Gravitational Fluctuations as an Alternative to Inflation

TL;DR

This paper proposes an alternative to inflation for explaining the matter power spectrum, using quantum field theory and Einstein gravity, fitting observational data without relying on inflationary assumptions.

Contribution

It introduces a nonperturbative quantum field-theoretical approach to derive the power spectrum, offering a competing explanation to inflation-based models.

Findings

Power spectral index relates to critical scaling exponents from Wilson renormalization group.

Derived power spectrum fits Sloan Digital Sky Survey data.

Results align well with Cosmic Microwave Background observations.

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 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.