Probing the power spectrum bend with recent CMB data

TL;DR

The paper addresses whether the primordial fluctuation spectrum ${\cal P}(k)$ is consistent with a simple power law given Boomerang and MAXIMA CMB data within slow-roll inflation. It adopts a framework where ${\cal P}(k)$ is expanded to second order in $\ln k$ about a pivot $k_0$, introducing the parameters $n$, $r$, and $\partial_{\ln k}$, and performs a likelihood analysis with calibration uncertainties and BBN priors on $\Omega_b h^2$. The key findings are that allowing $\partial_{\ln k}$ to vary weakens or removes constraints on $r$, while the data favor a negative bend with a bump-like feature at $k_m \approx 0.004\, {\rm Mpc}^{-1}$ and a best-fit region near $(n,\partial_{\ln k}) \approx (0.5,-0.2)$, yielding substantially better fits than a pure power law. These results imply that current CMB data prefer scale-dependent primordial spectra, challenging simple power-law assumptions and informing inflationary model space, including scenarios with running or localized features.

Abstract

We constrain the primordial fluctuation spectrum P(k) by using the new data on the Cosmic Microwave Background (CMB) from the Boomerang and MAXIMA experiments. Our study is based on slow-roll inflationary models, and we consider the possibility of a running spectral index. Specifically, we expand the power spectrum P(k) to second order in ln(k), thus allowing the power spectrum to ``bend'' in k-space. We show that allowing the power spectrum to bend erases the ability of the present data to measure the tensor to scalar perturbation ratio. Moreover, if the primordial baryon density Ω_b h^2 is as low as found from Big Bang nucleosynthesis (BBN), the data favor a negative bending of the power spectrum, corresponding to a bump-like feature in the power spectrum around a scale of k=0.004 Mpc^-1.

Figures (6)

• Figure 1: The various slow-roll models presented in $(n,\partial_{{\rm ln} k})$ space. The dotted line is the conservative limit, $\epsilon < 0.1$. The two dashed lines are the two attractors.
• Figure 2: The various slow-roll models in $(n,\partial_{{\rm ln} k})$ space. The hybrid models correspond to $\alpha>1$, large fields means $-1 < \alpha < 1$, and small fields means $\alpha < -1$. The dashed lines are the two attractors.
• Figure 3: The allowed region in the $n,r$ parameter space, calculated from the combined COBE, Boomerang and MAXIMA data. The dark shaded (green) regions are $1\sigma$ and the light shaded (yellow) are $2\sigma$. The left panel assumes a BBN prior on $\Omega_b h^2 = 0.019$, whereas the right panel is for $\Omega_b h^2 = 0.030$, the value which best fits the CMB data. Note that the best-fit points, marked by diamonds, are really at $r=0$, but have been shifted slightly so that they are more visible.
• Figure 4: The allowed region in the $n,r,\partial_{{\rm ln} k}$ parameter space, calculated from the combined COBE, Boomerang and MAXIMA data. The dark shaded (green) regions are $1\sigma$ and the light shaded (yellow) are $2\sigma$. The left panels assume a BBN prior on $\Omega_b h^2 = 0.019$, whereas the right panels are for $\Omega_b h^2 = 0.030$, the value which best fits the CMB data. Note that the best-fit points, marked by diamonds, are really at $r=0$, but have been shifted slightly so that they are more visible. The solid line in the left $(n,\partial_{{\rm ln} k})$ panel corresponds to the power spectrum exhibiting a distinct feature at $k = 0.004 \, {\rm Mpc}^{-1}$ (see Eq. (8) and the surrounding discussion).
• Figure 5: Power spectra for four different models. Panel (a) is the best fit model with $\partial_{{\rm ln} k}=0,r=0$, (b) the best fit with $\partial_{{\rm ln} k}=0,r=2$, (c) the best fit with $\partial_{{\rm ln} k} \neq 0,r=0$, and (d) the best fit with $\partial_{{\rm ln} k} \neq 0,r=2$. The data points are from the Boomerang experiment boom. The curves show: The scalar component (dotted lines), tensor component (dashed lines), and the combined fluctuation spectrum (solid lines).