Constraints on the running of the running of the scalar tilt from CMB anisotropies and spectral distortions

Abstract

We use the recent observations of Cosmic Microwave Background temperature and polarization anisotropies provided by the Planck satellite experiment to place constraints on the running αs = dns/d log k and the running of the running βs = dαs/d log k of the spectral index ns of primordial scalar fluctuations. We find αs = 0.011 ± 0.010 and βs = 0.027 ± 0.013 at 68% CL, suggesting the presence of a running of the running at the level of two standard deviations. We find no significant correlation between βs and foregrounds parameters, with the exception of the point sources amplitude at 143 GHz, A P S 143 , which shifts by half sigma when the running of the running is considered. We further study the cosmological implications of such preference for αs, βs ∼ 0.01 by including in the analysis the lensing amplitude AL, the curvature parameter Ω k , and the sum of neutrino masses mν . We find that when the running of the running is considered, Planck data are more compatible with the standard expectations of AL = 1 and Ω k = 0 but still hint at possible deviations. The indication for βs > 0 survives at two standard deviations when external datasets such as BAO and CFHTLenS are included in the analysis, and persists at ∼ 1.7 standard deviations when CMB lensing is considered. We discuss the possibility of constraining βs with current and future measurements of CMB spectral distortions, showing that an experiment like PIXIE could provide strong constraints on αs and βs.

Towards a measurement of the spectral runnings

“…on β s (marginalizing over ΛCDM+α s ) will be σ(β s ) = 0.0045. This will shed light on the claimed detection of a non-zero second running β s = 0.02 ± 0.01 [11], and will have the power to test whether primordial black holes with tens of solar masses are formed from a positive second running. From these results we find that the S4 experiment alone will not suffice to determine the dynamics of inflation.…”

“…The first of these quantities is the scalar running α s = dn s /d log k, presently consistent with zero [2]. However, current Planck data seems to prefer a non-zero second running β s ≡ dα s /d log k = 0.02 ± 0.01, albeit only at 2−σ [11].…”

CMB spectral distortions in generic two-field models

“…The µ-values are positive apart from 9 parameter sets for which the adiabatic cooling µ ad ≈ −3 × 10 −9 generates a small negative µ. Configurations with R 0.05 shown in the first column of figure 1 effectively reduce to the single field case. Apart from the enhanced µ values for n 2 ∼ 2, the subdominant field has no effect on the distortion signal in this class and the dependence of µ on n 1 , α 1 , β 1 is that found in [15,16]. The enhanced distortion signal is also induced from the positive running and running of the running due to the large difference n 2 − n 1 as seen from the last terms of eqs.…”

Non-Standard Hierarchies of the Runnings of the Spectral Index in Inflation

“…One could also consider alternative scenarios in which ∆ is not small (e.g., when H/M Pl is larger for some reason, or for a larger choice ofk) and the final power spectrum (36) receives a greater contribution from quantum gravity effects. In such a scenario, to obtain a positive correction to β s as is found in the analysis of [7], from (40), one needs ∆ > 1 (though we note that, in this regime, higher order corrections would also likely be important). For such a large ∆, n s − 1 and α s are corrected by O(1), which likely ruins their fit to the data unless the uncorrected values ((n s − 1) (0) , etc.)…”

“…As well as the simple curiosity that the analysis may be unstable under the inclusion of an additional parameter, the Planck results note that "Allowing for running of the running provides a better fit to the temperature spectrum at low multipoles". An extended analysis of the Planck experiment's data detailed in [7], in which the lensing amplitude A L , density parameter of curvature Ω k and neutrino masses ∑ m ν are independently accounted for, find best fit values of n s = 0.9582…”