16 Dec 1998 | Paul J. Steinhardt, Limin Wang, and Ivaylo Zlatev
This paper introduces tracker fields as a solution to the coincidence problem in quintessence cosmology. Tracker fields are scalar fields that evolve to a common trajectory regardless of initial conditions, allowing the energy density of the field to match the matter density today without requiring fine-tuned initial conditions. The key property of tracker fields is that their equation-of-state parameter $ w_Q $ adjusts to match the background equation-of-state $ w_B $, ensuring that the energy densities of the field and matter evolve at similar rates. This mechanism allows the field to become dominant in the late universe, leading to an accelerating expansion.
The paper discusses the general conditions for tracker solutions, showing that they require a specific relationship between the potential $ V(Q) $ and the equation-of-state $ w_Q $. Tracker solutions are characterized by the condition $ \Gamma \equiv V''V/(V')^2 $ being nearly constant and greater than 1 for $ w_Q < w_B $, or less than 1 for $ w_Q > w_B $. These conditions ensure that the field evolves to a common trajectory, regardless of initial conditions.
The paper also explores the behavior of tracker solutions under different initial conditions, showing that they can either overshoot or undershoot the tracker value before converging to it. This convergence ensures that the field eventually dominates the universe, leading to an accelerating expansion. The paper also addresses the issue of the $ \Omega_Q - w_Q $ relation, showing that tracker solutions predict a specific relationship between the energy density and equation-of-state parameter of the field today. This relation distinguishes tracker fields from the cosmological constant, as the former cannot approach $ w_Q = -1 $ due to the observed matter density.
The paper concludes that tracker solutions provide a viable alternative to the cosmological constant for explaining the current accelerated expansion of the universe, with the potential to be distinguished from the cosmological constant through future observations of the cosmic microwave background and supernovae.This paper introduces tracker fields as a solution to the coincidence problem in quintessence cosmology. Tracker fields are scalar fields that evolve to a common trajectory regardless of initial conditions, allowing the energy density of the field to match the matter density today without requiring fine-tuned initial conditions. The key property of tracker fields is that their equation-of-state parameter $ w_Q $ adjusts to match the background equation-of-state $ w_B $, ensuring that the energy densities of the field and matter evolve at similar rates. This mechanism allows the field to become dominant in the late universe, leading to an accelerating expansion.
The paper discusses the general conditions for tracker solutions, showing that they require a specific relationship between the potential $ V(Q) $ and the equation-of-state $ w_Q $. Tracker solutions are characterized by the condition $ \Gamma \equiv V''V/(V')^2 $ being nearly constant and greater than 1 for $ w_Q < w_B $, or less than 1 for $ w_Q > w_B $. These conditions ensure that the field evolves to a common trajectory, regardless of initial conditions.
The paper also explores the behavior of tracker solutions under different initial conditions, showing that they can either overshoot or undershoot the tracker value before converging to it. This convergence ensures that the field eventually dominates the universe, leading to an accelerating expansion. The paper also addresses the issue of the $ \Omega_Q - w_Q $ relation, showing that tracker solutions predict a specific relationship between the energy density and equation-of-state parameter of the field today. This relation distinguishes tracker fields from the cosmological constant, as the former cannot approach $ w_Q = -1 $ due to the observed matter density.
The paper concludes that tracker solutions provide a viable alternative to the cosmological constant for explaining the current accelerated expansion of the universe, with the potential to be distinguished from the cosmological constant through future observations of the cosmic microwave background and supernovae.