CQW is an educational resource for theoretical physics and astrophysics, field theory, relativity and cosmology. we post a new question every wednesday for students to get and for teachers to stay in shape.

Wednesday, April 30, 2014

coasting dark energy universe

following up on the CQW from last week: is it possible to construct a dark energy component with an equation of state that would provide a stable balance between acceleration and deceleration and lead to a constant expansion speed?

bonus question: in what ways would this model be distinguishable from a universe with pure curvature?

The DE component would need to have an equation of state $w = -1/3$. According to the Friedmann equations, a universe with this equation of state does not experience an accelerated or decelerated expansion. The energy density of matter and radiation decays faster than this DE component such that the Universe will eventually be dominated by DE and approach $\ddot a = 0$.

If you don't want to wait until the energy fraction in matter and radiation decays by itself, coupled quintessence is an option (cf. Amendola 2000, astro-ph/9908023). There, the Dark Energy 'knows' the other components, and the universe can dynamically approach a future attractor with a total equation of state of $w = -1/3$.

The term 'Dark Energy' might be misleading for this component. Usually, one only denotes effective fluids as Dark Energy that satisfy $w < -1/3$ and thereby allow for an accelerated expansion.

A universe with no matter, no radiation, no Dark Energy in it also has, by the Friedmann equations, no accelerated or decelerated expansion. It differs from the DE model discussed here, however, by its geodesic equation in which the spatial curvature appears. The two scenarios can thus be distinguished by the paths that light rays take through the expanding Universe.

The question is only easy to answer if the Universe does not contain matter and radiation. Perhaps, this restriction should be clarified.

ReplyDeleteThe DE component would need to have an equation of state $w = -1/3$. According to the Friedmann equations, a universe with this equation of state does not experience an accelerated or decelerated expansion. The energy density of matter and radiation decays faster than this DE component such that the Universe will eventually be dominated by DE and approach $\ddot a = 0$.

ReplyDeleteIf you don't want to wait until the energy fraction in matter and radiation decays by itself, coupled quintessence is an option (cf. Amendola 2000, astro-ph/9908023). There, the Dark Energy 'knows' the other components, and the universe can dynamically approach a future attractor with a total equation of state of $w = -1/3$.

The term 'Dark Energy' might be misleading for this component. Usually, one only denotes effective fluids as Dark Energy that satisfy $w < -1/3$ and thereby allow for an accelerated expansion.

A universe with no matter, no radiation, no Dark Energy in it also has, by the Friedmann equations, no accelerated or decelerated expansion. It differs from the DE model discussed here, however, by its geodesic equation in which the spatial curvature appears. The two scenarios can thus be distinguished by the paths that light rays take through the expanding Universe.

It needs to be w=-1/3 and at the critical density to get uniform expansion.

ReplyDelete