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Alho, A., Hell, J. & Uggla, C. (2015). Global dynamics and asymptotics for monomial scalar field potentials and perfect fluids. Classical and quantum gravity, 32(14), Article ID 145005.
Open this publication in new window or tab >>Global dynamics and asymptotics for monomial scalar field potentials and perfect fluids
2015 (English)In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 32, no 14, article id 145005Article in journal (Refereed) Published
Abstract [en]

We consider a minimally coupled scalar field with a monomial potential and a perfect fluid in flat Friedmann-Lemaitre-Robertson-Walker cosmology. We apply local and global dynamical systems techniques to a new three-dimensional dynamical systems reformulation of the field equations on a compact state space. This leads to a visual global description of the solution space and asymptotic behavior. At late times we employ averaging techniques to prove statements about how the relationship between the equation of state of the fluid and the monomial exponent of the scalar field affects asymptotic source dominance and asymptotic manifest self-similarity breaking. We also situate the ’attractor’ solution in the three-dimensional state space and show that it corresponds to the one-dimensional unstable center manifold of a de Sitter fixed point, located on an unphysical boundary associated with the dynamics at early times. By deriving a center manifold expansion we obtain approximate expressions for the attractor solution. We subsequently improve the accuracy and range of the approximation by means of Pade approximants and compare with the slow-roll approximation. 

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2015
Keyword
riedmann–Lemaître–Robertson–Walker cosmology, monomial potential
National Category
Other Physics Topics
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-42371 (URN)10.1088/0264-9381/32/14/145005 (DOI)000357611500006 ()2-s2.0-84935462852 (Scopus ID)
Available from: 2016-06-07 Created: 2016-05-23 Last updated: 2017-09-11Bibliographically approved
Alho, A. & Uggla, C. (2015). Global dynamics and inflationary center manifold and slow-roll approximants. Journal of Mathematical Physics, 56(1), Article ID 012502.
Open this publication in new window or tab >>Global dynamics and inflationary center manifold and slow-roll approximants
2015 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 56, no 1, article id 012502Article in journal (Refereed) Published
Abstract [en]

We consider the familiar problem of a minimally coupled scalar field with quadratic potential in flat Friedmann-Lemaître-Robertson-Walker cosmology to illustrate a number of techniques and tools, which can be applied to a wide range of scalar field potentials and problems in, e.g., modified gravity. We present a global and regular dynamical systems description that yields a global understanding of the solution space, including asymptotic features. We introduce dynamical systems techniques such as center manifold expansions and use Padé approximants to obtain improved approximations for the “attractor solution” at early times. We also show that future asymptotic behavior is associated with a limit cycle, which shows that manifest self-similarity is asymptotically broken toward the future and gives approximate expressions for this behavior. We then combine these results to obtain global approximations for the attractor solution, which, e.g., might be used in the context of global measures. In addition, we elucidate the connection between slow-roll based approximations and the attractor solution, and compare these approximations with the center manifold based approximants.

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2015
Keyword
Cosmology, scalar fields, attractors
National Category
Natural Sciences Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-35243 (URN)10.1063/1.4906081 (DOI)000349019000022 ()
Available from: 2015-02-18 Created: 2015-02-18 Last updated: 2017-09-11Bibliographically approved
Alho, A. & Uggla, C. (2015). Scalar field deformations of Lambda CDM cosmology. Physical Review D, 92(10), Article ID 103502.
Open this publication in new window or tab >>Scalar field deformations of Lambda CDM cosmology
2015 (English)In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 92, no 10, article id 103502Article in journal (Refereed) Published
Abstract [en]

This paper treats nonrelativistic matter and a scalar field phi with a monotonically decreasing potential minimally coupled to gravity in flat Friedmann-Lemaitre-Robertson-Walker cosmology. The field equations are reformulated as a three-dimensional dynamical system on an extended compact state space, complemented with cosmographic diagrams. A dynamical systems analysis provides global dynamical results describing possible asymptotic behavior. It is shown that one should impose global and asymptotic bounds on lambda = -V-1 dV/d phi to obtain viable cosmological models that continuously deform Lambda CDM cosmology. In particular we introduce a regularized inverse power-law potential as a simple specific example.

