LiteBIRD Science Goals and Forecasts. A Case Study of the Origin of Primordial Gravitational Waves using Large-Scale CMB Polarization

$B$-mode power spectra, $D_{\ell}^{BB} = \ell(\ell + 1)C_{\ell}^{BB}/2\pi$, for the Starobinsky model with $r_{\rm vac}=0.00461$ and $n_{\rm t}=-r_{\rm vac}/8$ (black dotted line) and for axion-SU(2) inflation with two parameter sets (see section \ref{sec:theory}): one gives the ``high reionization bump'' model (dash-dotted orange) with parameters $r_*, \sigma, k_{\rm p}, r_{\rm vac}=[0.023, 1.1, 3.44\times10^{-4}\,\mathrm{Mpc}^{-1}, 0.00461]$; the other the ``low reionization bump'' model (dashed purple) with $r_*, \sigma, k_{\rm p}, r_{\rm vac}=[0.002, 1.9, 0.03\,\mathrm{Mpc}^{-1}, 0.002]$. The cosmic-variance-only (including primordial and lensing $B$-mode variance) and total {\sl LiteBIRD} $\pm 1\,\sigma$ binned error bars (including foreground residuals) are shown as the gray and blue regions, respectively.

Pipeline for inflationary model parameter constraints used in the paper. See sections \ref{sec:method}, \ref{sec:constraints} and \ref{sec:TBEB} for details.

: width=0.49\textwidth

: width=0.49\textwidth : Left panel: Binary mask ($f_{\rm sky}=47\,\%$) used for the large-scale power spectrum estimation (QML) at $N_{\rm side}=16$ resolution. Right panel: \textit{Planck} Galactic-plane apodized mask ($f_{\rm sky}=51\,\%$) at $N_{\rm side}=64$ used for intermediate/small-scale pseudo-$C_{\ell}$s estimation (see section \ref{sec:method} for details).

Correlation matrix for the BBBB covariance block. Here multipoles up to $\ell=35$ are unbinned, while larger multipoles are binned with $\Delta\ell=10$.

Histograms of the inferred vacuum tensor-to-scalar ratio $r_{\rm vac}$ values obtained from fitting an observed sky generated from the ``high reionization bump'' axion-SU(2) model (with parameters $r_*, \sigma, k_{\rm p}, r_{\rm vac}=[0.023, 1.1, 3.44\times10^{-4}\,\mathrm{Mpc}^{-1}, 0.00461]$) in three different ranges of multipoles: only the reionization bump range ($\ell=2-30$, in red), only the recombination bump range ($\ell=31-150$, in yellow) and the full range ($\ell=2-150$, light blue). We also show for reference the $r_{\rm vac}$ value for the Starobinsky model ($r_{\rm vac}=0.00461$).

FC construction for the 1-parameter fit (solid black lines), with $\sigma$ and $k_{\rm p}$ fixed to their ground truth. {\sl LiteBIRD} will be able to obtain a two-sided 95\,\% C.L. confidence interval $r_*=0.015^{+0.04}_{-0.008}$, if the observed sky has been generated from the ``high reionization bump'' model. The observed value $r_{*}^{\rm obs} = 0.015$ is indicated as a vertical solid red line, and its intersection with the confidence belt with two red dots. The color bar shows the distribution of $r_{*}^{\rm mle}$ obtained by fitting the simulations as a function of the input $r_{*}^{\rm in}$. See section \ref{sec:feldman} for details.

FC construction for the 1-parameter fit with $k_{\rm p}$ fixed to values different from its ground truth, i.e. $k_{\rm p}=[10^{-4},\, 5\times 10^{-4},\, 5\times 10^{-3}]\,\mathrm{Mpc}^{-1}$ (dotted orange, dot-dashed blue and dashed green, respecitvely), compared to the ground truth confidence belt (solid black, same as in Fig.~\ref{fig:beauty_full_1param}). We assume the ground truth for $\sigma$. The color bar shows the distribution of $r_{*}^{\rm mle}$ obtained by fitting the simulations (assuming the ground truth for $k_p$ and $\sigma$) as a function of the input $r_{*}^{\rm in}$. See section \ref{sec:robustness} for details.

FC construction for the 3-parameter fit (solid black lines) with free parameters $r_*$, $\sigma$ and $k_{\rm p}$. {\sl LiteBIRD} will be able to obtain a 95\,\% C.L. upper limit $r_{*}\leq 0.16$, if the observed sky has been generated from the ``high reionization bump'' model. The observed value $r_{*}^{\rm obs} = 0.05$ is indicated as a vertical solid red line. The color bar shows the distribution of $r_{*}^{\rm mle}$ obtained by fitting the simulations as a function of the input $r_{*}^{\rm in}$. See section \ref{sec:robustness} for details.

Comparison of $\Delta\chi^2$ (Eq.~\ref{eq:chi2}) between the axion-SU(2) and standard single-field slow-roll Starobinsky models from the full covariance matrix (top left panel), $BBBB$ (top right), $TBTB$ (bottom left) and $EBEB$ (bottom right) covariance blocks for {\sl LiteBIRD}, as a function of $r_*$ and $\sigma$ given $k_{\rm p}=3.44\times\,\mathrm{Mpc}^{-1}$. The contours show $1\,\sigma$, $3\,\sigma$, $5\,\sigma$ and $8\,\sigma$ significance (note that this $\sigma$, although named the same, is not the parameter of the axion-SU(2) model, which is instead plotted on the $x$-axis). The white area is excluded by current upper limits on the tensor-to-scalar ratio. The red $\star$ symbol in the upper right panel indicates the ``high reionization bump'' model. Note that the color scale changes in every panel.

