Breaking Eternal Inflation: Empirical Viability of a Spontaneous Collapse Scenario

TL;DR

The paper tackles the problem of generating primordial structure and avoiding eternal inflation within a CSL-based spontaneous collapse framework embedded in semiclassical gravity. It derives a CSL-modified primordial power spectrum $P(k)=A_s (k/k_*)^{n_s-1} C(k)$, where $C(k)$ encodes collapse effects and the two new parameters $\alpha$ and $\beta$ enter through $\lambda_k = \lambda_0 \frac{k^{\alpha+1}}{(\beta+k)^{\alpha}}$. By confronting the model with Planck 2018 data via MCMC, the authors show that the data do not fix $\alpha$ but constrain $\beta$, and that imposing a no-eternal-inflation condition further restricts the parameter space to $\alpha\gtrsim 6$ and $\beta\sim 2\times10^{-5}$ Mpc$^{-1}$, while leaving the remaining cosmological parameters consistent with $\Lambda$CDM. The results indicate that the CSL framework can simultaneously account for the emergence of cosmic structure and suppress eternal inflation, and it naturally yields a low-$\ell$ suppression compatible with CMB observations. Overall, the work provides a concrete, data-driven assessment of a CSL-driven inflationary scenario with clear predictions for the CMB that differ at low multipoles from standard inflation.

Abstract

We revisit an inflationary scenario in which primordial inhomogeneities arise from a quantum collapse, a stochastic mechanism described in the context of quantum collapse theories in its continuous version and within semiclassical gravity. The predictions of the model show a non-conventional scalar spectrum governed by two new parameters in the collapse rate, whose aim is twofold: on one side, to account for the primordial cosmic structure, and on the other to explain the suppression amplitude associated with long-wavelength modes, thereby eliminating the occurrence of eternal inflation. Furthermore, this model can contribute to accounting for the lack of power anomaly in the low $l$ angular power spectra of the Cosmic Microwave Background (CMB). Using the latest data from the Planck (2018) collaboration, we establish observational constraints on the model parameters, which produce a characteristic low-$\ell$ suppression in the cosmic microwave background spectrum. We conclude that the Planck data support the solution presented in the previous works, in other words, that the model allows us to solve simultaneously the emergence of the cosmic structure and, at the same time, avoid the eternal inflation scenario.

Figures (6)

• Figure 1: Primordial power spectrum with $\beta=0$ compared to standard $\Lambda$CDM (fiducial) model in dashed line. According to our proposal, selecting a null value for $\beta$ parameter recovers the functional form of the standard power law, except for the oscillations at low $k$.
• Figure 2: The units of $k$ and $\beta$ are given in Mpc$^{-1}$. When $\beta$ and $\alpha$ adopt nontrivial values, distinctive features appear in the power spectrum. Starting from the lowest $k$, which would contribute the most to generating eternal inflation, a significant departure from the fiducial model gradually arises. From left to right, $\alpha = 5$ (solid line), $6$ (long dashed), $7$ (short dashed), and $8$ (solid) for each value of $\beta$ shown in the legend.
• Figure 3: CMB angular anisotropies for $\alpha$ are shown for values of $5$ (solid line), $6$ (long‐dashed line), $7$ (short‐dashed line), and $8$ (solid line). A logarithmic scale was used for multipoles $2 \leq \ell \leq 40$, highlighting the main changes introduced by our model, while a linear scale was used for $41 \leq \ell \leq 2500$. It is important to note that the behavior at low $l$ is where the effect of CSL becomes evident. The parameter $\beta$ (specified in the legend) is in Mpc$^{-1}$ and takes the same values as those previously shown in the power spectrum $P(k)$. A black dashed line denotes the fiducial model, while the gray points with error bars represent the Planck data.
• Figure 4: In blue we depict the posterior probability distributions of $\alpha$ and $\beta$, together with their joint probability confidence levels at $68\%$ and $95\%$. The light red shaded region indicates where the condition for avoiding the eternal inflation problem is satisfied. It can be seen that setting $10^{-3}$ Mpc$^{-1}$ as an upper bound for $\beta$ is both a valid and conservative choice.
• Figure 5: Imposing the theoretical condition to avoid the eternal inflation problem and taking $\beta \le 10^{-3}$ Mpc$^{-1}$ leads to much more stringent constraints. The estimates are $\beta = 2.2 \times 10^{-5}$ Mpc$^{-1}$ and $\alpha > 6.28$ ($68 \%$ confidence level). The plot shows the $68\%$ and $95\%$ confidence level contours for the posterior probability of $\alpha$ and $\beta$: in blue, the results where no a priori condition was imposed; in red, the results when requiring the criterion for avoiding the eternal inflation problem to be satisfied. The light red shaded area denotes the region where this condition is met.