Friedmann–Lemaître–Robertson–Walker metric

About: Friedmann–Lemaître–Robertson–Walker metric is a research topic. Over the lifetime, 4113 publications have been published within this topic receiving 87752 citations. The topic is also known as: FLRW metric.

Cosmological models with variable gravitational and cosmological “constants”

Abstract: We consider the Einstein field equations with perfect fluid source and variable Λ andG for the Robertson-Walker metric. When conservation of energy momentum is postulated and the deceleration parameter is assumed constant, we find perfect gas equation of state models in the Euclidean and non-Euclidean cases. The resulting models offer an alternative to the inflationary scenario; they also explain the huge value of the cosmological term in the early universe.

Manifestly gauge-invariant general relativistic perturbation theory: I. Foundations

Abstract: Linear cosmological perturbation theory is pivotal to a theoretical understanding of current cosmological experimental data provided eg by cosmic microwave anisotropy probes A key issue in that theory is to extract the gauge-invariant degrees of freedom which allow unambiguous comparison between theory and experiment When one goes beyond first (linear) order, the task of writing the Einstein equations expanded to nth order in terms of quantities that are gauge-invariant up to terms of higher orders becomes highly non-trivial and cumbersome This fact has prevented progress for instance on the issue of the stability of linear perturbation theory and is a subject of current debate in the literature In this series of papers we circumvent these difficulties by passing to a manifestly gauge-invariant framework In other words, we only perturb gauge-invariant, ie measurable quantities, rather than gauge variant ones Thus, gauge invariance is preserved non-perturbatively while we construct the perturbation theory for the equations of motion for the gauge-invariant observables to all orders In this first paper we develop the general framework which is based on a seminal paper due to Brown and Kuchař as well as the relational formalism due to Rovelli In the second, companion, paper we apply our general theory to FRW cosmologies and derive the deviations from the standard treatment in linear order As it turns out, these deviations are negligible in the late universe, thus our theory is in agreement with the standard treatment However, the real strength of our formalism is that it admits a straightforward and unambiguous, gauge-invariant generalization to higher orders This will also allow us to settle the stability issue in a future publication

Observational constraints on inhomogeneous cosmological models without dark energy

Abstract: It has been proposed that the observed dark energy can be explained away by the effect of large-scale nonlinear inhomogeneities. In the present paper we discuss how observations constrain cosmological models featuring large voids. We start by considering Copernican models, in which the observer is not occupying a special position and homogeneity is preserved on a very large scale. We show how these models, at least in their current realizations, are constrained to give small, but perhaps not negligible in certain contexts, corrections to the cosmological observables. We then examine non-Copernican models, in which the observer is close to the center of a very large void. These models can give large corrections to the observables which mimic an accelerated FLRW model. We carefully discuss the main observables and tests able to exclude them.

An Exact quantification of backreaction in relativistic cosmology

Abstract: An important open question in cosmology is the degree to which the Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) solutions of Einstein's equations are able to model the large-scale behavior of the locally inhomogeneous observable universe. We investigate this problem by considering a range of exact n-body solutions of Einstein's constraint equations. These solutions contain discrete masses, and so allow arbitrarily large density contrasts to be modeled. We restrict our study to regularly arranged distributions of masses in topological 3-spheres. This has the benefit of allowing straightforward comparisons to be made with FLRW solutions, as both spacetimes admit a discrete group of symmetries. It also provides a time-symmetric hypersurface at the moment of maximum expansion that allows the constraint equations to be solved exactly. We find that when all the mass in the universe is condensed into a small number of objects ($\ensuremath{\lesssim}10$) then the amount of back-reaction in dust models can be large, with $O(1)$ deviations from the predictions of the corresponding FLRW solutions. When the number of masses is large ($\ensuremath{\gtrsim}100$), however, then our measures of back-reaction become small ($\ensuremath{\lesssim}1%$). This result does not rely on any averaging procedures, which are notoriously hard to define uniquely in general relativity, and so provides (to the best of our knowledge) the first exact and unambiguous demonstration of back-reaction in general relativistic cosmological modelling. Discrete models such as these can therefore be used as laboratories to test ideas about back-reaction that could be applied in more complicated and realistic settings.