Inflation lecture from Guth : why does d(ρ)/dt = 0 ?

In summary, Alan Guth said that the mass density ρ of the Universe is constant, even though the false vaccum energy density, V(Φ)/c2, is not constant.
  • #1
DoobleD
259
20
I watched a video lecture from Alan Guth on inflation (undergrad level), and there is something in it I don't understand.

He first presents the inflation scalar field, Φ, which has an energy density associated with it, V(Φ). V(Φ) is stuck at a local minimum, at Φ = 0 (what is called a "false vaccum") :

23_Inflation_You_Tube.png


He then invoke an equation, derived earlier in the course, which relates the derivative with respect to time of the mass density of the Universe, ρ, to its pressure p :

23_Inflation_You_Tube_1.png


Then, at around 9:43 prof. Guth says that the left-hand side of the equation, d(ρ)/dt, is 0, because the scalar field is stuck at the false vacuum value. Leading to :

23_Inflation_You_Tube_2.png


Where u is the energy density of the Universe.

Here is what bugs me : ρ represents the mass density of the Universe, not the energy density of the false vaccum, V(Φ). I get that V(Φ) is constant, but why does that implies that the mass density ρ is also constant ?
 
Space news on Phys.org
  • #2
I realize that if the false vacuum energy density is constant, the mass density associated with it, V(Φ)/c2, is also constant. But what about the mass density from the primordial matter in the Universe ? This part shouldn't be constant.

BUT, actually, a bit later in the lecture, Guth says that we assume the Universe is dominated by the false vaccum. So, in the equation for d(ρ)/dt, maybe he is simply making the approximation that there is no matter in the Universe, so that ρ is pretty much only the masse density corresponding of the false vacuum energy density ?
 
Last edited:
  • #3
Inflation would quickly dilute any other contribution to the energy density. You can also solve the Friedmann equations with several different components, but if you have a dark energy component, it will dilute much slower than a matter or radiation component. One of the points of inflation is that when it ends you have essentially gotten rid of all other components and you can start to repopulate them by reheating.
 
  • Like
Likes DoobleD
  • #4
Orodruin said:
Inflation would quickly dilute any other contribution to the energy density. You can also solve the Friedmann equations with several different components, but if you have a dark energy component, it will dilute much slower than a matter or radiation component. One of the points of inflation is that when it ends you have essentially gotten rid of all other components and you can start to repopulate them by reheating.

Thank you, that answers the question.
 

1. What is the significance of d(ρ)/dt = 0 in the context of inflation?

Inflation refers to the rapid expansion of the universe in the first moments after the Big Bang. The equation d(ρ)/dt = 0 indicates that the rate of change of the energy density of the universe is constant during inflation. This means that the universe is expanding at a constant rate, allowing for the rapid expansion that is characteristic of inflation.

2. How does d(ρ)/dt = 0 relate to the theory of cosmic inflation proposed by Alan Guth?

In his theory of cosmic inflation, Guth proposed that the universe underwent a period of rapid expansion driven by a hypothetical field known as the inflaton. The equation d(ρ)/dt = 0 is a key component of this theory, as it describes the constant rate of expansion during inflation.

3. Does d(ρ)/dt = 0 apply to the entire duration of inflation?

No, the equation d(ρ)/dt = 0 only applies to the early stages of inflation. As the universe continues to expand, the energy density decreases and the equation is no longer valid. Eventually, inflation comes to an end and the universe enters a period of slower expansion.

4. What evidence supports the equation d(ρ)/dt = 0 during inflation?

One of the key pieces of evidence for cosmic inflation is the observation of cosmic microwave background radiation. This radiation is a remnant of the hot, dense early universe and its patterns and fluctuations provide support for the concept of constant expansion during inflation.

5. How does the equation d(ρ)/dt = 0 impact our understanding of the early universe?

The equation d(ρ)/dt = 0 is a fundamental aspect of the theory of cosmic inflation, which has greatly enhanced our understanding of the early universe. It helps to explain many observed phenomena, such as the uniformity of the universe on a large scale and the absence of certain predicted relics from the Big Bang.

Similar threads

Replies
2
Views
2K
Replies
7
Views
1K
Replies
3
Views
1K
Replies
6
Views
1K
  • Cosmology
Replies
1
Views
1K
Replies
7
Views
2K
Replies
6
Views
2K
  • Electromagnetism
Replies
6
Views
2K
Replies
1
Views
7K
Replies
4
Views
2K
Back
Top