# Dark energy time dilation

I have read here that dark energy is somewhat like negative mass. Here Wikipedia states:

... that the cosmological constant required that 'empty space takes the role of gravitating negative masses which are distributed all over the interstellar space'.

If you take the equation for spherically symmetric time dilation $$t_0 = t_f \sqrt{1 - \frac{2GM}{rc^2}}$$ and substitute a negative mass, you get a $$t_0 >1$$ time dilation factor, suggesting that time moves faster under gravitating negative masses.

Is this consistent with observations (say, are photons traveling through the intergalactic medium 'time-accelerated' [I have never heard of such a thing, so this must be wrong]) or is dark energy not a gravitating negative mass, or am I looking at this all wrong?

The Wikipedia article is inaccurate. Dark energy doesn't act like negative mass. It acts more like a combination of some mass and some negative pressure.

It's not accurate to describe that equation from the WP article as "the" equation for time dilation. It applies to a spherically symmetric gravitational field, in vacuum. That's not what cosmological models look like.

The concept of gravitational time dilation only means anything in a static gravitational field. It isn't a well-defined concept in a cosmological model, which isn't static.

• By saying dark energy acts like "some mass," do you mean our familiar positive mass? Also, in the first question I linked, the answers seem to suggest that dark energy could be negative mass. (The answers don't directly address it, but they seem to treat it as given that dark energy acts like negative mass except that particles are expected to diffuse as space expands.) I've also seen serious research into the idea arxiv.org/pdf/1712.07962 – BMF Sep 26 '19 at 20:46
• I'm a layman with this. I used the spherically-symmetric equation to describe the generic case of just a static, symmetric, negative gravitational field. I don't know the first thing about cosmological models, but are the properties of a negative gravitational field different when nonstatic and asymmetric? (Does it not have a >1 time dilation factor?) – BMF Sep 26 '19 at 20:49
• @BMF: For the sign of $\Lambda$ that we observe in our universe, dark energy acts like a perfect fluid with a positive mass-energy density and a negative pressure. Also, in the first question I linked, the answers seem to suggest that dark energy could be negative mass. No, they don't. And it's good that they don't, because that would be incorrect. I've also seen serious research into the idea arxiv.org/pdf/1712.07962 That paper is discussing a whole different, non-mainstream model. – user4552 Sep 26 '19 at 21:37
• Actually, most of the answers do suggest negative mass particles could act as dark energy, while others present the issues with the idea or refute it. So, based on the mainstream lambda-CDM model, dark energy does not curve space-time as if it were negative mass? Being an energy density, does it curve space-time at all? Also, do you have any further reading suggestions for lambda-CDM dark energy? – BMF Sep 26 '19 at 21:56
• @BMF: The source of spacetime curvature is not mass, it's the stress-energy tensor. – user4552 Sep 27 '19 at 21:45