Computational complexity of the landscape II—Cosmological considerations

Abstract

We propose a new approach for multiverse analysis based on computational complexity, which leads to a new family of "computational" measure factors. By defining a cosmology as a space-time containing a vacuum with specified properties (for example small cosmological constant) together with rules for how time evolution will produce the vacuum, we can associate global time in a multiverse with clock time on a supercomputer which simulates it. We argue for a principle of "limited computational complexity" governing early universe dynamics as simulated by this supercomputer, which translates to a global measure for regulating the infinities of eternal inflation. The rules for time evolution can be thought of as a search algorithm, whose details should be constrained by a stronger principle of "minimal computational complexity." Unlike previously studied global measures, ours avoids standard equilibrium considerations and the well-known problems of Boltzmann Brains and the youngness paradox. We also give various definitions of the computational complexity of a cosmology, and argue that there are only a few natural complexity classes. arXiv:1706.06430v3 [hep-th]

Estimating Calabi-Yau hypersurface and triangulation counts with equation learners

“…For example, dynamical vacuum selection [8] on a network of string geometries [9] in a well-studied bubble cosmology [10] selects models with large numbers of gauge groups and axions, as well as strong coupling. However, concrete studies of the landscape are difficult due to its enormity [11,12,13,14,9,15], computational complexity [16,17,18,19,20], and undecidability [17]. It is therefore natural to expect that, in addition to the formal progress that is clearly required, data science techniques such as supervised machine learning will be necessary to understand the landscape; see for initial works [21,22,8,23] in this directions and [24,25,26,27,28,29,30] for additional promising results.…”

TASI Lectures on Remnants from the String Landscape

“…For these reasons a statistical approach [111] to the landscape seems critical, and a natural question is how to study statistics (including possible vacuum and / or anthropic selection) of a set of vacua that cannot be read into memory or scanned over, particularly given that the difficulty of the problem is exacerbated by computational complexity [117][118][119].…”

Topological data analysis for the string landscape

“…Persistent homology can be used to compare different distributions of string vacua (by summarizing what topological features are present and how they relate) and to understand where individual vacua reside within a distribution. We imagine that applying persistent homology to distributions of string vacua could be potentially useful for understanding vacuum selection (which becomes even more interesting when issues of computational complexity are considered [56][57][58][59]) or tunneling in the landscape. Moreover, by choosing only special vacua with certain phenomenologically interesting properties and studying the restricted distributions with persistent homology, we may learn which low-energy properties of a string vacuum are simultaneously allowed, and where they live.…”