We have estimated the $\lambda$ parameter in such a way that the transition red shift is found similar in the deceleration parameter, pressure and the equation of state parameter $\omega$. For this, we have considered field equations of $f(R,T)$ gravity and have taken $f(R,T) = R + 2 \lambda T$, $\lambda$ being an arbitrary constant. In this work, we have developed an FLRW type model of a universe which displays transition from deceleration in the past to the acceleration at the present. A detailed analysis of the cosmological implications of the measurements of the Ly α autocorrelation and the quasar-Ly α cross-correlation will be presented in a future publication, which will include the DR11 results from the Ly α auto-correlation, together with a more complete examination of potential correlations between the two. We have shown that adding the cross-correlation of Ly α and quasars to the autocorrelation of Ly α can certainly improve the constraints on BAO scales at high redshfit. 36 are much less restrictive compared to a flat model. 4 Note that by allowing for space curvature, the Planck constraints on the distance and expansion rate at our mean redshift z = 2. We compare these constraints with the 68% and 95% confidence limits obtained from the Planck results in an open ΛCDM cosmology, shown in green. In figure 6 we compare the contours on ( α, α ⊥ ) from the Ly α auto-correlation function from DR9 ( in blue, generated from the files in baofit/ ), and compare it to our measurement from the cross-correlation function from DR11 (red) and the sum of their χ 2 surfaces (in black), assuming they are independent.
Assuming that the shot noise in the quasar density field is uncorrelated with the small scale fluctuations in the Ly α absorption and with the instrumental noise, we can then combine both BAO measurements as if they were independent. 05 h Mpc − 1 ) cosmic variance is not the dominant contribution to our error budget. In the same appendix we also show that on the scales of interest for BAO measurements ( k > 0. The Fisher forecast formalism predicted similar uncertainties in α ⊥, and we find that our measurement is ∼ 20% better than the extrapolated results from the autocorrelation. Our measurement of α is ∼ 55% worse than the results from the Ly α auto-correlation of extrapolated to DR11, in good agreement with the prediction of ∼ 40% computed in the appendix. In this analysis we used data cuts similar to those in, and therefore we compare here our uncertainties with those from extrapolated to DR11 (see table 4). Most of the difference between the uncertainties in these results can be explained by the looser data cuts used in, that included lines with DLAs and that defined their Ly α forest with a wider wavelength range. The measurement of BAO from the Ly α auto-correlation in DR9 was presented in and. In a BOSS-like survey, both probes should measure the transverse BAO scale with similar uncertainties, while the Ly α auto-correlation should be able to measure the line of sight scale ∼ 40% better than the cross-correlation with quasars. In appendix B we present a Fisher matrix projection comparing the relative strength of measuring BAO with the Ly α auto-correlation and with the quasar-Ly α cross-correlation. although a detailed study on mock data sets revealed a large scatter in the gain from realization to realization.
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