Topology from Cosmology

TL;DR

The paper demonstrates that cosmological observables from inflation can impose strong constraints on the topology of hidden extra dimensions in string theory, by linking observable parameters to microscopic string data within a multi-field Large Volume Scenario (Type IIB) framework. It develops a general slow-roll analysis for non-canonical, multi-field kinetics, and derives expressions for ${\\cal P}$, $r$, $n_s$, and $\\alpha_s$ in terms of effective parameters $z_i$ that encode topology and initial conditions, showing that discrete topological invariants like the Euler number $\\chi$ cannot be freely tuned. In a concrete two-field LVS model, observables depend on $z_i$ and initial conditions, and variations in topology (e.g., $\\xi$ via $\\chi$) tend to spoil slow-roll unless finely tuned, implying that cosmological data can significantly constrain or falsify classes of string inflation models. The work highlights that many-field, non-canonical inflation retains rich dynamics and that cosmology can probe the geometry and topology of extra dimensions in ways complementary to collider experiments. The methodology is general and could be extended to other string-motivated inflationary setups to assess topology-driven constraints from precise CMB measurements.

Abstract

We show that cosmological observables can constrain the topology of the compact additional dimensions predicted by string theory. To do this, we develop a general strategy for relating cosmological observables to the microscopic parameters of the potentials and field-dependent kinetic terms of the multiple scalar fields that arise in the low-energy limit of string theory. We apply this formalism to the Large Volume Scenarios in Type IIB flux compactifications where analytical calculations are possible. Our methods generalize to other settings.