Slow-roll inflation and CMB anisotropy data

TL;DR

The study addresses how to extract cosmological parameters from CMB anisotropies by emphasizing the need to specify the primordial spectra. It shows that slow-roll inflation yields distinct scalar and tensor spectra from the commonly assumed power-law form, with $n_S=1-4\\epsilon+2\\delta$ and $n_T=-2\\epsilon$, and a pivotal scale $k_0$ that shapes predictions. By implementing a full Boltzmann treatment and confronting BOOMERanG/MAXIMA-1 data under $\\Lambda$CDM and SCDM priors, the authors demonstrate that a substantial region of the slow-roll parameter space—including cases with $n_S-1 \neq n_T$ and non-negligible gravitational waves—fits the data as well as traditional analyses. They identify several misconceptions in the literature that have biased parameter inferences and argue for future analyses to fit $\\epsilon$ and $\\delta$ directly, laying groundwork for more precise tests of slow-roll inflation with upcoming CMB measurements.

Abstract

We emphasize that the estimation of cosmological parameters from cosmic microwave background (CMB) anisotropy data, such as the recent high resolution maps from BOOMERanG and MAXIMA-1, requires assumptions about the primordial spectra. The latter are predicted from inflation. The physically best-motivated scenario is that of slow-roll inflation. However, very often, the unphysical power-law inflation scenario is (implicitly) assumed in the CMB data analysis. We show that the predicted multipole moments differ significantly in both cases. We identify several misconceptions present in the literature (and in the way inflationary relations are often combined in popular numerical codes). For example, we do not believe that, generically, inflation predicts the relation n_S - 1 = n_T for the spectral indices of scalar and tensor perturbations or that gravitational waves are negligible. We calculate the CMB multipole moments for various values of the slow-roll parameters and demonstrate that an important part of the space of parameters (n_S, n_T) has been overlooked in the CMB data analysis so far.

Figures (4)

• Figure 1: Comparison of CMB band powers from power-law and slow-roll inflation in the SCDM scenario. The slow-roll model has $\epsilon =\delta =0.050$ such that the scalar and tensor spectral indices agree in both cases ($n_{\rm S}=0.9$, $n_{\rm T}=-0.1$), which means for the power-law model $\epsilon = \delta \simeq 0.053$. For $\ell _{\rm opt}=2$, the usual pivot, the difference between the power-law and slow-roll spectra is large, which improves for a pivot $\ell _{\rm opt}=200$. The contribution of gravitational waves is displayed for power-law and slow-roll inflation ($\ell _{\rm opt}=2$).
• Figure 2: CMB band powers for a power-law spectrum ($n_{\rm S}=0.9$) in the $\Lambda$CDM scenario with correct (red line) and incorrect (green line) contribution of gravitational waves.
• Figure 3: CMB band powers for slow-roll inflation in the SCDM scenario for different values of the slow-roll parameters together with the data points of the COBE/DMR (crosses), BOOMERanG (open boxes) and MAXIMA-1 (filled boxes) experiments.
• Figure 4: As Fig. 3 but for the $\Lambda$CDM scenario.