The golden days of Cosmology:
A ~five parameter Universe
\Omega_m
\Omega_b
\Omega_\Lambda
A_s
n_s
Initial Conditions
Dynamics
Dark energy
Dark matter
Ordinary matter
Amplitude initial density field
Scale dependence
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/9949238/fs8-1.png)
z \approx 1100
(46 billion light years)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/6926200/pasted-from-clipboard.png)
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![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/6926201/pasted-from-clipboard.png)
P(\mathcal{C}|\,\,\,\,\,\,\,\,\,\,)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/6926201/pasted-from-clipboard.png)
?
(C from 6D to 16D)
The DESI galaxy survey
~ 10 Million galaxies
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/9963459/pasted-from-clipboard.png)
1. Point cloud generation
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/9963639/pasted-from-clipboard.png)
Cosmological parameters
+ Stochasticity initial conditions
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/9262739/pngwing.com.png)
\delta = \frac{\rho - \bar{\rho}}{\bar{\rho}}
t = 380,000 \: \mathrm{years}
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/9270568/pasted-from-clipboard.png)
\delta = \red{F}(\delta_i)
Linear
2. Parameter estimation
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/9270580/pasted-from-clipboard.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/5824826/pasted-from-clipboard.png)
Early Universe
~linear
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/5824855/pasted-from-clipboard.png)
Gravity
Late Universe
Non-linear
Credit: S. Codis+16
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/9265878/pasted-from-clipboard.png)
Non-Guassianity
Second moment not optimal
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/9190560/pasted-from-clipboard.png)
\delta = \frac{\rho - \bar{\rho}}{\bar{\rho}} << 1
\delta >> 1
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/6926201/pasted-from-clipboard.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/6926201/pasted-from-clipboard.png)
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P(\mathcal{C}|\mathrm{GNN}(G))
\mathcal{L} = - \frac{1}{N} \sum_i \log\left(P(\theta|\mathrm{GNN}(G))\right)
(r_{ij}, \theta_{ij}, \phi_{ij})
G(r_\mathrm{max})
Input
Output
Rotation and translation Invariant
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/9963800/pasted-from-clipboard.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/9963801/pasted-from-clipboard.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/993552/images/9963802/pasted-from-clipboard.png)
Current Issues
- Why is 2pcf performing better? Try to predict 2pcf
- Scaling up! Right now using 5000 objects, would like to scale to ~100_000 / 1M
- Graph aggregations seem silly
- Can it really extract all the information there is? i.e. voids
deck
By carol cuesta
deck
- 203