Generation of inflationary perturbations in the continuous spontaneous localization model: The second order power spectrum

Cosmic inflation, which describes an accelerated expansion of the early Universe, yields the most successful predictions regarding temperature anisotropies in the cosmic microwave background (CMB). Nevertheless, the precise origin of the primordial perturbations and their quantum-to-classical transition is still an open issue. The continuous spontaneous localization model (CSL), in the cosmological context, might be used to provide a solution to the mentioned puzzles by considering an objective reduction of the inflaton wave function. In this work, we calculate the primordial power spectrum at the next leading order in the Hubble flow functions that results from applying the CSL model to slow roll inflation within the semiclassical gravity framework. We employ the method known as uniform approximation along with a second order expansion in the Hubble flow functions. We analyze some features in the CMB temperature and primordial power spectra that could help to distinguish between the standard prediction and our approach.

Figure 1

Comparison between the CSLIM power spectrum and the canonical model. The wave number $k$ is given in ${\mathrm{Mpc}}^{-1}$. A good agreement is shown at high scales, while for $k<0.0001{\mathrm{Mpc}}^{-1}$ oscillatory features introduced by the CSLIM become evident.

Figure 2

Temperature auto-correlation (TT) spectrum comparison between the canonical model (boxes) and the CSLIM (blue solid line), the latter using the parametrization ${\lambda }_k={\lambda }_{0}k$. No difference is shown among them. Oscillations at low values of $k$ in the primordial power spectrum, as shown in Fig. 1, are wiped off in the TT spectrum.

Figure 3

Here we appreciate small departures from the canonical power spectrum. The departures are parametrized by $B$. The set of $B$ values considered show effects properly attributed to the CSLIM, and become explicitly manifest in the primordial power spectrum. Power suppression is seen at low scales for negative values of $B$, whereas positive values imply an upper departure from the canonical model. In this figure, $B$ and $k$ are given in ${\mathrm{Mpc}}^{-1}$.

Figure 4

The temperature auto-correlation (TT) spectrum including the $B$ parameter, the values of the cosmological parameters considered are the same as in Fig. 2. The negative $B$ value does not exhibit any difference at all with respect to the canonical model (boxes). On the other hand, for positive $B$ values there is a progressive departure from the canonical model at low $l$ (big angular scales). The case $B={10}^{-3}{\mathrm{Mpc}}^{-1}$ can be discarded in advance as it modifies substantially the position of the first peak, which is constrained at a high degree of accuracy by current data.