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Dark Energy Spectroscopic Instrument, or DESI at the end of it's 5 years operation will create the largest 3-D spectroscopic map of the universe.
How the data collected during 5 year DESI operation will be analyzed with regards to finding out what dark energy really is?
Please have a look at this forecast paper: 1611.00036. I will cite some important figures.
There are two important observables in the large-scale structures: Baryon Acoustic Oscillations(BAO) and Redshift-space Distortions(RSD). BAO tells us the expansion history of the universe, so measuring BAO puts constraints on the equation of state(EoS) of dark energy.
For example, if the EoS is parameterized like $w=w_0+w_a(1-a)$. DESI expects to see such a contour plot($68\%$ limit) if the "true" value is $w_0=-1$ and $w_a=0$:
Here "P" means Planck prior and "BB" means the case when board band information (the shape of measured density power spectrum) is used. Blue line is previous result obtained by BOSS project, so we see huge improvements.
Similarly, RSD tells us how structures are clustered and grow, while different gravity theories predict different growth rate. Therefore DESI will give stronger constraints on gravity theory (modified gravity is an alternative explanation of the acceleration of the universe):
And of course DESI will have better measurement of the total amount of dark energy:
update:
It is a long story from raw data to cosmological parameters, but the procedure can be briefly but not precisely summarized:
The raw data is the positions (RA, DEC, redshift) of many galaxies/quasars. These positions will be transformed into statistics, e.g. power spectrum and correlation function.
And then people adopt one kind of parameterization/model to establish the likelihood $\mathcal{L}(d|\boldsymbol{\theta})$, here $d$ means data and $\boldsymbol{\theta}$ means parameters.
With the aid of Bayes theorem $p(\boldsymbol{\theta}|d)\propto\mathcal{L}(d|\boldsymbol{\theta})p_{\mathrm{prior}}(\boldsymbol{\theta})$, we will obtain the constraints/measurements on these parameters.
From Martini et al. 2018:
The Dark Energy Spectroscopic Instrument (DESI) to measure the expansion history of the Universe using the Baryon Acoustic Oscillation technique. The spectra of 35 million galaxies and quasars over 14000 sqdeg is measured during the life of the experiment. A new prime focus corrector for the KPNO Mayall telescope delivers light to 5000 fiber optic positioners. The fibers in turn feed ten broad-band spectrographs.
A large amount of images was recorded, from 1,000 to 3,000 depending on the spectrograph during the performance series phase, and about 23,000 in total. Not all these data have been analyzed, among them there is a lot of dark images. Most images have been acquired for a specific purpose, but could be used later on for another. For instance this has proven useful to understand an issue found with the collimator coating.
