Inflationary predictions for scalar and tensor fluctuations reconsidered

TL;DR

If ns > or= 0.95, in accord with current measurements, the tensor/scalar ratio satisfies r >or= 10(-2), a range that should be detectable in proposed cosmic microwave background polarization experiments and direct gravitational wave searches.

Abstract

We reconsider the predictions of inflation for the spectral index of scalar (energy density) fluctuations (n_s) and the tensor/scalar ratio (r) using a discrete, model-independent measure of the degree of fine-tuning required to obtain a given combination of (n_s, r). We find that, except for cases with numerous unnecessary degrees of fine-tuning, n_s is less than 0.98, measurably different from exact Harrison-Zel'dovich. Furthermore, if n_s \gtrsim 0.95, in accord with current measurements, the tensor/scalar ratio satisfies r \gtrsim 10^{-2}, a range that should be detectable in proposed cosmic microwave background polarization experiments and direct gravitational wave searches.

Figures (2)

• Figure 1: Predictions for tensor/scalar ratio $r$ versus spectral tilt $n_{s}$ for minimal tuning ($Z_{\eta}=0$) and for different degrees of extra fine-tuning ($Z_{\eta} \ge 1$). The small white circles correspond to monomial potentials (from right to left: quadratic, cubic, quartic). The thick curve enclosing all models with zero or one extra degree of fine-tuning has $n_s < 0.98$ and $r> 10^{-2}$; hatched portion has $Z_{\eta} =0$ or 1 but is only accessible for polynomials of degree greater than four ($Z_{order} \ge 1$). Nine or more extra degrees of fine-tuning are required to obtain $n_s$ close to 1 or small $r$ (gray).
• Figure 2: Inflationary predictions of $\Omega_{gw}(f)$ vs. $f$ with present (solid bars) and future (dashed bars) observational limits. The solid blue and green bands represent the predicted range for models with minimal tuning, or one extra degree of tuning, respectively, that satisfy the current observational bounds. The thick curve represents the lower-bound for $\Omega_{gw}$ from among the region enclosed by the black curve in Fig. 1. The purple curve is the lower bound for models with $Z_{\eta}<6$. The dashed curve ($r=10^{-3}$) is the lowest prediction among all models shown in Fig. 1.