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, November 18, 2015

let it rip!

what property of dark energy would lead to an infinite scale factor in a finite time in the future? would a cosmological constant be able to do this?

A universe with only a cosmological constant, the de Sitter universe, is exponential expansion. This is also the asymptotic state of many cosmological models which expand forever. In this special case, the Hubble sphere is an event horizon. (In general, this is not the case. This led to some confusion decades ago, perhaps because the de Sitter model was often used as a model of the expanding universe. This was all cleared up in Rindler's landmark paper in MNRAS in the 1950s. Nevertheless, some people have apparently not read the literature and there are some recently published papers which are simply wrong concerning horizons, the Hubble sphere, etc.)

Exponential expansion leads to an infinite scale factor, but in an infinite time. In such a universe, the Hubble sphere and, more importantly in this context, the event horizon, is at a fixed proper distance. So, nothing strange happens, but with time everything which is not gravitationally bound to an observer will recede from view as it crosses the event horizon. (More precisely, from the observer's point of view, it will become infinitely redshifted.)

The cosmological constant corresponds to w = -1, where Iw is the equation of state. If this is < -1, then the event horizon will contract with time. This means that for any scale, the event horizon will eventually become smaller, and different parts of such an object will a) be out of causal contact and b) move away from each other even faster than exponentially.

So, the big rip is possible if w < -1. Since the cosmological constant has w = 1, this won't happen if dark energy is the cosmological constant.

A universe with only a cosmological constant, the de Sitter universe, is exponential expansion. This is also the asymptotic state of many cosmological models which expand forever. In this special case, the Hubble sphere is an event horizon. (In general, this is not the case. This led to some confusion decades ago, perhaps because the de Sitter model was often used as a model of the expanding universe. This was all cleared up in Rindler's landmark paper in

ReplyDeleteMNRASin the 1950s. Nevertheless, some people have apparently not read the literature and there are some recently published papers which are simply wrong concerning horizons, the Hubble sphere, etc.)Exponential expansion leads to an infinite scale factor, but in an infinite time. In such a universe, the Hubble sphere and, more importantly in this context, the event horizon, is at a fixed proper distance. So, nothing strange happens, but with time everything which is not gravitationally bound to an observer will recede from view as it crosses the event horizon. (More precisely, from the observer's point of view, it will become infinitely redshifted.)

The cosmological constant corresponds to

w= -1, whereIwis the equation of state. If this is < -1, then the event horizon will contract with time. This means that for any scale, the event horizon will eventually become smaller, and different parts of such an object will a) be out of causal contact and b) move away from each other even faster than exponentially.So, the big rip is possible if

w< -1. Since the cosmological constant hasw= 1, this won't happen if dark energy is the cosmological constant.