If the universe is modelled as a fluid, without viscosity and heat-conductivity, a stress tensor is used involving density and pressure. I can understand (I think) the significance of density (the density of matter on a scale rather larger than the galactic scale); what is the significance of pressure? Do galaxies "collide"?
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In cosmology, what is meant by pressure?
- Thread starter NJF
- Start date
When we normally think of fluids and pressure , the forces we deal with are actually associated with pressure differentials.
When pressure is used in the cosmological sense , the (gravitational) forces involved are associated with the energy content of space.Normal ,attractive gravity (due to mass and energy) is associated with positive pressure energy and expansive gravity (due to dark energy) is associated with negative pressure energy.
Galaxies do collide --our own Milky Way and the Andromeda galaxy have such a date in the future
When pressure is used in the cosmological sense , the (gravitational) forces involved are associated with the energy content of space.Normal ,attractive gravity (due to mass and energy) is associated with positive pressure energy and expansive gravity (due to dark energy) is associated with negative pressure energy.
Galaxies do collide --our own Milky Way and the Andromeda galaxy have such a date in the future
When we normally think of fluids and pressure , the forces we deal with are actually associated with pressure differentials.
When pressure is used in the cosmological sense , the (gravitational) forces involved are associated with the energy content of space.Normal ,attractive gravity (due to mass and energy) is associated with positive pressure energy and expansive gravity (due to dark energy) is associated with negative pressure energy.
Galaxies do collide --our own Milky Way and the Andromeda galaxy have such a date in the future
When pressure is used in the cosmological sense , the (gravitational) forces involved are associated with the energy content of space.Normal ,attractive gravity (due to mass and energy) is associated with positive pressure energy and expansive gravity (due to dark energy) is associated with negative pressure energy.
Galaxies do collide --our own Milky Way and the Andromeda galaxy have such a date in the future
When we normally think of fluids and pressure , the forces we deal with are actually associated with pressure differentials.
When pressure is used in the cosmological sense , the (gravitational) forces involved are associated with the energy content of space.Normal ,attractive gravity (due to mass and energy) is associated with positive pressure energy and expansive gravity (due to dark energy) is associated with negative pressure energy.
Galaxies do collide --our own Milky Way and the Andromeda galaxy have such a date in the future
When pressure is used in the cosmological sense , the (gravitational) forces involved are associated with the energy content of space.Normal ,attractive gravity (due to mass and energy) is associated with positive pressure energy and expansive gravity (due to dark energy) is associated with negative pressure energy.
Galaxies do collide --our own Milky Way and the Andromeda galaxy have such a date in the future
When we normally think of fluids and pressure , the forces we deal with are actually associated with pressure differentials.
When pressure is used in the cosmological sense , the (gravitational) forces involved are associated with the energy content of space.Normal ,attractive gravity (due to mass and energy) is associated with positive pressure energy and expansive gravity (due to dark energy) is associated with negative pressure energy.
Galaxies do collide --our own Milky Way and the Andromeda galaxy have such a date in the future
When pressure is used in the cosmological sense , the (gravitational) forces involved are associated with the energy content of space.Normal ,attractive gravity (due to mass and energy) is associated with positive pressure energy and expansive gravity (due to dark energy) is associated with negative pressure energy.
Galaxies do collide --our own Milky Way and the Andromeda galaxy have such a date in the future
When we normally think of fluids and pressure , the forces we deal with are actually associated with pressure differentials.
When pressure is used in the cosmological sense , the (gravitational) forces involved are associated with the energy content of space.Normal ,attractive gravity (due to mass and energy) is associated with positive pressure energy and expansive gravity (due to dark energy) is associated with negative pressure energy.
Galaxies do collide --our own Milky Way and the Andromeda galaxy have such a date in the future
When pressure is used in the cosmological sense , the (gravitational) forces involved are associated with the energy content of space.Normal ,attractive gravity (due to mass and energy) is associated with positive pressure energy and expansive gravity (due to dark energy) is associated with negative pressure energy.
Galaxies do collide --our own Milky Way and the Andromeda galaxy have such a date in the future
?
'.. ...'
Guest
If it is assumed that for the universe: -
i. Space-time may be cut into hyper-surfaces (metrics h(ij)) of constant time, which are homogeneous and isotropic.
ii. the mean-rest frames of the galaxies agree with the definition of simultaneity.
