Redshift Drift

1. Redshift Drift

2. Introduction • The redshifts of all cosmologically distant sources are expected to experience a small, systematic drift as a function of time due to the evolution of the Universe’s expansion rate • A measurement of this effect would represent a direct and entirely model-independent determination of the expansion history of the Universe • The redshift drift is a direct, entirely model-independent measurement of the expansion history of the Universe which does not require any cosmological assumptions

3. MEASURING THE DYNAMICS • we observe the change of “a” with time by its wavelength-stretching effect on photons traversing the Universe. • A photon emitted by some object at comoving distance χ at time tem and observed by us at tobs • is a small, systematic drift as a function of time in the redshift of a cosmologically distant source as observed by us today • Measuring for a number of objects at different z hence gives us the function • The point is that given a(z) and , one can reconstruct a(t).

4. MEASURING THE DYNAMICS • A measurement of ˙z(z) therefore amounts to a purely dynamical reconstruction of the expansion history of the Universe. • Predicting the redshift drift ˙z(z) requires a theory of gravity • Two components: 1. cold (dark) matter (CDM) with wm =0 • 2. dark energy in the form of a cosmological constant with

5. MEASURING THE DYNAMICS Redshiftevolution of three objects with present-day redshiftsz(t0) = 0.5, 3 and 8 as a function of time of observation, for three different combinations of omegas. For each case the dotted lines indicate the big bang. The solid (dotted) lines and left-hand axis (right-hand axis) show the redshift drift ˙z (˙v) as a function of redshift

6. The Lyα forest • The term ‘Lyα forest’ refers to the absorption lines observed in the spectra of all quasi-stellar objects (QSOs) shortwards of the Lyα emission line. • The redshift drift is a very small effect • In order to detect it, an experiment must achieve an overall accuracy with which radial velocity shifts can be determined of the order of ∼1 cm/s. • Using Monte Carlo (MC) simulations of the Lyα forest to quantify how its properties translate to a radial velocity accuracy σv • And… • How σvdepends on the instrumental characteristics of the spectra and on redshift

7. Simulated absorption line lists • Forming simulated MC line lists by simply randomly drawing values for the absorption-line parameters from their observed distributions • Each line is characterized by three parameters: redshift, z, HI column density, NHI, and velocity width, b • γ = 2.2, β = 1.5,¯b = 30 km/s and σb = 8 km/s • Imposing: 15 < b < 100 km/s & 12 < logNHI(cm-2) < 16 • First, generating line lists from MC simulations based on the statistics of the largest available samples of absorption lines. • Secondly, to validate the simulations, using eight line lists available in the literature that have previously been derived from high-resolution observations.

8. Real absorption line lists

9. The second epoch • Simulating a ˙z measurement requires a second epoch ‘observation’ of the same LOS: by generating a second epoch absorption line list from the original line list (both real and simulated) • by simply shifting the redshift of each line according to a given cosmological model is: Generating spectra • Given an absorption line list a normalized spectrum is generated by • λ is the observed wavelength, Nal is the number of absorption lines in the spectrum • τ is the optical depth, λα = 1215.67 Å is the rest wavelength of the HI Lyα transition.

10. Defining σv • In principle, a ˙z determination will involve the measurement of radial velocity differences between the corresponding features of a pair of spectra of the same object taken several years apart. • We now need a method to estimate the accuracy to which these differences can be determined. • we begin by expressing the flux observed in pixel i at the second epoch as a small perturbation on the first epoch flux in the same pixel: • small velocity shift Δvifor each pixel • λi is the observed wavelength of the ithpixel • dSi /dλ is the spectral slope of the flux at that pixel • the weight for the ith pixel should be chosen as the inverse variance of Δvi

11. Defining σv • where σ1i and σ2i are the flux errors in the ith pixel of the first and second epoch spectra • σS′iis the error on the slope of the flux at pixel i. • Finally, with the above choice of weights the error on Δv is given by

12. Results The green triangles show the results for simulations where the redshift evolution of the Lyα forest has been switched off, i.e. where γ = 0

13. Results • we can see that the real line lists do not cover the full Lyα forest regions, with differently sized pieces missing both at the low- and high-redshift ends. Therefore we must correct the σv values derived from the real line lists in order to make them directly comparable to the values from the simulated lists. • we find that the accuracy with which a radial velocity shift can be determined from the Lyα forest scales as