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##### Questions and discussions regarding the projects / Re: Task 4

« Last post by**Anonymous**on

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**Today**at 14:06I see, thank you Any tips on the interval w should take?

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I see, thank you Any tips on the interval w should take?

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If you completed task 6 you now have a code that evaluates \( \chi ^2 \) as a function of \( \Omega_{\rm m 0} \) and $\Omega_{\Lambda 0}$. All you need to do then is to change the part of the code where the Hubble parameter is evaluated, and calculate \( \chi ^2 \) as a function of \( \Omega_{w0} \) and \( w \) on a suitably chosen grid of values for those parameters.

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Okay, so I chose different values for all three variables: \( \Omega_{m0},\Omega_{w0} \) and w. Not just w. I see:)

I am also wondering how we can find a value for w on task 7. I know (think at least) how I should go about to find \( \Omega_{w0} \) with the code I made in 6. But I don't quite understand how to find a w-value from this.

I am also wondering how we can find a value for w on task 7. I know (think at least) how I should go about to find \( \Omega_{w0} \) with the code I made in 6. But I don't quite understand how to find a w-value from this.

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Yes. Just try different values of \( w \) (but always choose w<-1 in this task), \( \Omega_{w0} \), and

\( \Omega_{\rm m 0} \), make plots, see how \( a \) will behave in each case, and report what you find.

\( \Omega_{\rm m 0} \), make plots, see how \( a \) will behave in each case, and report what you find.

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Hi, I am struggling to understand what is meant by varying w.

Are we supposed to choose a certain value of \( \Omega_{m0} \) and \( \Omega_{w0} \) (which as I have undserstood is \( \Omega_{\Lambda0} \) since we are studying the \( \Lambda CDM \) model) and just vary the power of the latter? Speaking more technically, should we just plot this

\[ -\left( \frac{\Omega_{m0}}{x}+\frac{\Omega_{\Lambda0}}{x^{1+3w}}\right) \]

for different values of w?

Are we supposed to choose a certain value of \( \Omega_{m0} \) and \( \Omega_{w0} \) (which as I have undserstood is \( \Omega_{\Lambda0} \) since we are studying the \( \Lambda CDM \) model) and just vary the power of the latter? Speaking more technically, should we just plot this

\[ -\left( \frac{\Omega_{m0}}{x}+\frac{\Omega_{\Lambda0}}{x^{1+3w}}\right) \]

for different values of w?

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Here are some basic questions about how thing evolve with time (we are looking for \( n \sim 1/ a^3\) type of answers). These things are very useful to know (and something you should know) when trying to understand things in cosmology and especially when we just want to estimate roughly how things evolve which comes up quite often so its good to review them and make sure you know it by heart as they come up again and again:

**[1] ** What is the definition of the equation of state \(w\)? What is the equation of state for all the components (baryons, CDM, photons, neutrinos, dark energy (cosmological constant) and curvature)?

**[2]** How does the energy density \(\rho(a)\) of the different components vary with the scale-factor? How can we explain the result for matter and radiation physically?

**[3]** What equation of state (for the total matter budget) do we need to get accelerated expansion \(\ddot{a} > 0\)

**[4]** How does the Hubble factor evolve with \(a\) (i.e. \( H \sim a^n\)) in the radiation and matter eras? What is \(H\) when dark energy dominates? What is \(a(t)\) when \(H\) is constant?

**[5]** How does the temperature evolve with scalefactor \(T(a)\) ?

**[6]** How does the energy density \(\rho\) and numberdensity \(n\) evolve with temperature \(T\) for a relativistic gas?

**[7]** What is the energy density \(\rho\) in terms of the number density \(n\) for non-relativistic matter?

**[8]** How does the conformal time \(\eta \) evolve with both \(\mathcal{H}\) and \(a\) in the radiation dominated era?

**[9]** What are some different measures of time in cosmology (name atleast 3) and how are they related?

**[10]** What is the definition of matter-radiation equality and at roughly what redshift is this in our Universe? At (roughly) what redshift, time and temperature is the CMB released? At what redshift does dark energy start to dominate?

**[11]** We often have to change between different times. What is \(\frac{d}{dt}\) in terms of \(\frac{d}{dx}\) (\(x=\log a\)) ? What is \(\frac{d}{d\eta}\) in terms of \(\frac{d}{dt}\) ? (Chain rule)

See also https://cmb.wintherscoming.no/problems.php#b8

See also https://cmb.wintherscoming.no/problems.php#b8

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Next week I was thinking we would skip normal lectures and focus on working on the project and/or solving some problem sets. What do you guys want?

For the problem set option I thought about giving you a list of problems on monday so you have the opportunity to look over it beforehand and then go through them in the usual lecture slot (live or on zoom).

For the project help you can for example bring laptops and we can provide some help (or do something over zoom).

We could also review some things we have gone through in the lectures (which has been a lot so I'm sure there are many things that are not super clear - the good thing is that we are close to done with the theory part of the course and will mainly be focusing on understanding the stuff we have gone through so far)

If there are other suggestions we are open to that so please add it below.

For the problem set option I thought about giving you a list of problems on monday so you have the opportunity to look over it beforehand and then go through them in the usual lecture slot (live or on zoom).

For the project help you can for example bring laptops and we can provide some help (or do something over zoom).

We could also review some things we have gone through in the lectures (which has been a lot so I'm sure there are many things that are not super clear - the good thing is that we are close to done with the theory part of the course and will mainly be focusing on understanding the stuff we have gone through so far)

If there are other suggestions we are open to that so please add it below.

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We will look at the formation of the first neutral atoms, an epoch known as recombination, 4.7 in the lecture notes. This epoch was also important for the cosmic microwave background.

Why is the baryyyon-to-photon ratio so small? We will look at this question and learn that the real mystery is why there are any baryons at all. Then we will go through the so-called Sakharov conditions that a successful theory of so-called baryogenesis must satisfy. This material is not covered in the lecture notes.

Why is the baryyyon-to-photon ratio so small? We will look at this question and learn that the real mystery is why there are any baryons at all. Then we will go through the so-called Sakharov conditions that a successful theory of so-called baryogenesis must satisfy. This material is not covered in the lecture notes.

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Er det mulig å få kommentar på prosjektet med hva som var bra og hva man kunne gjort bedre i tillegg til poengsum? Eller vil vi bare få poengsum?

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Dette er for å få en fornemelse av om dere ville delta eller ikke.