Comparison of $\Delta\chi^2$ (Eq.~\ref{eq:chi2}) between the axion-SU(2) and standard single-field slow-roll Starobinsky models from the full covariance matrix (top left panel), $BBBB$ (top right), $TBTB$ (bottom left) and $EBEB$ (bottom right) covariance blocks for {\sl LiteBIRD}, as a function of $r_*$ and $\sigma$ given $k_{\rm p}=3.44\times\,\mathrm{Mpc}^{-1}$. The contours show $1\,\sigma$, $3\,\sigma$, $5\,\sigma$ and $8\,\sigma$ significance (note that this $\sigma$, although named the same, is not the parameter of the axion-SU(2) model, which is instead plotted on the $x$-axis). The white area is excluded by current upper limits on the tensor-to-scalar ratio. The red $\star$ symbol in the upper right panel indicates the ``high reionization bump'' model. Note that the color scale changes in every panel.

Comparison of $\Delta\chi^2$ (Eq.~\ref{eq:chi2}) between the axion-SU(2) and standard single-field slow-roll Starobinsky models from the full covariance matrix (top left panel), $BBBB$ (top right), $TBTB$ (bottom left) and $EBEB$ (bottom right) covariance blocks for {\sl LiteBIRD}, as a function of $r_*$ and $\sigma$ given $k_{\rm p}=3.44\times\,\mathrm{Mpc}^{-1}$. The contours show $1\,\sigma$, $3\,\sigma$, $5\,\sigma$ and $8\,\sigma$ significance (note that this $\sigma$, although named the same, is not the parameter of the axion-SU(2) model, which is instead plotted on the $x$-axis). The white area is excluded by current upper limits on the tensor-to-scalar ratio. The red $\star$ symbol in the upper right panel indicates the ``high reionization bump'' model. Note that the color scale changes in every panel.

Comparison of $\Delta\chi^2$ (Eq.~\ref{eq:chi2}) between the axion-SU(2) and standard single-field slow-roll Starobinsky models from the full covariance matrix (top left panel), $BBBB$ (top right), $TBTB$ (bottom left) and $EBEB$ (bottom right) covariance blocks for {\sl LiteBIRD}, as a function of $r_*$ and $\sigma$ given $k_{\rm p}=3.44\times\,\mathrm{Mpc}^{-1}$. The contours show $1\,\sigma$, $3\,\sigma$, $5\,\sigma$ and $8\,\sigma$ significance (note that this $\sigma$, although named the same, is not the parameter of the axion-SU(2) model, which is instead plotted on the $x$-axis). The white area is excluded by current upper limits on the tensor-to-scalar ratio. The red $\star$ symbol in the upper right panel indicates the ``high reionization bump'' model. Note that the color scale changes in every panel.

Same as Fig.~\ref{fig:delta_chi_onescale} but each panel has a different $k_{\rm p}$ and we use the full covariance matrix for all panels. Here we assume $r_{*}=5r_{\rm vac}$ in the top two and bottom left panels, while the bottom right panel assumes $r_{*}=r_{\rm vac}$, following Ref.~\cite{Ishiwata:2021yne}. Note that the color scale changes in every panel and $y$-axis range changes in the bottom right panel.

Same as Fig.~\ref{fig:delta_chi_onescale} but each panel has a different $k_{\rm p}$ and we use the full covariance matrix for all panels. Here we assume $r_{*}=5r_{\rm vac}$ in the top two and bottom left panels, while the bottom right panel assumes $r_{*}=r_{\rm vac}$, following Ref.~\cite{Ishiwata:2021yne}. Note that the color scale changes in every panel and $y$-axis range changes in the bottom right panel.

Same as Fig.~\ref{fig:delta_chi_onescale} but each panel has a different $k_{\rm p}$ and we use the full covariance matrix for all panels. Here we assume $r_{*}=5r_{\rm vac}$ in the top two and bottom left panels, while the bottom right panel assumes $r_{*}=r_{\rm vac}$, following Ref.~\cite{Ishiwata:2021yne}. Note that the color scale changes in every panel and $y$-axis range changes in the bottom right panel.

Same as Fig.~\ref{fig:delta_chi_onescale} but each panel has a different $k_{\rm p}$ and we use the full covariance matrix for all panels. Here we assume $r_{*}=5r_{\rm vac}$ in the top two and bottom left panels, while the bottom right panel assumes $r_{*}=r_{\rm vac}$, following Ref.~\cite{Ishiwata:2021yne}. Note that the color scale changes in every panel and $y$-axis range changes in the bottom right panel.

$BB$ power spectra for each of the parameter sets used in each panel of Fig.~\ref{fig:delta_chi_scales}. They correspond to spectra computed on a grid of 100 linearly spaced values of $r_*$ in the range $0.001-0.36$ and 50 values of $\sigma$ in the range $1-10$ at each fixed $k_{\rm p}$ value, excluding spectra not compatible with theoretical consistency arguments and observational bounds (see section \ref{sec:theory} for details). Darker color lines correspond to larger $r_*$ and $\sigma$ in this range. We also show for reference the $BB$ spectrum for standard single-field slow-roll inflation obtained for $r_{\rm vac}=0.037$ (solid red), saturating the current upper at scales $0.05\,\mathrm{Mpc}^{-1}$, the ``high reionization bump'' axion-SU(2) model (dot-dashed orange, see section\ref{sec:theory}) and the Starobinsky model (dotted black).

Same as Fig.~\ref{fig:plot_raphael} but for $|TB|$ power spectra. We also show for reference the $|TB|$ spectrum for the ``high reionization bump'' axion-SU(2) model (dot-dashed orange, see section~\ref{sec:theory}).

Same as Fig.~\ref{fig:plot_raphael_TB} but for $|EB|$ power spectra.