Essentials of k-Essence

Essentials of k-Essence

February 1, 2008 | C. Armendariz-Picon, V. Mukhanov and Paul J. Steinhardt
The paper introduces k-essence as a dynamical solution to explain the universe's accelerated expansion at late times without requiring fine-tuning or anthropic arguments. K-essence is based on a dynamical attractor solution that causes it to behave like a cosmological constant at the onset of matter domination, leading to cosmic acceleration at the present epoch. The theory is built on scalar fields with non-linear kinetic energy terms in the action, allowing for two classes of solutions: one where cosmic acceleration continues indefinitely and another where it has finite duration. The paper discusses the cosmic coincidence problem, which asks why dark energy has a small energy density and why cosmic acceleration begins at a late stage. K-essence avoids this by relying on dynamical attractor behavior, making cosmic evolution insensitive to initial conditions. This behavior is similar to quintessence models, but k-essence only tracks the equation-of-state during the radiation-dominated epoch, not during matter domination. At the onset of matter domination, k-essence's energy density drops significantly, allowing it to overtake the matter density and induce cosmic acceleration. K-essence models are classified into two types: trackers, which mimic the equation-of-state of the background, and attractors, which correspond to different energy components. Radiation trackers exist when k-essence mimics radiation, while dust trackers mimic cold matter. De Sitter attractors correspond to a cosmological constant, and k-attractors are dominant energy components. The paper shows that k-essence can transition between these attractors as the universe evolves, leading to cosmic acceleration today. The paper also discusses the construction of k-essence models, emphasizing the need for specific conditions on the function g(y) to ensure the existence of attractors and the correct equation-of-state. These conditions include the positivity of energy density and the stability of the k-essence background. The paper concludes that k-essence provides a natural explanation for cosmic acceleration without requiring fine-tuning, making it a promising candidate for dark energy.The paper introduces k-essence as a dynamical solution to explain the universe's accelerated expansion at late times without requiring fine-tuning or anthropic arguments. K-essence is based on a dynamical attractor solution that causes it to behave like a cosmological constant at the onset of matter domination, leading to cosmic acceleration at the present epoch. The theory is built on scalar fields with non-linear kinetic energy terms in the action, allowing for two classes of solutions: one where cosmic acceleration continues indefinitely and another where it has finite duration. The paper discusses the cosmic coincidence problem, which asks why dark energy has a small energy density and why cosmic acceleration begins at a late stage. K-essence avoids this by relying on dynamical attractor behavior, making cosmic evolution insensitive to initial conditions. This behavior is similar to quintessence models, but k-essence only tracks the equation-of-state during the radiation-dominated epoch, not during matter domination. At the onset of matter domination, k-essence's energy density drops significantly, allowing it to overtake the matter density and induce cosmic acceleration. K-essence models are classified into two types: trackers, which mimic the equation-of-state of the background, and attractors, which correspond to different energy components. Radiation trackers exist when k-essence mimics radiation, while dust trackers mimic cold matter. De Sitter attractors correspond to a cosmological constant, and k-attractors are dominant energy components. The paper shows that k-essence can transition between these attractors as the universe evolves, leading to cosmic acceleration today. The paper also discusses the construction of k-essence models, emphasizing the need for specific conditions on the function g(y) to ensure the existence of attractors and the correct equation-of-state. These conditions include the positivity of energy density and the stability of the k-essence background. The paper concludes that k-essence provides a natural explanation for cosmic acceleration without requiring fine-tuning, making it a promising candidate for dark energy.
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