f(R) gravity theory and CMBR constraints

TL;DR

The paper investigates inflation driven by $f(R)$ gravity, arguing that the Zel'dovich spectral condition selects the unique case $f(R) \propto R^2$ that yields near-scale-invariant scalar and tensor seeds. It derives the perturbation spectra in both the original $f(R)$ frame and the conformally related Einstein frame, showing a negligibly small gravitational-wave contribution under COBE-DMR constraints. The analysis provides explicit COBE-based constraints on the mass scale $M$ and demonstrates exact observational equivalence between frames. It makes two testable predictions—nearly scale-invariant Zel'dovich spectra for both perturbation types and a suppressed tensor signal—that future CMB measurements can validate or falsify.

Abstract

We consider the large-scale cosmic structure generation by an inflation based on a pure f(R)-type gravity theory. Comparison with recent CMBR observations gives the following results: (1) The near Zel'dovich spectral conditions uniquely choose R^2-type gravity. (2) The R^2 gravity predicts specific nearly scale-invariant Zel'dovich spectra for both the scalar- and tensor-type perturbations. Thus, (3) the considered model survives current observational data. The COBE-DMR quadrupole data (4) give constraints on the coupling constant and the energy scale during inflation, and (5) require the gravitational wave contribution to be suppressed. (6) Therefore, future observations of (2) and (5) can provide strong tests of the inflation scenario based on R^2 gravity. Parallel analyses made in the conformally transformed Einstein frame give the observationally identical results.