New action for cosmology

Sloan, David

doi:10.1103/physrevd.103.043524

Cited by 20 publications

(31 citation statements)

References 29 publications

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“…The first is that this arises as an action principle that can be expressed as: 'Extremize the Hubble parameter at time t, subject to the acceleration Equation (53) and given an initial value H 0 at time t 0 '. It should be no surprise that this is in close correspondence with the action described in [18] as it was derived in the same manner but for a simpler treatment of matter. The second is that the Herglotz-Lagrange equations for z i become…”

Section: Cosmologysupporting

confidence: 78%

“…We first begin with the Lagrangian of Equation (18). At each point on the tangent bundle, we consider the transformations ∆ : {r,ṙ, θ,θ} → {r + δr,ṙ + δṙ, θ + δθ,θ + δθ} (A1)…”

Section: Discussionmentioning

confidence: 99%

“…In previous work [18], we have treated the general case in which the matter Lagrangian, L m , is left as a general function of q andq. Here, for clarity of exposition and to allow more direct comparison to the usual cosmological literature, we will simplify the situation by restricting ourselves to considering the matter to be a mixture of perfect fluids with a constant barotropic parameter.…”

Section: Cosmologymentioning

confidence: 99%

“…In this work, we have only considered a description of the FLRW cosmological models with simple matter sources. Both of these restrictions can be relaxed, and a more general prescription is given in [18], wherein the isotropy restriction is removed, considering homogeneous cosmological solutions wherein the spatial slice is a manifold of the type classified by Bianchi. Further, we leave the matter source as that which can be described through a general matter Lagrangian, which is minimally coupled to gravity.…”

Section: Cosmologymentioning

confidence: 99%

“…Symmetries from this general set are referred to as Dynamical Similarities [12][13][14]. It has been shown that such symmetries are commonplace in physical systems and have particularly important philosophical and mathematical implications in the cosmological sector [15][16][17][18]. In previous work [12], we have dealt with the case where a single force was acting and chosen the appropriate symmetry that kept the coupling of the relevant potential fixed.…”

Section: Introduction: Poincaré's Dreammentioning

confidence: 99%

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Scale Symmetry and Friction

Sloan

2021

Symmetry

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Dynamical similarities are non-standard symmetries found in a wide range of physical systems that identify solutions related by a change of scale. In this paper, we will show through a series of examples how this symmetry extends to the space of couplings, as measured through observations of a system. This can be exploited to focus on observations that can be used to distinguish between different theories and identify those which give rise to identical physical evolutions. These can be reduced into a description that makes no reference to scale. The resultant systems can be derived from Herglotz’s principle and generally exhibit friction. Here, we will demonstrate this through three example systems: the Kepler problem, the N-body system and Friedmann–Lemaître–Robertson–Walker cosmology.

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Section: Cosmologysupporting

confidence: 78%

Section: Discussionmentioning

confidence: 99%

Section: Cosmologymentioning

confidence: 99%

Section: Cosmologymentioning

confidence: 99%

Section: Introduction: Poincaré's Dreammentioning

confidence: 99%

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Scale Symmetry and Friction

Sloan

2021

Symmetry

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New Directions for Contact Integrators

Bravetti¹,

Seri

Zadra

2021

Lecture Notes in Computer Science

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Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.

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When scale is surplus

Gryb

Sloan

2021

Synthese

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We study a long-recognised but under-appreciated symmetry called dynamical similarity and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a system where the unit of Hamilton’s principal function is rescaled, and therefore represent a kind of dynamical scaling symmetry with formal properties that differ from many standard symmetries. To study this symmetry, we develop a general framework for symmetries that distinguishes the observable and surplus structures of a theory by using the minimal freely specifiable initial data for the theory that is necessary to achieve empirical adequacy. This framework is then applied to well-studied examples including Galilean invariance and the symmetries of the Kepler problem. We find that our framework gives a precise dynamical criterion for identifying the observables of those systems, and that those observables agree with epistemic expectations. We then apply our framework to dynamical similarity. First we give a general definition of dynamical similarity. Then we show, with the help of some previous results, how the dynamics of our observables leads to singularity resolution and the emergence of an arrow of time in cosmology.

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New action for cosmology

Cited by 20 publications

References 29 publications

Scale Symmetry and Friction

Scale Symmetry and Friction

New Directions for Contact Integrators

When scale is surplus

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