# Benjamin L’Huillier(벤자민)

Cosmologist and Astrophysicist, Research Fellow at KASI, Daejeon, South Korea

# Cosmology

## Model-independent reconstruction of the expansion history

L'Huiller & Shafieloo (2017) JCAP01(2017)015, arXiv:1606.06832

With Arman Shafieloo, we have used the luminosity distances from the JLA supernovae compilation to reconstruct model-independently the expansion history of the Universe. We combined it with measurements of $H(z)$ and $d_\mathrm{A}(z)$ from BOSS DR12 to test in a model-independent fashion the Friedman-Lemaitre-Robertson-Walker metric and the flatness of the Universe

The data are available upon request.

## Model-independent measurement of $H_0 r_\mathrm{d}$

We can write $$H_0r_\mathrm{d} = \frac{H(z)r_\mathrm{d}} {h(z)}, \qquad (1)$$ where (assuming a flat Universe) $h(z) = 1/\mathcal{D}'(z)$.

Another way to express $H_0r_\mathrm{d}$, which does not assume flatness, is $$H_0r_\mathrm{d} = \frac {c}{1+z} \frac{r_\mathrm{d}}{d_\mathrm{A}(z)} \mathcal{D}(z). \qquad (2)$$

## Model-independent test of the FLRW metric and the flatness of the Universe

We calculated $$\mathcal{O}_k(z) = \frac{(H(z)\mathcal{D}'(z))^2-1}{\mathcal{D^2(z)}} \qquad (3)$$ and $$\Theta(z) = H(z)\mathcal{D'}(z). \qquad (4)$$ For a FLRW metric, one has $\mathcal{O}_k(z) = \Omega_k$ (constant), therefore $\mathcal{O}_k(z)=0$ for a flat-FLRW. This translates as $\Theta(z) = 1$.

This can be rewritten as $$\Theta(z) = \frac c {1+z} d_\mathrm{A}(z) H(z) \frac{\mathcal{D}'(z)}{\mathcal{D}(z)}, \qquad (5)$$ which can be fully expressed in terms of BAO and supernovae data. Fig. 3 shows $\mathcal{O}_k(z)$ and $\Theta(z)$ for each reconstruction of Fig. 1.

Coming soon