Keyword
SCALING SOLUTIONS; POTENTIALS
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-40685 (URN)10.1103/PhysRevD.92.103502 (DOI)000364020800003 ()
Available from: 2016-02-24 Created: 2016-02-24 Last updated: 2017-11-30Bibliographically approved
Uggla, C. & Wainwright, J. (2014). Second order density perturbations for dust cosmologies. Physical Review D, D90, 043511
Open this publication in new window or tab >>Second order density perturbations for dust cosmologies
2014 (English)In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. D90, p. 043511-Article in journal (Refereed) Published
Abstract [en]

We present simple expressions for the relativistic first and second order fractional density perturbations for FL cosmologies with dust, in four different gauges: the Poisson, uniform curvature, total matter and synchronous gauges. We include a cosmological constant and arbitrary spatial curvature in the background. A distinctive feature of our approach is our description of the spatial dependence of the perturbations using a canonical set of quadratic differential expressions involving an arbitrary spatial function that arises as a conserved quantity. This enables us to unify, simplify and extend previous seemingly disparate results. We use the primordial matter and metric perturbations that emerge at the end of the inflationary epoch to determine the additional arbitrary spatial function that arises when integrating the second order perturbation equations. This introduces a non-Gaussianity parameter into the expressions for the second order density perturbation. In the special case of zero spatial curvature we show that the time evolution simplifies significantly, and requires the use of only two non-elementary functions, the so-called growth supression factor at the linear level, and one new function at the second order level. 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.

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2014
Keyword
Cosmology
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-33954 (URN)10.1103/PhysRevD.90.043511 (DOI)000341106500003 ()
Available from: 2014-10-02 Created: 2014-10-02 Last updated: 2017-12-05Bibliographically approved
Uggla, C. & Wainwright, J. (2014). Simple expressions for second order density perturbations in standard cosmology. Classical and quantum gravity, 31(10), 105008
Open this publication in new window or tab >>Simple expressions for second order density perturbations in standard cosmology
2014 (English)In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 31, no 10, p. 105008-Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2014
Keyword
Cosmology
National Category
Physical Sciences Astronomy, Astrophysics and Cosmology
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-33953 (URN)10.1088/0264-9381/31/10/105008 (DOI)000336092700009 ()
Available from: 2014-10-02 Created: 2014-10-02 Last updated: 2017-12-05Bibliographically approved
Uggla, C. & Wainwright, J. (2013). A simplified structure for second order cosmological perturbation equations. General Relativity and Gravitation, 45(3), 643-674
Open this publication in new window or tab >>A simplified structure for second order cosmological perturbation equations
2013 (English)In: General Relativity and Gravitation, ISSN 0001-7701, E-ISSN 1572-9532, Vol. 45, no 3, p. 643-674Article in journal (Refereed) Published
Abstract [en]

Increasingly accurate observations of the cosmic microwave background and the large scale distribution of galaxies necessitate the study of nonlinear perturbations of Friedmann–Lemaitre cosmologies, whose equations are notoriously complicated. In this paper we present a new derivation of the governing equations for second order perturbations within the framework of the metric-based approach that is minimal, as regards amount of calculation and length of expressions, and flexible, as regards choice of gauge and stress–energy tensor. Because of their generality and the simplicity of their structure our equations provide a convenient starting point for determining the behaviour of nonlinear perturbations of FL cosmologies with any given stress–energy content, using either the Poisson gauge or the uniform curvature gauge.

Place, publisher, year, edition, pages
Berlin: Springer, 2013
Keyword
Second order cosmological perturbations, Poisson gauge, Uniform curvature gauge
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-15616 (URN)10.1007/s10714-012-1492-7 (DOI)000314885500006 ()
Available from: 2012-11-14 Created: 2012-11-14 Last updated: 2017-12-07Bibliographically approved
Uggla, C. & Wainwright, J. (2013). Asymptotic analysis of perturbed dust cosmologies to second order. General Relativity and Gravitation, 45(8), 1467-1492
Open this publication in new window or tab >>Asymptotic analysis of perturbed dust cosmologies to second order
2013 (English)In: General Relativity and Gravitation, ISSN 0001-7701, E-ISSN 1572-9532, Vol. 45, no 8, p. 1467-1492Article in journal (Refereed) Published
Abstract [en]

Nonlinear perturbations of Friedmann-Lemaitre cosmologies with dust and a cosmological constant Lambda>0 have recently attracted considerable attention. In this paper our first goal is to compare the evolution of the first and second order perturbations by determining their asymptotic behaviour at late times in ever-expanding models. We show that in the presence of spatial curvature K or a cosmological constant, the density perturbation approaches a finite limit both to first and second order, but the rate of approach depends on the model, being power law in the scale factor if Lambda>0 but logarithmic if Lambda=0 and K<0. Scalar perturbations in general contain a growing and a decaying mode. We find, somewhat surprisingly, that if Lambda>0 the decaying mode does not die a way, i.e.  it contributes on an equal footing as the growing mode to the asymptotic expression for the density perturbation. On the other hand, the future asymptotic regime of the Einstein-de Sitter universe (K=Lambda=0) is completely different, as exemplified by the density perturbation which diverges; moreover, the second order perturbation diverges faster than the first order perturbation, which suggests that the Einstein-de Sitter universe is unstable to perturbations, and that the perturbation series do not converge towards the future. We conclude that the presence of spatial curvature or a cosmological constant stabilizes the perturbations. Our second goal is to derive an explicit expression for the second order density perturbation that can be used to study the effects of including a cosmological constant and spatial curvature.

