[Paper Review] Eternal inflation and collapse theories

Rosa-Laura Lechuga, Daniel Sudarsky|arXiv (Cornell University)|Aug 2, 2023

Cosmology and Gravitation TheoriesPhysics and Astronomy3 citations

TL;DR

This paper resolves the eternal inflation problem in quantum cosmology by introducing a modified spontaneous collapse theory (CSL-type) that breaks spatial homogeneity and isotropy to generate primordial density fluctuations. It shows that by adjusting the collapse rate's dependence on mode wave number, the theory avoids eternal inflation while preserving a viable power spectrum for cosmic structure formation.

ABSTRACT

The eternal inflation problem continues to be considered one of standard's cosmology most serious shortcomings. This arises when one considers the effects of "quantum fluctuations" (QF) on the zero mode of inflaton field during a Hubble time in the inflationary epoch. In the slow-roll regime it is quite clear that such QF could dwarf the classical rolling down of the inflaton, and with overwhelming probability this prevents inflation from ever ending. When one recognizes that QF can not be taken as synonymous of stochastic fluctuations, but rather intrinsic levels of indefiniteness in the quantities, one concludes that the eternal inflation problem simply does not exist. However, the same argument would serve to invalidate the account for the generation of the primordial seeds of cosmic structure. In order to do address that issue, one must explain the breaking of homogeneity and isotropy of the early inflationary epoch. The so called spontaneous collapse theories offer an additional element namely the stochastic and spontaneous state reduction characteristic of those proposals possesses the basic features to break those symmetries. In fact, a version of the CSL theory adapted to the cosmological context has been shown to offer a satisfactory account for the origin the seeds of cosmic structure with an adequate power spectrum, and will serve as the basis of our analysis. However, once such stochastic collapse is introduced into the theoretical framework the eternal inflation problem has the potential reappear. In this manuscript we explore those issues in detail and discuss an avenue that seems to allow for a satisfactory account for the generation of the primordial inhomogeneities and anisotropies while freeing the theory from the eternal inflation problem.

Motivation & Objective

• To address the eternal inflation problem in inflationary cosmology, which arises when quantum fluctuations prevent the inflaton field from rolling to the potential minimum.
• To reconcile the need for a mechanism to break homogeneity and isotropy—essential for generating primordial inhomogeneities—with the avoidance of eternal inflation.
• To investigate whether spontaneous collapse theories, which can break symmetries and generate cosmic seeds, reintroduce the eternal inflation problem when applied to the inflaton zero mode.
• To derive a condition on the collapse rate parameters that prevents eternal inflation while maintaining consistency with cosmological observations like CMB and BAO.
• To demonstrate that a modified collapse rate, dependent on mode wave number, can suppress the eternal inflation problem without invalidating the standard mechanism for primordial structure generation.

Proposed method

• Adapts a cosmological version of the Continuous Spontaneous Localization (CSL) theory to the inflationary epoch, introducing a stochastic, spontaneous state reduction mechanism.
• Modifies the collapse rate to depend on the wave number of field modes, ensuring that the zero mode (responsible for accelerated expansion) remains unaffected by collapse.
• Identifies modes with physical wavelengths larger than the particle horizon as critical for the eternal inflation problem, as they can experience significant quantum fluctuations.
• Derives a condition on the collapse rate parameters (α and b) using a modified rate function that accounts for both observable modes and those potentially leading to eternal inflation.
• Uses estimates from cosmological parameters (e.g., Hubble scale, Planck mass, inflaton mass) to constrain the parameter space and derive a quantitative bound on the collapse rate.
• Applies bounds from CMB and BAO observations to ensure the model remains observationally viable while avoiding eternal inflation.

Experimental results

Research questions

• RQ1 Can a spontaneous collapse theory that generates primordial inhomogeneities also reintroduce the eternal inflation problem?
• RQ2 How does the dependence of the collapse rate on mode wave number affect the stability of the inflaton zero mode and the potential for eternal inflation?
• RQ3 What conditions on the collapse rate parameters (α and b) prevent the eternal inflation problem while preserving a viable power spectrum for cosmic structure?
• RQ4 Is it possible to reconcile the measurement problem solution via collapse theories with the requirement that inflation ends in a finite time?
• RQ5 Can the effective collapse rate in cosmological contexts be context-dependent, and how does this flexibility help resolve the eternal inflation problem?

Key findings

• The eternal inflation problem does not arise if the collapse rate satisfies the condition $10^{15}\frac{1}{\alpha+2}\left(\frac{2\pi}{b\tau}\right)^{\alpha} < 1$, which can be met for appropriate values of α and b.
• The zero mode remains unaffected by collapse due to its scale-invariant nature, preventing runaway inflation driven by quantum fluctuations.
• Modes with physical wavelengths exceeding the particle horizon are the primary candidates for triggering eternal inflation, and their behavior is controlled by the modified collapse rate.
• Parameter values exist—specifically $b \leq 10^{-3}\,\text{Mpc}^{-1}$—that satisfy both the condition to avoid eternal inflation and observational constraints from CMB and BAO.
• The model remains consistent with the observed power spectrum of primordial fluctuations, as established in prior work [2], while resolving the eternal inflation issue.
• The flexibility in the collapse rate's parametrization suggests that effective collapse dynamics could vary across cosmological contexts, offering a way to avoid eternal inflation without altering the core mechanism of structure formation.