Inflationary cosmology from quantum conformal gravity

Petr Jizba,Fabio Scardigli,Hagen Kleinert

doi:10.1140/epjc/s10052-015-3441-6

Abstract

We analyze the functional integral for quantum Conformal Gravity and show that with the help of a Hubbard-Stratonovich transformation, the action can be broken into a local quadratic-curvature theory coupled to a scalar field. A one-loop effective action calculation reveals that strong fluctuations of the metric field are capable of spontaneously generating a dimensionally transmuted parameter which in the weak-field sector of the broken phase induces a Starobinsky-type f(R)-model with a gravi-cosmological constant. A resulting non-trivial relation between Starobinsky'sparameter and the cosmological constant is highlighted and implications for cosmic inflation are briefly discussed and compared with recent PLANCK and BICEP2 data.

Highlights

The idea that Einstein’s gravity may be considered as a large-distance effective theory arising from a spontaneous or dynamical symmetry breakdown in some underlying scale-invariant quantum field theory dates back to work of Minkowski [1], Smolin [2], Adler [3,4], Zee [5], Spokoiny [6], Kleinert and Schmidt [7], and others, even though the motivations can be traced back to seminal papers in the 1960s of Zeldovich [9] and Sakharov [10]
We analyze the functional integral for quantum conformal gravity and show that, with the help of a Hubbard– Stratonovich transformation, the action can be broken into a local quadratic-curvature theory coupled to a scalar field
The ensuing mechanisms for symmetry breaking are realized typically by spontaneously breaking a scale invariance in appropriate scale-invariant quantum field theory propagating in a curved spacetime [3,4] or by a conformal gravity (CG) which is dynamically broken via additional scalar fields [11,12]

Summary

Introduction

The idea that Einstein’s gravity may be considered as a large-distance effective theory arising from a spontaneous or dynamical symmetry breakdown in some underlying scale-invariant quantum field theory dates back to work of Minkowski [1], Smolin [2], Adler [3,4], Zee [5], Spokoiny [6], Kleinert and Schmidt [7], and others (see, e.g., Ref. [8] for recent review), even though the motivations can be traced back to seminal papers in the 1960s of Zeldovich [9] and Sakharov [10]. Should the Einstein gravity be induced within CG at low energies, the absence of a fundamental scalar poses immediately two problems: (a) it is difficult to break a conformal symmetry (either spontaneously or dynamically) without a fundamental spinless boson [26]; (b) the scalar degree of freedom is of a central importance to generate correct primordial density perturbations during inflation [8]. For these reasons an external scalar field is sometimes artificially coupled to CG [11,12]. A scalaron field helps to form a (composite) inflaton and assists during the inflaton decay in the reheating phase

Quantum conformal gravity

Uncompleting the R2-term

Emergence of Starobinsky’s model

Gradient term for λ

Cosmological implications