Conservative Constraints on Early Cosmology: an illustration of the Monte Python cosmological parameter inference code

TL;DR

The paper develops an approach to constrain early cosmology by marginalizing over late-time effects, including CMB lensing, using the latest WMAP7+SPT data. It introduces Monte Python, a Python-based cosmological parameter inference code interfaced with the Boltzmann solver class, and demonstrates its use in implementing an ‘agnostic’ analysis that fixes late-time priors while preserving early-universe information. The minimal early cosmology constraints are weaker than standard LCDM yet fully compatible, and extending the framework to N_eff and M_nu yields conservative bounds that reduce apparent hints for extra relativistic species. The work highlights the robustness of early-unology constraints to late-time modeling and provides a practical tool for flexible cosmological inference with public accessibility.

Abstract

Models for the latest stages of the cosmological evolution rely on a less solid theoretical and observational ground than the description of earlier stages like BBN and recombination. As suggested in a previous work by Vonlanthen et al., it is possible to tweak the analysis of CMB data in such way to avoid making assumptions on the late evolution, and obtain robust constraints on "early cosmology parameters". We extend this method in order to marginalise the results over CMB lensing contamination, and present updated results based on recent CMB data. Our constraints on the minimal early cosmology model are weaker than in a standard LCDM analysis, but do not conflict with this model. Besides, we obtain conservative bounds on the effective neutrino number and neutrino mass, showing no hints for extra relativistic degrees of freedom, and proving in a robust way that neutrinos experienced their non-relativistic transition after the time of photon decoupling. This analysis is also an occasion to describe the main features of the new parameter inference code Monte Python, that we release together with this paper. Monte Python is a user-friendly alternative to other public codes like CosmoMC, interfaced with the Boltzmann code class.

Figures (4)

• Figure 1: Dimensionless temperature (left) and E-polarization (right) unlensed spectra of two $\Lambda$CDM models with the same value of "early cosmology" parameters ($\omega_b$, $\omega_{cdm}$, $A_s$, $n_s$) (fixed to WMAP best-fitting values), and different values of "late cosmology" parameters: ($\Omega_\Lambda$, $z_{reio}$) = (0.720,10) (solid curves) or (0.619, 5) (dashed curve). The dashed curves have been rescaled vertically by the ratio of $e^{-2 \tau}$ and horizontally by the ratio of $d_A(\tau_{rec})$ in each model, using the values of $\tau$ and $d_A(\tau_{rec})$ calculated by class for each model. At $\ell=40$, the difference between the dashed and solid line in the temperature plot is under $2\,\mu$K$^2$. At $\ell=80$, it is already below $1\,\mu$K$^2$.
• Figure 2: Constraints on the five parameters of the minimal early cosmology model (red), compared to usual constraints on the minimal $\Lambda$CDM model (black). The $\Lambda$CDM has a sixth independent parameter, the reionization optical depth. The constraints on early cosmology (called "agnostic constraints" in the text) includes a marginalization over the amplitude and tilt of the matter power spectrum leading to CMB lensing. We do not show here the posterior of the three nuisance parameter used to fit SPT data.
• Figure 3: One and two-dimensional posterior distribution (solid line) of the parameters of the "agnostic" run with a free effective neutrino number. The dashed line stands for the average likelihood distribution. The concentric contour lines in the two-dimensional posteriors stand for 68, 95 and 99% CL.
• Figure 4: One and two-dimensional posterior distribution (solid line) of the parameters of the "agnostic" run with a total neutrino mass $M_\nu$ (assuming three degenerate neutrinos of individual mass $m_\nu$). Again, dashed line stands for average likelihood distribution, contour lines indicate the 68, 95 and 99% CL.