Co-moving coordinates may be adopted in which each galaxy has no random velocity but has a fixed set of coordinates x(i), 1, 2, 3, ... With the time coordinates, the proper time for each galaxy will be found from the time-dependent metric coefficients. Thus, if at one moment, t0 the hyper-surface of constant time has a line element
dl²(t0) =h(ij)(t0)dx(i)dx(j)
(The brackets contain the coefficients). The expansion hyper-surfaces can be represented as follows: -
dl²(t1) =f(t1, t0).h(ij)(t0)dx(i)dx(j)
........ =h(ij)(t1)dx(i)dx(j)
It is assumed that the h(ij)'s expand at the same rate to maintain isotropic expansion. In general this equation, in terms of the overall scale factor R, is: -
dl²(t) =R².h(ij)(t0)dx(i)dx(j)
By constraining the requirement for homogeneity and isotropy, places R = constant = k. It is, thus, possible to derive the Robertson-Walker metric for cosmological space-time, namely: -
ds² = -dt² + R²(t).((dr²/(1 - kr²)) + r².dΩ)
In this metric k may take values 1, 0, -1 and give rise to: closed or spherical, Euclidean, and or hyperbolic or open space-time respectively.
If the universe is filled with a perfect fluid ρ = ρ(t), p = p(t). If the stress-energy tensor T(μν;ν) = 0, then due to spacial homogeneity, only the time component will be non-trivial and it is possible to show: -
d(ρR³) = -pd(R³)
__ .......... __
dt ........... dt
where R(t) is the cosmological expansion factor. Here R³ is proportional to the volume of any fluid element. Thus, the LHS of the equation is the rate of energy total change, whilst the RHS is the work done -pdV whilst it expands.
In the current 'matter dominated' era p=0, thus, the equation becomes : -
d(ρR³) = 0
__
dt
In the early radiation dominated era, the main energy density is that of radiation of relativistic particles (equation p = ⅓p), thus, the equation becomes: -
d(ρR³) = -⅓pd(R³)
__ ............ __
dt ............. dt
Thus, to answer your question - within this idealised model - galaxies do not collide and pressure is only significant during the radiation dominated era of the universe. The density is a measure of the cosmological scale factor (see above argument).
I hope this helps!!
i. Space-time may be cut into hyper-surfaces (metrics h(ij)) of constant time, which are homogeneous and isotropic.
ii. the mean-rest frames of the galaxies agree with the definition of simultaneity.
Co-moving coordinates may be adopted in which each galaxy has no random velocity but has a fixed set of coordinates x(i), 1, 2, 3, ... With the time coordinates, the proper time for each galaxy will be found from the time-dependent metric coefficients. Thus, if at one moment, t0 the hyper-surface of constant time has a line element
dl²(t0) =h(ij)(t0)dx(i)dx(j)
(The brackets contain the coefficients). The expansion hyper-surfaces can be represented as follows: -
dl²(t1) =f(t1, t0).h(ij)(t0)dx(i)dx(j)
........ =h(ij)(t1)dx(i)dx(j)
It is assumed that the h(ij)'s expand at the same rate to maintain isotropic expansion. In general this equation, in terms of the overall scale factor R, is: -
dl²(t) =R².h(ij)(t0)dx(i)dx(j)
By constraining the requirement for homogeneity and isotropy, places R = constant = k. It is, thus, possible to derive the Robertson-Walker metric for cosmological space-time, namely: -
ds² = -dt² + R²(t).((dr²/(1 - kr²)) + r².dΩ)
In this metric k may take values 1, 0, -1 and give rise to: closed or spherical, Euclidean, and or hyperbolic or open space-time respectively.
If the universe is filled with a perfect fluid ρ = ρ(t), p = p(t). If the stress-energy tensor T(μν;ν) = 0, then due to spacial homogeneity, only the time component will be non-trivial and it is possible to show: -
d(ρR³) = -pd(R³)
__ .......... __
dt ........... dt
where R(t) is the cosmological expansion factor. Here R³ is proportional to the volume of any fluid element. Thus, the LHS of the equation is the rate of energy total change, whilst the RHS is the work done -pdV whilst it expands.
In the current 'matter dominated' era p=0, thus, the equation becomes : -
d(ρR³) = 0
__
dt
In the early radiation dominated era, the main energy density is that of radiation of relativistic particles (equation p = ⅓p), thus, the equation becomes: -
d(ρR³) = -⅓pd(R³)
__ ............ __
dt ............. dt
Thus, to answer your question - within this idealised model - galaxies do not collide and pressure is only significant during the radiation dominated era of the universe. The density is a measure of the cosmological scale factor (see above argument).
I hope this helps!!
When we normally think of fluids and pressure , the forces we deal with are actually associated with pressure differentials.
When pressure is used in the cosmological sense , the (gravitational) forces involved are associated with the energy content of space.Normal ,attractive gravity (due to mass and energy) is associated with positive pressure energy and expansive gravity (due to dark energy) is associated with negative pressure energy.
Galaxies do collide --our own Milky Way and the Andromeda galaxy have such a date in the future
When pressure is used in the cosmological sense , the (gravitational) forces involved are associated with the energy content of space.Normal ,attractive gravity (due to mass and energy) is associated with positive pressure energy and expansive gravity (due to dark energy) is associated with negative pressure energy.
Galaxies do collide --our own Milky Way and the Andromeda galaxy have such a date in the future