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Uggla, C. & Wainwright, J. (2019). Second order cosmological perturbations: simplified gauge change formulas. Classical and quantum gravity, 36(3), 1-19, Article ID 035004.
Open this publication in new window or tab >>Second order cosmological perturbations: simplified gauge change formulas
2019 (English)In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 36, no 3, p. 1-19, article id 035004Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2019
Keywords
cosmology, perturbations, gauge
National Category
Probability Theory and Statistics
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-71074 (URN)10.1088/1361-6382/aaf924 (DOI)000455932900002 ()
Available from: 2019-02-14 Created: 2019-02-14 Last updated: 2019-02-18Bibliographically approved
Uggla, C. & Wainwright, J. (2019). Second-order cosmological perturbations: New conserved quantities and the general solution at super-horizon scale. Physical Review D: covering particles, fields, gravitation, and cosmology, 100(2), Article ID 023544.
Open this publication in new window or tab >>Second-order cosmological perturbations: New conserved quantities and the general solution at super-horizon scale
2019 (English)In: Physical Review D: covering particles, fields, gravitation, and cosmology, ISSN 2470-0010, E-ISSN 2470-0029, Vol. 100, no 2, article id 023544Article in journal (Refereed) Published
Abstract [en]

The study of long-wavelength scalar perturbations, in particular the existence of conserved quantities when the perturbations are adiabatic, plays an important role in e.g., inflationary cosmology. In this paper we present some new conserved quantities at second order and relate them to the curvature perturbation in the uniform density gauge, zeta, and the comoving curvature perturbation, R. We also, for the first time, derive the general solution of the perturbed Einstein equations at second order, which thereby contains both growing and decaying modes, for adiabatic long-wavelength perturbations for a stress-energy tensor with zero anisotropic stresses and zero heat flux. The derivation uses the total matter gauge, but results are subsequently translated to the uniform curvature and Poisson (longitudinal, zero shear) gauges.

Place, publisher, year, edition, pages
American Physical Society, 2019
Keywords
GRAVITATIONAL-INSTABILITY; DENSITY PERTURBATIONS; EVOLUTION; GROWTH
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-74337 (URN)10.1103/PhysRevD.100.023544 (DOI)000477908400004 ()
Available from: 2019-08-15 Created: 2019-08-15 Last updated: 2019-08-15
Uggla, C. & Wainwright, J. (2019). The general solution at large scale for second order perturbations in a scalar field dominated universe. Journal of Cosmology and Astroparticle Physics (6), Article ID 021.
Open this publication in new window or tab >>The general solution at large scale for second order perturbations in a scalar field dominated universe
2019 (English)In: Journal of Cosmology and Astroparticle Physics, ISSN 1475-7516, E-ISSN 1475-7516, no 6, article id 021Article in journal (Refereed) Published
Abstract [en]

In this paper we consider second order perturbations of a flat Friedmann-Lemaitre universe whose stress-energy content is a single minimally coupled scalar field with an arbitrary potential. We derive the general solution of the perturbed Einstein equations in explicit form for this class of models when the perturbations are in the super-horizon regime. As a by-product we obtain a new conserved quantity for long wavelength perturbations of a single scalar field at second order.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2019
Keywords
cosmological perturbation theory, inflation
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-73320 (URN)10.1088/1475-7516/2019/06/021 (DOI)000471172400002 ()
Available from: 2019-07-02 Created: 2019-07-02 Last updated: 2019-07-02Bibliographically approved
Uggla, C. & Wainwright, J. (2018). Dynamics of cosmological perturbations at first and second order. Physical Review D: covering particles, fields, gravitation, and cosmology, 98(10), Article ID 103534.
Open this publication in new window or tab >>Dynamics of cosmological perturbations at first and second order
2018 (English)In: Physical Review D: covering particles, fields, gravitation, and cosmology, ISSN 2470-0010, E-ISSN 2470-0029, Vol. 98, no 10, article id 103534Article in journal (Refereed) Published
Abstract [en]

In this paper we give five gauge-invariant systems of governing equations for first and second order scalar perturbations of flat Friedmann-Lemaitre universes that are minimal in the sense that they contain no redundant equations or variables. We normalize the variables so that they are dimensionless, which leads to systems of equations that are simple and ready-to-use. We compare the properties and utility of the different systems. For example, they serve as a starting point for finding explicit solutions for two benchmark problems in cosmological perturbation theory at second order: adiabatic perturbations in the superhorizon regime (the long wavelength limit) and perturbations of ACDM universes. However, our framework has much wider applicability and serves as a reference for future work in the field.

