Origin of inflation in CFT driven cosmology: $$R^2$$ R 2 -gravity and non-minimally coupled inflaton models

Abstract

We present a detailed derivation of the recently suggested new type of hill-top inflation [arXiv:1509.07270] originating from the microcanonical density matrix initial conditions in cosmology driven by conformal field theory (CFT). The cosmological instantons of topology S 1 × S 3 , which set up these initial conditions, have the shape of a garland with multiple periodic oscillations of the scale factor of the spatial S 3 -section. They describe underbarrier oscillations of the inflaton and scale factor in the vicinity of the inflaton potential maximum, which gives a sufficient amount of inflation required by the known CMB data. We build the approximation of two coupled harmonic oscillators for these garland instantons and show that they can generate inflation consistent with the parameters of the CMB primordial power spectrum in the non-minimal Higgs inflation model and in R 2 gravity. In particular, the instanton solutions provide smallness of inflationary slow-roll parameters and η < 0 and their relation ∼ η 2 characteristic of these two models. We present the mechanism of formation of hill-like inflaton potentials, which is based on logarithmic loop corrections to the asymptotically shift-invariant tree-level potentials of these models in the Einstein frame. We also discuss the role of R 2 -gravity as an indispensable finite renormalization tool in the CFT driven cosmology, which guarantees the nondynamical (ghost free) nature of its scale factor and special properties of its cosmological garland-type instantons. Finally, as a solution to the problem of hierarchy between the Planckian scale and the inflation scale we discuss the concept of a hidden sector of conformal higher spin fields. a

Inflation and gauge field holonomy

“…Note that γ does not contribute to the above equations in view of conformal flatness of the FRW metric, while the coefficient α can always be renormalized to zero by a local R 2 counterterm, changes in α thus being equivalent to the inclusion of the non-minimally coupled scalaron of the Starobinsky model, see discussion in [12,13].…”

“…In particular, the role of ρ could be played by a fundamental cosmological constant, its particular value being selected from the existence of the periodic Euclidean saddle-point solution, as it was in the simplest model of [9]. In more realistic models the role of ρ is played by the non-conformal inflaton field in the slow roll regime or the scalaron field of the Starobinsky R 2 -model [12,13], see below. Moreover, ρ can contain ordinary particle matter of negligible amount in the early Universe, but quantum created during inflation in view of its non-conformal nature and, therefore, starting to dominate at later stages of the evolution, see footnote 4.…”

Wormholes in $$R^2$$ R 2 -gravity within the f(R, T) formalism

“…[4,5] (see also the review [6]). Moreover, the inflationary era and dark matter issues are also addressed in this theory [7][8][9][10]. a e-mail: pksahoo@hyderabad.bits-pilani.ac.in b e-mail: moraes.phrs@gmail.com c e-mail: sahooparbati1990@gmail.com…”

Inflationary perturbations in no-scale theories

“…It has been proposed that such theory could make sense above M 2 as a Lee-Wick theory [29][30][31][32]: the ghost is unstable and does not appear among the asymptotic states, leading to a unitary Smatrix. Also, recently there has been progress on the quantum mechanics of four-derivative theories [33,34] and renewed further interest in four-derivative gravity [35][36][37][38][39][40][41][42][43][44][45][46][47]. References [48,49] claimed, however, that the Lee-Wick option might result in a violation of causality.…”