CMB line-of-sight integrators for nearly-isotropic cosmological models

Abstract

Homogeneous and nearly-isotropic cosmological models are natural extensions of standard Friedmann cosmologies. Constraining their features is crucial, as any detection of their properties would impact our understanding of inflation and the cosmological principle. Since these models evolve as a set of non-interacting scalar, vector, and tensor modes on top of homogeneous and isotropic spacetimes, their imprints on cosmological observables, particularly the CMB, can be obtained using standard line-of-sight methods. This requires (1) that one resorts on Laplacian eigenmodes on spatially curved spaces and (2) that radial functions for these modes are analytically continued to accommodate complex (i.e., supercurvature) wavenumbers. We introduce two line-of-sight integrators implementing the evolution of the CMB anisotropies in these models: \texttt{AniLoS}, a user-friendly and easy to modify \texttt{Python} package, and \texttt{AniCLASS}, an advanced and efficient extension of the Boltzmann solver \texttt{CLASS}. We discuss possible initial conditions that could generate such fluctuations and provide illustrative examples using our codes. This work offers a pathway for leveraging diverse cosmological datasets to constrain superhorizon anisotropies of the late-time universe.

Figures (8)

• Figure 1: Time performances in AniCLASS and AniLoS as a function of increasing multipole $\ell$, running on a Intel Core I5-8250U laptop. Overall, AniCLASS is about 10 times faster than AniLoS.
• Figure 2: Flowchart of the Python package AniLoS. The colors refer to the module where each step is found: green for anilos.py, red for hierarchy.py and yellow for hybess.pyx. The final output is an array containing the CMB multipolar coefficients $a_{\ell m}^T$, $a_{\ell m}^E$ and $a_{\ell m}^B$ (blue box).
• Figure 3: Left: evolution of $\beta'_{(1)}$ and the neutrino quadrupole ${\cal N}^{(1)}_2$ for vector modes. Right: evolution of $\beta_{(2)}$ and the neutrino quadrupole ${\cal N}^{(2)}_2$ for tensor modes. Both panels show the real (continuous) and imaginary (dashed) parts of the solution. For this plot we have used: $\Omega_K^0 = 0.1$ (VII$_h$ and V), $10^{-5}$ (VII$_0$), and $- 0.1$ (IX); $\sqrt{h}= 0.01$ (VII$_h$), $10^4$ (V), and $10^{-3}$ (VII$_0$). For the vector modes, the neutrino isocurvature quadrupole initial condition was used. Recall that model IX has no vector modes, and is thus shown only on the right panel.
• Figure 4: CMB anisotropies in model VII$_0$, with three different initial conditions: regular tensor modes (top row), isocurvature vector modes (middle row) and octopole vector modes (botton row). The cosmological parameters used in this plot are $\Omega^0_m=0.31$, $\Omega^0_\Lambda=0.69$, $\Omega_K=10^{-5}$ and $\ell_s=884\,\text{Mpc}\approx20\% H^{-1}_0$.
• Figure 5: Same as Figure \ref{['fig:alms-VII0']} but for model VII$_h$. For this plot we have used $\Omega^0_m=0.3$, $\Omega^0_\Lambda=0.6$, $\Omega_K^0 = 0.1$, and $\ell_s= 800$ Mpc.