Place, publisher, year, edition, pages
Berlin: Springer, 2013
Keyword
Cosmology
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-27133 (URN)10.1007/s10714-013-1559-0 (DOI)000322177600001 ()
Note

Paper available on arXiv:1303.4516

Available from: 2013-04-30 Created: 2013-04-30 Last updated: 2017-12-06Bibliographically approved
Uggla, C. (2013). Global cosmological dynamics for the scalar field representation of the modified Chaplygin gas. Physical Review D, D88, 064040-1-064040-7
Open this publication in new window or tab >>Global cosmological dynamics for the scalar field representation of the modified Chaplygin gas
2013 (English)In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. D88, p. 064040-1-064040-7Article in journal (Refereed) Published
Abstract [en]

In this paper we investigate the global dynamics for the minimally coupled scalar field representation of the modified Chaplygin gas in the context of flat Friedmann-Lemaître-Robertson Walker cosmology. The tool for doing this is a new set of bounded variables that lead to a regular dynamical system. It is shown that the exact modified Chaplygin gas perfect fluid solution appears as a straight line in the associated phase plane. It is also shown that no other solutions stay close to this solution during their entire temporal evolution, but that there exists an open subset of solutions that stay arbitrarily close during an intermediate time interval, and into the future in the case when the scalar field potential exhibits a global minimum.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC, 2013
Keyword
Cosmology
National Category
Natural Sciences Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-30483 (URN)10.1103/PhysRevD.88.064040 (DOI)000324635700005 ()
External cooperation:
Available from: 2013-11-30 Created: 2013-11-30 Last updated: 2017-12-06Bibliographically approved
Uggla, C. (2013). Recent developments concerning generic spacelike singularities. General Relativity and Gravitation, 45, 1669-1710
Open this publication in new window or tab >>Recent developments concerning generic spacelike singularities
2013 (English)In: General Relativity and Gravitation, ISSN 0001-7701, E-ISSN 1572-9532, Vol. 45, p. 1669-1710Article in journal (Refereed) Published
Abstract [en]

This is a review of recent progress concerning generic spacelikesingularities in general relativity. For brevity the main focus is on singularities in vacuum spacetimes, although the connection with, and the role of, matter for generic singularity formation is also commented on. The paper describes recent developments in two areas and show how these are connected within the context of the conformally Hubble-normalized state space approach. The first area is oscillatory singularities in spatially homogeneous cosmology and the connection between asymptotic behaviour and heteroclinic chains. The second area concerns oscillatory singularities in inhomogeneous models, especially spike chains and recurring spikes. The review also outlines some underlying reasons for why the structures that are the foundation for generic oscillatory behaviour exists at all, which entails discussing how underlying physical principles and applications of solutiongenerating techniques yield hierarchical structures and connections between them. Finally, it is pointed out that recent progress concerning generic singularities motivates some speculations that suggest that a paradigm shift concerning their physical role, and what mathematical issues to address,might be in order.

Place, publisher, year, edition, pages
Berlin: Springer, 2013
Keyword
Generic spacetime singularities
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-27132 (URN)10.1007/s10714-013-1556-3 (DOI)000322900500002 ()
Note

The paper is also available on arXiv:1304.6905

Available from: 2013-04-30 Created: 2013-04-30 Last updated: 2017-12-06Bibliographically approved
Uggla, C. (2013). Spacetime singularities: Recent developments. International Journal of Modern Physics D, 22(3), 1330002-1330022
Open this publication in new window or tab >>Spacetime singularities: Recent developments
2013 (English)In: International Journal of Modern Physics D, ISSN 0218-2718, Vol. 22, no 3, p. 1330002-1330022Article in journal (Refereed) Published
Abstract [en]

Recent developments concerning oscillatory spacelike singularities in general relativity are taking place on two fronts. The first treats generic singularities in spatially homogeneous cosmology, most notably Bianchi types VIII and IX. The second deals with generic oscillatory singularities in inhomogeneous cosmologies, especially those with two commuting spacelike Killing vectors. This paper describes recent progress in these two areas: in the spatially homogeneous case, focus is on mathematically rigorous results, while analytical and numerical results concerning generic behavior and so-called recurring spike formation are the main topics in the inhomogeneous case. Unifying themes are connections between asymptotic behavior, hierarchical structures and solution generating techniques, which provide hints for a link between the nature of generic singularities and a hierarchy of hidden asymptotic symmetries.

Place, publisher, year, edition, pages
Singapore: , 2013
Keyword
Spacetime singularities
National Category
Natural Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-16185 (URN)10.1142/S0218271813300024 (DOI)000316908000001 ()
Available from: 2012-12-15 Created: 2012-12-15 Last updated: 2017-12-06Bibliographically approved
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ORCID iD: ORCID iD iconorcid.org/0000-0002-0906-8808

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