Employing a nonparametric approach of the principal component analysis (PCA), we forecast the future constraint on the equation of state $w(z)$ of dark energy, and on the effective Newton constant $mu(k,z)$, which parameterise the effect of modified
gravity, using the planned SKA HI galaxy survey. Combining with the simulated data of Planck and Dark Energy Survey (DES), we find that SKA Phase 1 (SKA1) and SKA Phase 2 (SKA2) can well constrain $3$ and $5$ eigenmodes of $w(z)$ respectively. The errors of the best measured modes can be reduced to 0.04 and 0.023 for SKA1 and SKA2 respectively, making it possible to probe dark energy dynamics. On the other hand, SKA1 and SKA2 can constrain $7$ and $20$ eigenmodes of $mu(k,z)$ respectively within 10% sensitivity level. Furthermore, 2 and 7 modes can be constrained within sub percent level using SKA1 and SKA2 respectively. This is a significant improvement compared to the combined datasets without SKA.
If dark energy and dark matter interact via exchange of energy and momentum, then this may affect the galaxy power spectrum on large scales. When this happens, it may be degenerate with the signal from primordial non-Gaussianity via scale-dependent b
ias. We consider a class of interacting dark energy models and show that the matter overdensity is scale-dependent on large scales. We estimate the effective non-Gaussianity arising from the large-scale effects of interaction in the dark sector. The signal of dark sector interaction can be disentangled from a primordial non-Gaussian signal by measuring the power at two redshifts.
We present a detailed derivation of the observed galaxy number over-density on cosmological scales up to second order in perturbation theory. We include all relativistic effects that arise from observing on the past lightcone. The derivation is in a
general gauge, and applies to all dark energy models (including interacting dark energy) and many modified gravity models. The result will be important for accurate cosmological parameter estimation, including non-Gaussianity, since all projection effects need to be taken into account. It also offers the potential for new probes of General Relativity, dark energy and modified gravity. This paper accompanies Paper I which presents the key results for the concordance model in Poisson gauge.
We present the galaxy number overdensity up to second order in redshift space on cosmological scales for a concordance model. The result contains all general relativistic effects up to second order that arise from observing on the past light cone, in
cluding all redshift effects, lensing distortions from convergence and shear, and contributions from velocities, Sachs-Wolfe, integrated SW and time-delay terms. This result will be important for accurate calculation of the bias on estimates of non-Gaussianity and on precision parameter estimates, introduced by nonlinear projection effects.
Galaxy clustering on very large scales can be probed via the 2-point correlation function in the general case of wide and deep separations, including all the lightcone and relativistic effects. Using our recently developed formalism, we analyze the b
ehavior of the local and integrated contributions and how these depend on redshift range, linear and angular separations and luminosity function. Relativistic corrections to the local part of the correlation can be non-negligible but they remain generally sub-dominant. On the other hand, the additional correlations arising from lensing convergence and time-delay effects can become very important and even dominate the observed total correlation function. We investigate different configurations formed by the observer and the pair of galaxies, and we find that the case of near-radial large-scale separations is where these effects will be the most important.
Quintessence can cluster only on horizon scales. What is the effect on the observed matter distribution? To answer this, we need a relativistic approach that goes beyond the standard Newtonian calculation and deals properly with large scales. Such an
approach has recently been developed for the case when dark energy is vacuum energy, which does not cluster at all. We extend this relativistic analysis to deal with dynamical dark energy. Using three quintessence potentials as examples, we compute the angular power spectrum for the case of an HI intensity map survey. Compared to the concordance model with the same small-scale power at z=0, quintessence boosts the angular power by up to ~15% at high redshifts, while power in the two models converges at low redshifts. The difference is mainly due to the background evolution, driven mostly by the normalization of the power spectrum today. The dark energy perturbations make only a small contribution on the largest scales, and a negligible contribution on smaller scales. Ironically, the dark energy perturbations remove the false boost of large-scale power that arises if we impose the (unphysical) assumption that the dark energy is smooth.
The standard model of cosmology is based on the existence of homogeneous surfaces as the background arena for structure formation. Homogeneity underpins both general relativistic and modified gravity models and is central to the way in which we inter
pret observations of the CMB and the galaxy distribution. However, homogeneity cannot be directly observed in the galaxy distribution or CMB, even with perfect observations, since we observe on the past lightcone and not on spatial surfaces. We can directly observe and test for isotropy, but to link this to homogeneity, we need to assume the Copernican Principle. First, we discuss the link between isotropic observations on the past lightcone and isotropic spacetime geometry: what observations do we need to be isotropic in order to deduce spacetime isotropy? Second, we discuss what we can say with the Copernican assumption. The most powerful result is based on the CMB: the vanishing of the dipole, quadrupole and octupole of the CMB is sufficient to impose homogeneity. Real observations lead to near-isotropy on large scales - does this lead to near-homogeneity? There are important partial results, and we discuss why this remains a difficult open question. Thus we are currently unable to prove homogeneity of the Universe on large-scales, even with the Copernican Principle. However we can use observations of the CMB, galaxies and clusters to test homogeneity itself.
We examine the dynamical consequences of homogeneous cosmological magnetic fields in the framework of loop quantum cosmology. We show that a big-bounce occurs in a collapsing magnetized Bianchi I universe, thus extending the known cases of singularit
y-avoidance. Previous work has shown that perfect fluid Bianchi I universes in loop quantum cosmology avoid the singularity via a bounce. The fluid has zero anisotropic stress, and the shear anisotropy in this case is conserved through the bounce. By contrast, the magnetic field has nonzero anisotropic stress, and shear anisotropy is not conserved through the bounce. After the bounce, the universe enters a classical phase. The addition of a dust fluid does not change these results qualitatively.
