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High precision astrometry now enables to measure the time drift of astrophysical observables in real time, hence providing new ways to probe different cosmological models. This article presents a general derivation of the redshift and direction drifts for general observers. It is then applied to the standard cosmological framework of a Friedmann-Lemaitre space- time including all effects at first order in the cosmological perturbations, as well as in the class of spatially anisotropic universe models of the Bianchi I family. It shows that for a general observer, the direction drift splits into a parallax and an aberration drifts and order of magnitude estimates of these two components are provided. The multipolar decomposition of the redshift and aberration drifts is also derived and shows that the observers peculiar velocity contributes only as a dipole whereas the anisotropic shear contributes as a quadrupole.
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The quantum contributions to the gravitational action are relatively easy to calculate in the higher derivative sector of the theory. However, the applications to the post-inflationary cosmology and astrophysics require the corrections to the Einstein-Hilbert action and to the cosmological constant, and those we can not derive yet in a consistent and safe way. At the same time, if we assume that these quantum terms are covariant and that they have relevant magnitude, their functional form can be defined up to a single free parameter, which can be defined on the phenomenological basis. It turns out that the quantum correction may lead, in principle, to surprisingly strong and interesting effects in astrophysics and cosmology.
We derive a redshift drift formula for the spherically symmetric inhomogeneous pressure Stephani universes which are complementary to the spherically symmetric inhomogeneous density Lema^itre-Tolman-Bondi models. We show that there is a clear difference between redshift drift predictions for these two models as well as between the Stephani models and the standard $Lambda$CDM Friedmann models. The Stephani models have positive drift values at small redshift and behave qualitatively (but not quantitatively) as the $Lambda$CDM models at large redshift, while the drift for LTB models is always negative. This prediction may perhaps be tested in future telescopes such as European Extremely Large Telescope (EELT), Thirty Meter Telescope (TMT), Giant Magellan Telescope (GMT), and especially, in gravitational wave interferometers DECi-Hertz Interferometer Gravitational Wave Observatory and Big Bang Observer (DECIGO/BBO), which aim at low redshift.
Cosmic voids in the large-scale structure of the Universe affect the peculiar motions of objects in their vicinity. Although these motions are difficult to observe directly, the clustering pattern of their surrounding tracers in redshift space is influenced in a unique way. This allows to investigate the interplay between densities and velocities around voids, which is solely dictated by the laws of gravity. With the help of $N$-body simulations and derived mock-galaxy catalogs we calculate the average density fluctuations around voids identified with a watershed algorithm in redshift space and compare the results with the expectation from general relativity and the $Lambda$CDM model. We find linear theory to work remarkably well in describing the dynamics of voids. Adopting a Bayesian inference framework, we explore the full posterior of our model parameters and forecast the achievable accuracy on measurements of the growth rate of structure and the geometric distortion through the Alcock-Paczynski effect. Systematic errors in the latter are reduced from $sim15%$ to $sim5%$ when peculiar velocities are taken into account. The relative parameter uncertainties in galaxy surveys with number densities comparable to the SDSS MAIN (CMASS) sample probing a volume of $1h^{-3}{rm Gpc}^3$ yield $sigma_{f/b}left/(f/b)right.sim2%$ ($20%$) and $sigma_{D_AH}/D_AHsim0.2%$ ($2%$), respectively. At this level of precision the linear-theory model becomes systematics dominated, with parameter biases that fall beyond these values. Nevertheless, the presented method is highly model independent; its viability lies in the underlying assumption of statistical isotropy of the Universe.
We constrain deviations from general relativity (GR) including both redshift and scale dependencies in the modified gravity (MG) parameters. In particular, we employ the under-used binning approach and compare the results to functional forms. We use available datasets such as Cosmic Microwave Background (CMB) from Planck 2018, Baryonic Acoustic Oscillations (BAO) and Redshift Space Distortions (BAO/RSD) from the BOSS DR12, the 6DF Galaxy Survey, the SDSS DR7 Main Galaxy Sample, the correlation of Lyman-$alpha$ forest absorption and quasars from SDSS-DR14, Supernova Type Ia (SNe) from the Pantheon compilation, and DES Y1 data. Moreover, in order to maximize the constraining power from available datasets, we analyze MG models where we alternatively set some of the MG parameters to their GR values and vary the others. Using functional forms, we find an up to 3.5-$sigma$ tension with GR in $Sigma$ (while $mu$ is fixed) when using Planck+SNe+BAO+RSD; this goes away when lensing data is included, i.e. CMB lensing and DES (CMBL+DES). Using different binning methods, we find that a tension with GR above 2-$sigma$ in the (high-z, high-k) bin is persistent even when including CMBL+DES to Planck+SNe+BAO+RSD. Also, we find another tension above 2-$sigma$ in the (low-z, high-k) bin, but that can be reduced with the addition of lensing data. Furthermore, we perform a model comparison using the Deviance Information Criterion statistical tool and find that the MG model ($mu=1$, $Sigma$) is weakly favored by the data compared to $Lambda$CDM, except when DES data is included. Another noteworthy result is that we find that the binning methods do not agree with the widely-used functional parameterization where the MG parameters are proportional to $Omega_{text{DE}}(a)$, and this is clearly apparent in the high-z and high-k regime where this parameterization underestimates the deviations from GR.
We present GRAMSES, a new pipeline for nonlinear cosmological $N$-body simulations in General Relativity (GR). This code adopts the Arnowitt-Deser-Misner (ADM) formalism of GR, with constant mean curvature and minimum distortion gauge fixings, which provides a fully nonlinear and background independent framework for relativistic cosmology. Employing a fully constrained formulation, the Einstein equations are reduced to a set of ten elliptical equations which are solved using multigrid relaxation with adaptive mesh refinements (AMR), and three hyperbolic equations for the evolution of tensor degrees of freedom. The current version of GRAMSES neglects the latter by using the conformal flatness approximation, which allows it to compute the two scalar and two vector degrees of freedom of the metric. In this paper we describe the methodology, implementation, code tests and first results for cosmological simulations in a $Lambda$CDM universe, while the generation of initial conditions and physical results will be discussed elsewhere. Inheriting the efficient AMR and massive parallelisation infrastructure from the publicly-available $N$-body and hydrodynamic simulation code RAMSES, GRAMSES is ideal for studying the detailed behaviour of spacetime inside virialised cosmic structures and hence accurately quantifying the impact of backreaction effects on the cosmic expansion, as well as for investigating GR effects on cosmological observables using cosmic-volume simulations.
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