Correlated adiabatic and isocurvature perturbations from double inflation

TL;DR

This paper demonstrates that double inflation with two massive scalar fields can generate correlated adiabatic and isocurvature primordial perturbations, quantified by explicit spectra and a cross-correlation spectrum. It derives the background and perturbation dynamics in a slow-roll, two-field setting, relates inflationary fluctuations to radiation-era initial conditions, and provides analytical and numerical predictions for CMBR anisotropies and matter power spectra. The key finding is that mixing and correlation between perturbation types can significantly alter temperature fluctuations and acoustic peak structures, potentially enabling discrimination between single-field and multi-field inflation with forthcoming data. Overall, the work highlights the observable implications of primordial perturbation correlations in multi-field inflationary theories and outlines a framework for confronting them with CMBR and large-scale structure measurements.

Abstract

It is shown that double inflation (two minimally coupled massive scalar fields) can produce correlated adiabatic and isocurvature primordial perturbations. Depending on the two relevant parameters of the model, the contributions to the primordial perturbations are computed, with special emphasis on the correlation, which can be quantitatively represented by a correlation spectrum. Finally the primordial spectra are evolved numerically to obtain the CMBR anisotropy multipole expectation values. It turns out that the existence of mixing and correlation can alter very significantly the temperature fluctuation predictions.

Figures (7)

• Figure 1: Relative amplitude of the $\phi_h$ contributions to the adiabatic perturbations, $\hat{\Phi}_h$ (dashed line), to the isocurvature perturbations, $\hat{S}_h$ (dotted dashed line), and of the $\phi_l$ contribution to the adiabatic perturbations, $\hat{\Phi}_l$ (continuous line), and to the isocurvature perturbations, $\hat{S}_l$ (dotted line). The last quantity, the only one which depends on $R$, has been plotted for $R=5$ (upper dotted line) and $R=10$ (lower dotted line).
• Figure 2: Correlation spectrum for various parameters. Continuous curves from bottom to top (on the left hand side of the figure) correspond respectively to $(R=5,s_0=30)$, $(R=5,s_0=50)$ and $(R=10,s_0=50)$. The dashed curve corresponds to $(R=5,s_0=60)$, the dotted dashed curve to $(R=5,s_0=70)$ and finally the dotted curve to $(R=5,s_0=80)$.
• Figure 3: Temperature anisotropies for the double inflation scenario with $R=5$, $s_0=30$. The total anisotropies (continuous line) are the sum of a contribution due to the heavy scalar field (dashed line) and of a contribution of the light scalar field (dotted line). To make the comparison, the anisotropies due to standard (adiabatic scale-invariant) perturbations are also plotted (dotted dashed line), using $C_{10}$ for normalization.
• Figure 4: Temperature anisotropies for the double inflation scenario with $R=5$, $s_0=50$ (same conventions as in Fig.3).
• Figure 5: Temperature anisotropies for the double inflation scenario with $R=5$, $s_0=80$.