All Questions
Tagged with cosmology homework-and-exercises
136
questions
1
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Cosmological Scalar Field Density Dilution
Consider a homogeneous free scalar field $\phi$ of mass m which has a
potential
$$V(\phi) = \frac{1}{2}m^2\phi^2$$
Show that, for $m ≫ H$, the scalar field undergoes oscillations with
frequency given ...
- 191
0
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0
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20
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Relativistic Fluid Equation - Density Perturbations in Cosmology
While I am deriving the relativistic fluid equation for the radiation component I am getting an extra term like $\vec{v} \cdot \vec{\nabla}P$ where $\vec{v}$ is the velocity and $P$ is the pressure.
...
- 3,122
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60
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Robertson-Walker metric exercise [closed]
I'm trying to solve an exercise from my astrophysics and cosmology class, the request is the following, starting from the RW metric expression:
$$ \begin{equation*}
ds^2=c^2 dt^2 - a^2 \left ( \frac{...
- 41
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60
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Solution for the scale factor for a curved universe containing only matter
In my textbook, Introduction to cosmology by Barbara Ryden, the author gives directly the solution for the following integral if $\Omega_0 > 1$:
$$H_ot = \int^a_0 \frac{da}{[\Omega_0/a + (1-\...
3
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1
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158
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Problem in deriving Friedman equations from Einstein-Hilbert Lagrangian
The Einstein-Hilbert Lagrangian (along with a scalar field) in FRW spacetime reads:
\begin{equation}
\mathcal{L} = - \frac{1}{8 \pi G} (3 a \dot{a}^2 - 3 k a + \Lambda a^3) + \frac{1}{2} \dot{\phi}^2 ...
- 682
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56
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Gravitational potential in an expanding universe during the matter era
In the book Cosmology, by Daniel Baumann, there is an exercise to show, using the Poisson equation, that the gravitational potential is a constant during the matter era. As I understand, the Poisson ...
- 11
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230
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Deriving the Ricci tensor on the flat FLRW metric
I am currently with a difficulty in deriving the space-space components of the Ricci tensor in the flat FLRW metric
$$ds^2 = -c^2dt^2 + a^2(t)[dx^2 + dy^2 + dz^2],$$ to find:
$$R_{ij} = \delta_{ij}[2\...
- 1
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0
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65
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Hydrogen atom in void
We have a hydrogen atom, in a gravitationally bound system nothing interesting happens to it. Let's put it in an empty world where there are only an electron and a proton. Several forces act on it: ...
- 1
1
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3
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279
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Can the age of the universe actually be calculated through Hubble's constant?
I was reading a high-school physics textbook, and it stated that the age of the universe is equal to 1 / Hubble's constant. They even give a derivation: $v = H_{0} D$ and $D = vt$, so subbing in gives ...
- 25
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105
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Area of a sphere in curved 3D space
I'm having trouble finding any information on the derivation of the area of sphere in curved 3D space: $A = 4 \pi S^2_{\kappa}$, where $S_{\kappa} = R_o \sin(r/R_o)$.
How did it come about from $ds^2 =...
- 161
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99
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Are my assumptions about universe thermodynamics right?
Let's find the temperature of universe for times between
$$10^{-30}s-1000\;years$$
These times are bigger than inflation era but smaller than nonrelativistic matter dominance (50000 years) and smaller ...
- 509
1
vote
1
answer
159
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Spin Connection Vanishes?
I'm trying to reproduce a result for the components of the spin connection in FRW spacetime. The formula for the spin connection $\Gamma_{\mu}$ is
$$\Gamma_{\mu} = \frac{1}{2} \Sigma^{a b} L_{a}^{\nu} ...
1
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1
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78
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Clarify derivation: Why is the last term of (5.37) in Modern Cosmology by Dodelson and Schmidt zero?
I'm going through Modern Cosmology by Dodelson and Schmidt 2nd edition, and I'm stuck at (5.37) where they present the Boltzmann equation for dark matter and take the integral of all the terms over ...
- 8,640
1
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63
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Clarify derivation: Relating matter density parameter $\Omega_{\text{m}}$ to the scale factor $a$ at which $\rho_{\text{matter}} = \rho_{\text{rad}}$
The derivation and background here isn't really important. The reader should skip to the bottom of this post for the actual question before reading the background.
Background
In Modern Cosmology by ...
- 8,640
2
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1
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239
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Trying (and failing) to calculate baryon/photon ratio
I'm reading through Modern Cosmology by Dodelson and Schmidt 2nd edition on my own, and at the start of Section 4.2 the book says that we can compute the baryon/photon ratio at the time of big bang ...
- 8,640