Lights' speed is constant, just because it is being effected by gravity does not mean it slows down, it just takes a slightly longer path. And yes, we know how fast light goes, it has been calculated in a vacuum.
Also Neutrinos are not effected by mass, so density is not a factor.
From:
http://www.desy.de/user/projects/Physics/Relativity/SpeedOfLight/speed_of_light.htmlIs The Speed of Light Constant?
There are a number of senses to the meaning of this question and so there are a number of different answers. Firstly . . .
Does the speed of light change in air or water?
Yes. Light is slowed down in transparent media such as air, water and glass. The ratio by which it is slowed is called the refractive index of the medium and is always greater than one.* This was discovered by Jean Foucault in 1850.
When people talk about "the speed of light" in a general context, they usually mean the speed of light in a vacuum. This quantity is also referred to as c.
Is c, the speed of light in vacuum, constant?
At the 1983 Conference Generale des Poids et Mesures, the following SI (Systeme International) definition of the metre was adopted:
The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.
This defines the speed of light in vacuum to be exactly 299,792,458 m/s. This provides a very short answer to the question "Is c constant": Yes, c is constant by definition!