Non-Vacuum Initial States for Cosmological Perturbations of Quantum-Mechanical Origin

TL;DR

This work investigates non-vacuum initial states for cosmological perturbations that introduce a built-in scale during inflation, parameterized by a privileged wavenumber $k_0$. By quantizing the perturbations and considering three rotationally invariant states with a scale-shell around $k_0$, the authors show that the Bardeen potential power spectrum acquires a step or a bump around $k_0$, with the amplitude controlled by the number of quanta ($n$) or an effective number ($n_{\rm eff}$) and the width by $\Sigma$. Comparing the resulting spectra to CMBR anisotropies and galaxy power spectra in SCDM and ΛCDM cosmologies, they identify a viable window for the free parameters; however, when tensor modes are included, larger $n_{\rm eff}$ values are favored, indicating the initial state must be close to vacuum. The study predicts a higher first acoustic peak and a non-Gaussian signature in higher-order statistics, and it emphasizes that upcoming missions like MAP/Planck and the Sloan Survey will critically test the viability of this non-vacuum paradigm as an alternative to standard inflationary models.

Abstract

In the context of inflation, non-vacuum initial states for cosmological perturbations that possess a built in scale are studied. It is demonstrated that this assumption leads to a falsifiable class of models. The question of whether they lead to conflicts with the available observations is addressed. For this purpose, the power spectrum of the Bardeen potential operator is calculated and compared with the CMBR anisotropies measurements and the redshift surveys of galaxies and clusters of galaxies. Generic predictions of the model are: a high first acoustic peak, the presence of a bump in the matter power spectrum and non-Gaussian statistics. The details are controlled by the number of quanta in the non-vacuum initial state. Comparisons with observations show that there exists a window for the free parameters such that good agreement between the data and the theoretical predictions is possible. However, in the case where the initial state is a state with a fixed number of quanta, it is shown that this number cannot be greater than a few. On the other hand, if the initial state is a quantum superposition, then a larger class of initial states could account for the observations, even though the state cannot be too different from the vacuum. Planned missions such as the MAP and Planck satellites and the Sloan Survey, will demonstrate whether the new class of models proposed here represents a viable alternative to the standard theory.

Figures (10)

• Figure 1: Initial power spectrum for $n_{\rm eff}$ ranging from 0 to 2 with steps of 0.5. Vertical units are arbitrary.
• Figure 2: Multipole moments for the SCDM model with $n_{\rm eff}$ (and $n$ if it is integer) ranging from 0 to 2 with step of 0.5 (from the bottom to the top). Diamonds represent COBE data, squares the Saskatoon data, and crosses the CAT data.
• Figure 3: Power spectrum for the SCDM model, with $n_{\rm eff}$ ranging from 0 to 2 with step of 0.5 (from the bottom to the top). Diamonds represent the APM data, squares the velocities field measurements, and crosses the data by Einasto et al.
• Figure 4: Same as Fig. \ref{['cl_1']}, but for the $\Lambda$CDM model, with $\Omega_\Lambda = 0.6$.
• Figure 5: Same as Fig. \ref{['ps_2']}, but for the $\Lambda$CDM model.