Metric-affine cosmological models and the inverse problem of the calculus of variations. Part II: Variational bootstrapping of the $$\Lambda $$ Λ CDM model
Abstract The method of variational bootstrapping, based on canonical variational completion, allows one to construct a Lagrangian for a physical theory depending on two sets of field variables, starting from a guess of the field equations for only one such set. This setup is particularly appealing f...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-01-01
|
| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-025-13790-1 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832571365039800320 |
|---|---|
| author | Ludovic Ducobu Nicoleta Voicu |
| author_facet | Ludovic Ducobu Nicoleta Voicu |
| author_sort | Ludovic Ducobu |
| collection | DOAJ |
| description | Abstract The method of variational bootstrapping, based on canonical variational completion, allows one to construct a Lagrangian for a physical theory depending on two sets of field variables, starting from a guess of the field equations for only one such set. This setup is particularly appealing for the construction of modified theories of gravity, since one can take lessons from GR for an “educated guess” of the metric field equations; the field equations for the other fields are then fixed by the obtained Lagrangian (up to terms that are completely independent from the metric tensor). In the present paper, we apply variational bootstrapping to determine metric-affine models which are, in a variational sense, closest to the $$\Lambda $$ Λ CDM model of cosmology. Starting from an “educated guess” that formally resembles the Einstein field equations with a cosmological “constant” (actually, a scalar function built from the metric and the connection) and a dark matter term, the method then allows to find “corrected” metric equations and to “bootstrap” the connection field equations. Lagrangians obtained via this method, though imposing some restricting criteria, still encompass a wide variety of metric-affine models. In particular, they allow for a subclass of quadratic metric-affine theories restricted to linear terms in the curvature tensor. |
| format | Article |
| id | doaj-art-3316e0bb52064ca7a892b1688c8e25b9 |
| institution | Kabale University |
| issn | 1434-6052 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj-art-3316e0bb52064ca7a892b1688c8e25b92025-02-02T12:38:22ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522025-01-0185111310.1140/epjc/s10052-025-13790-1Metric-affine cosmological models and the inverse problem of the calculus of variations. Part II: Variational bootstrapping of the $$\Lambda $$ Λ CDM modelLudovic Ducobu0Nicoleta Voicu1Department of Mathematics and Computer Science, Transilvania University of BrasovDepartment of Mathematics and Computer Science, Transilvania University of BrasovAbstract The method of variational bootstrapping, based on canonical variational completion, allows one to construct a Lagrangian for a physical theory depending on two sets of field variables, starting from a guess of the field equations for only one such set. This setup is particularly appealing for the construction of modified theories of gravity, since one can take lessons from GR for an “educated guess” of the metric field equations; the field equations for the other fields are then fixed by the obtained Lagrangian (up to terms that are completely independent from the metric tensor). In the present paper, we apply variational bootstrapping to determine metric-affine models which are, in a variational sense, closest to the $$\Lambda $$ Λ CDM model of cosmology. Starting from an “educated guess” that formally resembles the Einstein field equations with a cosmological “constant” (actually, a scalar function built from the metric and the connection) and a dark matter term, the method then allows to find “corrected” metric equations and to “bootstrap” the connection field equations. Lagrangians obtained via this method, though imposing some restricting criteria, still encompass a wide variety of metric-affine models. In particular, they allow for a subclass of quadratic metric-affine theories restricted to linear terms in the curvature tensor.https://doi.org/10.1140/epjc/s10052-025-13790-1 |
| spellingShingle | Ludovic Ducobu Nicoleta Voicu Metric-affine cosmological models and the inverse problem of the calculus of variations. Part II: Variational bootstrapping of the $$\Lambda $$ Λ CDM model European Physical Journal C: Particles and Fields |
| title | Metric-affine cosmological models and the inverse problem of the calculus of variations. Part II: Variational bootstrapping of the $$\Lambda $$ Λ CDM model |
| title_full | Metric-affine cosmological models and the inverse problem of the calculus of variations. Part II: Variational bootstrapping of the $$\Lambda $$ Λ CDM model |
| title_fullStr | Metric-affine cosmological models and the inverse problem of the calculus of variations. Part II: Variational bootstrapping of the $$\Lambda $$ Λ CDM model |
| title_full_unstemmed | Metric-affine cosmological models and the inverse problem of the calculus of variations. Part II: Variational bootstrapping of the $$\Lambda $$ Λ CDM model |
| title_short | Metric-affine cosmological models and the inverse problem of the calculus of variations. Part II: Variational bootstrapping of the $$\Lambda $$ Λ CDM model |
| title_sort | metric affine cosmological models and the inverse problem of the calculus of variations part ii variational bootstrapping of the lambda λ cdm model |
| url | https://doi.org/10.1140/epjc/s10052-025-13790-1 |
| work_keys_str_mv | AT ludovicducobu metricaffinecosmologicalmodelsandtheinverseproblemofthecalculusofvariationspartiivariationalbootstrappingofthelambdalcdmmodel AT nicoletavoicu metricaffinecosmologicalmodelsandtheinverseproblemofthecalculusofvariationspartiivariationalbootstrappingofthelambdalcdmmodel |