories in the context of asymptotically safe gravity. On the phase space of the Hubble parameter, there exists a critical point which corresponds to the slow-roll inflation in Einstein frame. Most of the e-foldings are attained around the critical point for each inflationary trajectories. If the coupling constants gi have the parametric relations generated as the power of the relative energy scale of inflation H0 to the cutoff, a successful inflation with more than 60 e-foldings occurs near the critical point. One can find the quantum fluctuations in Jordan frame from to perform the stochastic simulation. In Chapter 2, we explore the nucleation of vacuum bubbles in the Brans-Dicke type theory of gravity. In the Euclidean signature, we evaluate the fields at the vacuum bubbles as solutions of the Euler-Lagrange equations of motion as well as the bubble nucleation probabilities by integrating the Euclidean action. We illustrate three possible ways to obtain vacuum bubbles: true vacuum bubbles for w > -3/2, false vacuum bubbles for w < -3/2, and false vacuum bubbles for w > -3/2 when the vacuum energy of the false vacuum in the potential of the Einstein frame is less than that of the true vacuum. After the bubble is nucleated at the t = 0 surface, we can smoothly interpolate the field combinations to some solutions in the Lorentzian signature and consistently continue their subsequent evolutions. Therefore, we conclude that, in general scalar-tensor theories like this Brans-Dicke type theories, which may include and represent certain features of string theory, vacuum bubbles come in false vacuum bubbles as well as in true vacuum bubbles, as long as a special condition is assumed on the potential.