Place, publisher, year, edition, pages
American Physical Society, 2018
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-70558 (URN)10.1103/PhysRevD.98.103534 (DOI)000451995400002 ()
Available from: 2018-12-20 Created: 2018-12-20 Last updated: 2019-01-16Bibliographically approved
Alho, A. & Uggla, C. (2017). Inflationary alpha-attractor cosmology: A global dynamical systems perspective. Physical Review D: covering particles, fields, gravitation, and cosmology, 95(8), Article ID 083517.
Open this publication in new window or tab >>Inflationary alpha-attractor cosmology: A global dynamical systems perspective
2017 (English)In: Physical Review D: covering particles, fields, gravitation, and cosmology, ISSN 2470-0010, E-ISSN 2470-0029, Vol. 95, no 8, article id 083517Article in journal (Refereed) Published
Abstract [en]

We study flat Friedmann-Lemaitre-Robertson-Walker alpha-attractor E- and T-models by introducing a dynamical systems framework that yields regularized unconstrained field equations on two-dimensional compact state spaces. This results in both illustrative figures and a complete description of the entire solution spaces of these models, including asymptotics. In particular, it is shown that observational viability, which requires a sufficient number of e-folds, is associated with a particular solution given by a one-dimensional center manifold of a past asymptotic de Sitter state, where the center manifold structure also explains why nearby solutions are attracted to this "inflationary attractor solution." A center manifold expansion yields a description of the inflationary regime with arbitrary analytic accuracy, where the slow-roll approximation asymptotically describes the tangency condition of the center manifold at the asymptotic de Sitter state.

Place, publisher, year, edition, pages
American Physical Society, 2017
National Category
Mathematics
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-65520 (URN)10.1103/PhysRevD.95.083517 (DOI)000399807000001 ()
Available from: 2018-01-04 Created: 2018-01-04 Last updated: 2018-12-19Bibliographically approved
Alho, A., Carloni, S. & Uggla, C. (2016). On dynamical systems approaches and methods in f (R) cosmology. Journal of Cosmology and Astroparticle Physics (8), Article ID 064.
Open this publication in new window or tab >>On dynamical systems approaches and methods in f (R) cosmology
2016 (English)In: Journal of Cosmology and Astroparticle Physics, ISSN 1475-7516, E-ISSN 1475-7516, no 8, article id 064Article in journal (Refereed) Published
Abstract [en]

We discuss dynamical systems approaches and methods applied to flat Robertson Walker models in f(R)-gravity. We argue that a complete description of the solution space of a model requires a global state space analysis that motivates globally covering state space adapted variables. This is shown explicitly by an illustrative example, f(R) = R + alpha R-2, alpha > 0, for which we introduce new regular dynamical systems on global compactly extended state spaces for the Jordan and Einstein frames. This example also allows us to illustrate several local and global dynamical systems techniques involving, e.g., blow ups of nilpotent fixed points, center manifold analysis, averaging, and use of monotone functions. As a result of applying dynamical systems methods to globally state space adapted dynamical systems formulations, we obtain pictures of the entire solution spaces in both the Jordan and the Einstein frames. This shows, e.g., that due to the domain of the conformal transformation between the Jordan and Einstein frames, not all the solutions in the Jordan frame are completely contained in the Einstein frame. We also make comparisons with previous dynamical systems approaches to f (R) cosmology and discuss their advantages and disadvantages.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2016
Keywords
dark energy theory, inflation, modified gravity
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-62616 (URN)10.1088/1475-7516/2016/08/064 (DOI)000389859100002 ()
Available from: 2017-08-10 Created: 2017-08-10 Last updated: 2019-06-10Bibliographically approved
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
Keywords
riedmann–Lemaître–Robertson–Walker cosmology, monomial potential, cosmology, scalar field, dynamical systems, averaging, center manifold, slow-roll, Pade approximants
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: 2019-07-10Bibliographically 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
Keywords
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: 2018-10-16Bibliographically 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.

Keywords
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: 2019-07-10Bibliographically 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
Keywords
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
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-0906-8808

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