Testing the cosmological Poisson equation in a model-independent way
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910436505419776 |
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| author | Zheng, Ziyang Sakr, Ziad Amendola, Luca |
| author_facet | Zheng, Ziyang Sakr, Ziad Amendola, Luca |
| contents | We show how one can test the cosmological Poisson equation by requiring only the validity of three main assumptions: the energy-momentum conservation equations of matter, the equivalence principle, and the cosmological principle. We first point out that one can only measure the combination ${\mathcal M}\equiv Ω_m^{(0)}μ$, where $μ$ quantifies the deviation of the Poisson equation from the standard one and $Ω_m^{(0)}$ is the fraction of matter density at present. Then we employ a recent model-independent forecast for the growth rate $f(z)$ and the expansion rate $E(z)$ to obtain constraints on ${\mathcal M}$ for a survey that approximates a combination of the Dark Energy Spectroscopic Instrument (DESI) and Euclid. We conclude that a constant ${\mathcal M}$ can be measured with a relative error $σ_{\mathcal{M}}=4.5\%$, while if ${\mathcal M}$ is arbitrarily varying in redshift, it can be measured only to within $13.4\%$ (1 $σ$ c.l.) at redshift $z=0.9$, and 15-22\% up to $z=1.5$. We also project our constraints on some parametrizations of ${\mathcal M}$ proposed in literature, while still maintaining model-independence for the background expansion, the power spectrum shape, and the non-linear corrections. Generally speaking, as expected, we find much weaker model-independent constraints than found so far for such models. This means that the cosmological Poisson equation remains quite open to various alternative gravity and dark energy models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_07436 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Testing the cosmological Poisson equation in a model-independent way Zheng, Ziyang Sakr, Ziad Amendola, Luca Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology We show how one can test the cosmological Poisson equation by requiring only the validity of three main assumptions: the energy-momentum conservation equations of matter, the equivalence principle, and the cosmological principle. We first point out that one can only measure the combination ${\mathcal M}\equiv Ω_m^{(0)}μ$, where $μ$ quantifies the deviation of the Poisson equation from the standard one and $Ω_m^{(0)}$ is the fraction of matter density at present. Then we employ a recent model-independent forecast for the growth rate $f(z)$ and the expansion rate $E(z)$ to obtain constraints on ${\mathcal M}$ for a survey that approximates a combination of the Dark Energy Spectroscopic Instrument (DESI) and Euclid. We conclude that a constant ${\mathcal M}$ can be measured with a relative error $σ_{\mathcal{M}}=4.5\%$, while if ${\mathcal M}$ is arbitrarily varying in redshift, it can be measured only to within $13.4\%$ (1 $σ$ c.l.) at redshift $z=0.9$, and 15-22\% up to $z=1.5$. We also project our constraints on some parametrizations of ${\mathcal M}$ proposed in literature, while still maintaining model-independence for the background expansion, the power spectrum shape, and the non-linear corrections. Generally speaking, as expected, we find much weaker model-independent constraints than found so far for such models. This means that the cosmological Poisson equation remains quite open to various alternative gravity and dark energy models. |
| title | Testing the cosmological Poisson equation in a model-independent way |
| topic | Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2312.07436 |