Gravitational Fluctuations as an Alternative to Inflation

Abstract

The ability to reproduce the observed matter power spectrum P ( k ) to high accuracy is often considered as a triumph of inflation. In this work, we explore an alternative explanation for the power spectrum based on nonperturbative quantum field-theoretical methods applied to Einstein’s gravity, instead of ones based on inflation models. In particular, the power spectral index, which governs the slope on the P ( k ) graph, can be related to critical scaling exponents derived from the Wilson renormalization group analysis. We find that the derived value fits favorably with the Sloan Digital Sky Survey telescope data. We then make use of the transfer functions, based only on the Boltzmann equations, which describe states out of equilibrium, and Einstein’s general relativity, to extrapolate the power spectrum to the Cosmic Microwave Background (CMB) regime. We observe that the results fit rather well with current data. Our approach contrasts with the conventional explanation, which uses inflation to generate the scale-invariant Harrison–Zel’dovich spectrum on CMB scales and uses the transfer function to extrapolate it to the galaxy regime. The results we present here only assume quantum field theory and Einstein’s gravity, and hence provide a competing explanation of the power spectrum, without relying on the assumptions usually associated with inflationary models. At the end, we also outline several testable predictions in this picture that deviate from the conventional picture of inflation and which hopefully will become verifiable in the near future with increasingly accurate measurements.