| 1. |
- Uggla, Claes, 1957-, et al.
(författare)
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Cosmological perturbation theory revisited
- 2011
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Ingår i: Classical and quantum gravity. - : Institute of Physics (IOP). - 0264-9381 .- 1361-6382. ; 28:17, s. 175017-175043
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Tidskriftsartikel (refereegranskat)abstract
- Increasingly accurate observations are driving theoretical cosmology towards the use of more sophisticated descriptions of matter and the study of nonlinear perturbations of Friedmann–Lemaitre cosmologies, whose governing equations are notoriously complicated. Our goal in this paper is to formulate the governing equations for linear perturbation theory in a particularly simple and concise form in order to facilitate the extension to nonlinear perturbations. Our approach has several novel features. We show that the use of so-called intrinsic gauge invariants has two advantages. It naturally leads to (i) a physically motivated choice of a gauge invariant associated with the matter density, and (ii) two distinct and complementary ways of formulating the evolution equations for scalar perturbations, associated with the work of Bardeen and of Kodama and Sasaki. In the first case, the perturbed Einstein tensor gives rise to a second-order (in time) linear differential operator, and in the second case to a pair of coupled first-order (in time) linear differential operators. These operators are of fundamental importance in cosmological perturbation theory, since they provide the leading order terms in the governing equations for nonlinear perturbations
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| 2. |
- Uggla, Claes, 1957-, et al.
(författare)
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Scalar cosmological perturbations
- 2012
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Ingår i: Classical and quantum gravity. - : Institute of Physics (IOP). - 0264-9381 .- 1361-6382. ; 29:10, s. 105002-105029
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Tidskriftsartikel (refereegranskat)abstract
- Scalar perturbations of Friedmann–Lemaitre cosmologies can be analyzed in a variety of ways using Einstein's field equations, the Ricci and Bianchi identities, or the conservation equations for the stress–energy tensor, and possibly introducing a timelike reference congruence. The common ground is the use of gauge invariants derived from the metric tensor, the stress–energy tensor, or from vectors associated with a reference congruence, as basic variables. Although there is a complication in that there is no unique choice of gauge invariants, we will show that this can be used to advantage. With this in mind our first goal is to present an efficient way of constructing dimensionless gauge invariants associated with the tensors that are involved, and of determining their inter-relationships. Our second goal is to give a unified treatment of the various ways of writing the governing equations in dimensionless form using gauge-invariant variables, showing how simplicity can be achieved by a suitable choice of variables and normalization factors. Our third goal is to elucidate the connection between the metric-based approach and the so-called 1 + 3 gauge-invariant approach to cosmological perturbations. We restrict our considerations to linear perturbations, but our intent is to set the stage for the extension to second-order perturbations
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| 3. |
- Uggla, Claes, 1957-, et al.
(författare)
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Simple expressions for second order density perturbations in standard cosmology
- 2014
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Ingår i: Classical and quantum gravity. - : Institute of Physics (IOP). - 0264-9381 .- 1361-6382. ; 31:10, s. 105008-
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we present four simple expressions for the relativistic first and second order fractional density perturbations for ΛCDM cosmologies in different gauges: the Poisson, uniform curvature, total matter and synchronous gauges. A distinctive feature of our approach is the use of a canonical set of quadratic differential expressions involving an arbitrary spatial function, the so-called comoving curvature perturbation, to describe the spatial dependence, which enables us to unify, simplify and extend previous seemingly disparate results. The simple structure of the expressions makes the evolution of the density perturbations completely transparent and clearly displays the effect of the cosmological constant on the dynamics, namely that it stabilizes the perturbations. We expect that the results will be useful in applications, for example, studying the effects of primordial non-Gaussianity on the large scale structure of the universe.
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| 4. |
- Alho, Artur, et al.
(författare)
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Dynamical systems in perturbative scalar field cosmology
- 2020
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Ingår i: Classical and quantum gravity. - : American Institute of Physics (AIP). - 0264-9381 .- 1361-6382. ; 37:22
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Tidskriftsartikel (refereegranskat)abstract
- We derive a newregulardynamical system on a three-dimensionalcompactstate space describing linear scalar perturbations of spatially flat Robertson-Walker geometries for relativistic models with a minimally coupled scalar field with an exponential potential. This enables us to construct the global solution space, illustrated with figures, where known solutions are shown to reside on special invariant sets. We also use our dynamical systems approach to obtain new results about the comoving and uniform density curvature perturbations. Finally we show how to extend our approach to more general scalar field potentials. This leads to state spaces where the state space of the models with an exponential potential appears as invariant boundary sets, thereby illustrating their role as building blocks in a hierarchy of increasingly complex cosmological models.
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| 5. |
- Uggla, Claes, 1957-, et al.
(författare)
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Second order cosmological perturbations : simplified gauge change formulas
- 2019
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Ingår i: Classical and quantum gravity. - : Institute of Physics (IOP). - 0264-9381 .- 1361-6382. ; 36:3, s. 1-19
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we present a new formulation of the change of gauge formulas in second order cosmological perturbation theory which unifies and simplifies known results. Our approach is based on defining new second order scalar perturbation variables by adding a multiple of the square of the corresponding first order variables to each second order variable. A bonus is that these new perturbation variables are of broader significance in that they also simplify the analysis of second order scalar perturbations in the super-horizon regime in a number of ways, and lead to new conserved quantities.
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