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Structure formation in a string-inspired modification of the cold dark matter model

Steven S. Gubser, P. J. E. Peebles

TL;DR

This work investigates a string-inspired modification of cold dark matter wherein two dark-matter species carry opposite scalar charges, yielding zero net scalar charge so linear growth of structure matches ΛCDM while enabling a charge-separation instability on nonlinear scales. The authors formulate a linear perturbation framework with a charge-encoded interaction matrix β_{pq}, perform an eigenmode analysis showing a robust adiabatic mode plus potentially growing isocurvature modes driven by scalar forces, and connect these dynamics to simple string-theory setups that yield order-unity scalar couplings to gravity. They discuss observational constraints from astronomy, arguing that adiabatic initial conditions and suppressed charge separation at decoupling are required to maintain consistency with large-scale structure and the CMB, while leaving room for novel small-scale signatures. The paper also addresses naturalness and phenomenology: the scalar must couple to the visible sector only weakly (dimension-six suppressed) to respect the weak equivalence principle, and the authors outline how a viable UV completion might arise in a supersymmetric or string-theoretic context, with further discussion in a companion paper. Overall, the work explores a theoretically motivated dark-sector interaction that can mimic ΛCDM on large scales but induce distinctive nonlinear structure formation, offering a path to testable deviations in galaxy-scale dynamics if initial isocurvature modes are sufficiently suppressed.

Abstract

Motivated in part by string theory, we consider the idea that the standard LambdaCDM cosmological model might be modified by the effect of a long-range scalar dark matter interaction. The variant of this widely-discussed notion considered here is suggested by the Brandenberger-Vafa picture for why we perceive three spatial dimensions. In this picture there may be at least two species of dark matter particles, with scalar ``charges'' such that the scalar interaction attracts particles with like sign and repels unlike signs. The net charge vanishes. Under this condition the evolution of the mass distribution in linear perturbation theory is the same as in the LambdaCDM cosmology, and both models therefore can equally well pass the available cosmological tests. The physics can be very different on small scales, however: if the scalar interaction has the strength suggested by simple versions of the string scenario, nonlinear mass concentrations are unstable against separation into charged halos with properties unlike the standard model prediction and possibly of observational interest.

Structure formation in a string-inspired modification of the cold dark matter model

TL;DR

This work investigates a string-inspired modification of cold dark matter wherein two dark-matter species carry opposite scalar charges, yielding zero net scalar charge so linear growth of structure matches ΛCDM while enabling a charge-separation instability on nonlinear scales. The authors formulate a linear perturbation framework with a charge-encoded interaction matrix β_{pq}, perform an eigenmode analysis showing a robust adiabatic mode plus potentially growing isocurvature modes driven by scalar forces, and connect these dynamics to simple string-theory setups that yield order-unity scalar couplings to gravity. They discuss observational constraints from astronomy, arguing that adiabatic initial conditions and suppressed charge separation at decoupling are required to maintain consistency with large-scale structure and the CMB, while leaving room for novel small-scale signatures. The paper also addresses naturalness and phenomenology: the scalar must couple to the visible sector only weakly (dimension-six suppressed) to respect the weak equivalence principle, and the authors outline how a viable UV completion might arise in a supersymmetric or string-theoretic context, with further discussion in a companion paper. Overall, the work explores a theoretically motivated dark-sector interaction that can mimic ΛCDM on large scales but induce distinctive nonlinear structure formation, offering a path to testable deviations in galaxy-scale dynamics if initial isocurvature modes are sufficiently suppressed.

Abstract

Motivated in part by string theory, we consider the idea that the standard LambdaCDM cosmological model might be modified by the effect of a long-range scalar dark matter interaction. The variant of this widely-discussed notion considered here is suggested by the Brandenberger-Vafa picture for why we perceive three spatial dimensions. In this picture there may be at least two species of dark matter particles, with scalar ``charges'' such that the scalar interaction attracts particles with like sign and repels unlike signs. The net charge vanishes. Under this condition the evolution of the mass distribution in linear perturbation theory is the same as in the LambdaCDM cosmology, and both models therefore can equally well pass the available cosmological tests. The physics can be very different on small scales, however: if the scalar interaction has the strength suggested by simple versions of the string scenario, nonlinear mass concentrations are unstable against separation into charged halos with properties unlike the standard model prediction and possibly of observational interest.

Paper Structure

This paper contains 10 sections, 51 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Brandenberger-Vafa scenario
  3. Density perturbations
  4. Linear Perturbation description of the Scalar Interaction
  5. Solutions
  6. Guidance on Charges and Masses from String Theory
  7. Constraints from astronomy
  8. Naturalness, coupling to the visible sector, and the weak equivalence principle
  9. The weak equivalence principle
  10. Other particle physics considerations

Figures (1)

  • Figure 1: An illustration of the development of a massive halo out of an initially isocurvature charge perturbation, that is, an initially homogeneous mass distribution with a small scalar charge separation. The system is spherically symmetric. The dashed curves are the densities relative to the mean for the two dark matter species, and the solid curve is the total mass density. All curves are plotted at the moment when the dense component has just stopped expanding in the center.