Relativistic effects in Lyman-alpha forest

TL;DR

This paper calculates relativistic effects in the Lyman-alpha forest, demonstrating their significance in cross-correlation measurements and proposing an observable to detect these effects, which are crucial for testing gravity theories.

Contribution

First to extend relativistic correction formalism to Lyman-alpha forest at redshift 2-5 and apply it to Quasar-Lyman-alpha cross-correlation analysis.

Findings

Relativistic effects are significant at BAO scales due to bias differences.

The anti-symmetric part of the cross-correlation isolates relativistic signals.

Relativistic effects must be included in future survey data analyses.

Abstract

We present the calculation of the Lyman-alpha (Lyman-$\alpha$) transmitted flux fluctuations with full relativistic corrections to the first order. Even though several studies exist on relativistic effects in galaxy clustering, this is the first study to extend the formalism to a different tracer of underlying matter at unique redshift range ($z=2-5$). Furthermore, we show a comprehensive application of our calculations of the Quasar-Lyman-$\alpha$ cross-correlation function. Our results indicate that the signal of relativistic effects is sizeable at Baryonic Acoustic Oscillation (BAO) scale mainly due to the large difference in density bias factors of our tracers. We construct an observable, the anti-symmetric part of the cross-correlation function, that is dominated by the relativistic signal and offers a new way to measure the relativistic terms at relatively small scales. The analysis shows that relativistic effects are important when considering cross-correlations between tracers with very different biases, and should be included in the data analysis of the current and future surveys. Moreover, the idea presented in this paper is highly complementary to other techniques and observable trying to isolate the effect of the relativistic corrections and thus test the validity of the theory of gravity beyond the Newtonian regime.