Relativistic corrections to the power spectrum
The matter power spectrum is key to understanding the growth of large-scale structure in the Universe. Upcoming surveys of galaxies in the optical and HI will probe increasingly large scales, approaching and even exceeding the Hubble scale at the survey redshifts. On these cosmological scales, surveys can in principle provide the best constraints on dark energy (DE) and modified gravity models and will be able to test general relativity itself. However, in order to realise the potential of these surveys, we need to ensure that we are using a correct analysis, i.e. a general relativistic analysis, on cosmological scales. There are two fundamental issues underlying the general relativistic (GR) analysis. Firstly, we need to correctly identify the galaxy overdensity that is observed on the past light cone. Secondly, we need to account for all the distortions arising from observing on the past light cone, including redshift distortions (with all general relativistic effects included) and volume distortions. These general elativistic effects appear in the angular power spectra of matter in redshift space. We compute these quantities, taking into account all general relativistic large-scale effects, and including the important contributions from redshift space distortions and lensing convergence. This is done for self-consistent models of DE, known as ‘quintessence’, which have only been very recently treated in the GR approach. Particularly, we focus mainly on computing the predictions (i.e. the power spectra) that need to be confronted with future data. Hence we compute the GR angular power spectra, correcting the 3D Newtonian calculation for several quintessence models. We also compute the observed 3D power spectra for interacting DE (which until now have not previously been studied in the GR approach) – in which dark matter and DE exchange energy and momentum. Interaction in the dark sector can lead to large-scale deviations in the power spectrum, similar to GR effects or modified gravity. For the quintessence case, we found that the DE perturbations make only a small contribution on the largest scales, and a negligible contribution on smaller scales. Ironically, the DE perturbations remove the false boost of large-scale power that arises if we impose the (unphysical) assumption that the DE perturbations vanish. However, for the interacting DE (IDE) case, we found that if relativistic effects are ignored, i.e. if they are not subtracted in order to isolate the IDE effects, the imprint of IDE will be incorrectly identified – which could lead to a bias in constraints on IDE, on horizon scales. Moreover, we found that on super-Hubble scales, GR corrections in the observed galaxy power spectrum are able to distinguish a homogeneous DE (being one whose density perturbation in comoving gauge vanishes) from the concordance model (and from a clustering DE) – at low redshifts and for high magnification bias. Whereas the matter power spectrum is incapable of distinguishing a homogeneous DE from the concordance model. We also found that GR effects become enhanced with decreasing magnification bias, and with increasing redshift.