Cosmology with a Primordial Scaling Field

TL;DR

The paper proposes a scalar field with an exponential potential, yielding a robust attractor that tracks the dominant cosmic component and contributes a fixed fraction to the energy density, avoiding late-time tuning and aligning with particle-physics motivated values of the potential parameter.Using a full Einstein–Boltzmann treatment, the authors show that a small but nonzero $\Omega_\phi \sim 0.08-0.12$ can reproduce large-scale CMB anisotropies, the observed linear matter power spectrum, and nucleosynthesis constraints, while suppressing growth on small scales similarly to but more effectively than massive neutrinos in MDM models.The model connects high-energy theories (Kaluza–Klein, supergravity, or higher-curvature theories) to cosmology, offers a natural parameter range ($\lambda \sim 5-6$) that yields viable structure formation, and remains testable via CMB, Lyman-α, and non-linear structure studies.

Abstract

A weakly coupled scalar field $Φ$ with a simple exponential potential $V=M_P^4\exp(-λΦ/M_P)$ where $M_P$ is the reduced Planck mass, and $λ> 2$, has an attractor solution in a radiation or matter dominated universe in which it mimics the scaling of the dominant component, contributing a fixed fraction $Ω_φ$ (determined by $λ$) to the energy density. Such fields arise generically in particle physics theories involving compactified dimensions, with values of $λ$ which give a cosmologically relevant $Ω_φ$. For natural initial conditions on the scalar field in the early universe the attractor solution is established long before the epoch of structure formation, and in contrast to the solutions used in other scalar field cosmologies, it is one which does not involve an energy scale for the scalar field characteristic of late times . We study in some detail the evolution of matter and radiation perturbations in a standard inflation-motivated $Ω=1$ dark-matter dominated cosmology with this extra field. Using a full Einstein-Boltzmann calculation we compare observable quantities with current data. We find that, for $Ω_φ\simeq 0.08-0.12$, these models are consistent with large angle cosmic microwave background anisotropies as detected by COBE, the linear mass variance as compiled from galaxy surveys, big bang nucleosynthesis, the abundance of rich clusters and constraints from the Lyman-$α$ systems at high redshift. Given the simplicity of the model, its theoretical motivation and its success in matching observations, we argue that it should be taken on a par with other currently viable models of structure formation.

Figures (19)

• Figure 1: In the left panel we plot the evolution of the energy density in the scalar field ($\rho_\phi$) and in a component of radiation-matter as a function of scale factor for a situation in which the scalar field (with $\lambda=4$) initially dominates, then undergoes a transient and finally locks on to the scaling solution. In the right panel we plot the evolution of the fractional density in the scalar field.
• Figure 2: The evolution of the fractional energy density in the scalar field for a selection of $\lambda$s
• Figure 3: In the left panel we plot the evolution of the energy density in the scalar field ($\rho_\phi$) with $\lambda=4$ and in the remaining matter as a function of scale factor (the units are arbitrary), in the case that the scalar field is initially sub-dominant. In the right panel we plot the evolution of the fractional density in the scalar field.
• Figure 4: Reheating by kination in a simple exponential potential: The solid region is that excluded by nucleosynthesis constraints. The solid line (dash-dot, dotted) show the models for which the attractor is established at the beginning of structure formation (matter domination, today).
• Figure 5: The fractional energy density as a function of temperature for $\Omega_\phi=0.3$ and three values of $H_i$.