Cosmological density perturbations from a quantum gravitational model of inflation (Q2753280)

The view that the very early universe underwent a period of inflation at some large mass scale M is strongly supported by the homogeneity and isotropy of the cosmic microwave background, and by the absence of relics such as magnetic monopoles. An large variety of models have been proposed to implement inflation, all of which involve a dynamical scalar degree of freedom in some form. Another common feature of these models is that the cosmological constant must be fine tuned so that inflation can end. Many models require additional fine tuning in order to make inflation last long enough and in order that quantum fluctuations near the end of inflation can generate a plausible spectrum of primordial density fluctuations. NEWLINENEWLINENEWLINERecently a model has been proposed in which fundamental scalars play no role and for which the cosmological constant is not fine tuned to zero [\textit{N. C. Tsamis} and \textit{R. P. Woodard}, Nucl. Phys. B 474, 235-248 (1996; Zbl 0925.83021)]. Indeed, inflation begins in this model for no other reason than that the cosmological constant is not unreasonably small. It ends due to the secular accumulation of gravitational binding energy between virtual gravitons which have become trapped in the superluminal expansion of spacetime and are therefore unable to recombine. This effect is unique to particles that are effectively massless and yet not conformally invariant, the only definitively known example of which is the graviton. The process is slow because gravity is a weak interaction. However, it must eventually null the bare cosmological constant since the effect is coherent and persists for as long as inflation does. NEWLINENEWLINENEWLINEIn this paper the authors derive the implications for anisotropies in the cosmic microwave background following from the model of inflation in which a bare cosmological constant is gradually screened by an infrared process in quantum gravity. In section 2 they derive a simple approximate form for the scalar potential which is valid until about the last five e-foldings of inflation. This is used in section 3 to compute the scalar and tensor amplitudes and spectral indices employing the standard formulae of scalar-driven inflation.