How does the equation-of-state depend on the Quintessence potential?

In summary, the conversation discusses how adding constants to the potential in quintessence fields does not affect the equation of motion, but it does change the pressure, energy density, and equation-of-state. By choosing a sufficiently large positive constant, the equation of state becomes indistinguishable from -1. The question is raised whether physics should remain invariant in this case, as the potential is a quantity of energy density and cannot be redefined by adding a constant.
  • #1
Amanheis
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Quintessence fields are supposed to slowly roll down a potential V(\phi). Adding constants to the potential obviously does not change the equation of motion for this field, but it does change the pressure, energy density and equation-of-state. In particular, if I choose a sufficiently large positive consant, the equation of state
[tex]w = \frac{\dot \phi^2/2 - V(\phi)}{\dot \phi^2/2+V(\phi)}[/tex]
becomes eventually indistinguishable from -1.

Shouldn't physics stay invariant in this case?
 
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  • #2
Amanheis said:
Quintessence fields are supposed to slowly roll down a potential V(\phi). Adding constants to the potential obviously does not change the equation of motion for this field, but it does change the pressure, energy density and equation-of-state. In particular, if I choose a sufficiently large positive consant, the equation of state
[tex]w = \frac{\dot \phi^2/2 - V(\phi)}{\dot \phi^2/2+V(\phi)}[/tex]
becomes eventually indistinguishable from -1.

Shouldn't physics stay invariant in this case?

yes,this potential is some quantily of energy density deimension and have absolute value to curve the space time.You can't redifine it by adding a constant. It is an extensive quantity right over there.
 

1. What is the equation-of-state and how does it relate to Quintessence potential?

The equation-of-state is a measure of the relationship between the pressure and energy density of a physical system. In the context of Quintessence potential, the equation-of-state describes the behavior of the potential energy as a function of the scalar field that is associated with Quintessence.

2. How does the equation-of-state change with different Quintessence potentials?

The equation-of-state is directly dependent on the form of the Quintessence potential. Different potentials will result in different values of the equation-of-state, which affects the overall behavior and properties of the Quintessence field.

3. How does the equation-of-state affect the expansion rate of the universe?

The equation-of-state plays a crucial role in determining the expansion rate of the universe. A high equation-of-state, or low pressure, will result in accelerated expansion, while a lower equation-of-state will lead to decelerated expansion.

4. Can the equation-of-state be used to differentiate between different models of Quintessence potential?

Yes, the equation-of-state is a key diagnostic tool for distinguishing between different models of Quintessence potential. By measuring the equation-of-state, scientists can determine which model best fits observations of the universe's expansion and other cosmological data.

5. How does the equation-of-state of Quintessence compare to that of Dark Energy?

Quintessence and Dark Energy are both considered to be candidates for explaining the accelerated expansion of the universe. However, they have different equation-of-state behaviors. Quintessence typically has a time-varying equation-of-state, while Dark Energy is typically assumed to have a constant equation-of-state equivalent to that of a cosmological constant.

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