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Obtaining the value of the dark energy from hyperconical universes

This presentation discusses the process of obtaining the value of dark energy from hyperconical universes, focusing on theoretical features and obtaining cosmological parameters. It also explores the geometric interpretation of dark energy. The model used is described in the references provided.

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Obtaining the value of the dark energy from hyperconical universes

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  1. VII Meeting on Fundamental Cosmology September 9-11, 2019. Madrid, Spain Obtaining the value of the dark energy from hyperconical universes Robert Monjo Department of Algebra, Geometry and Topology, Complutense University of Madrid

  2. Robert Monjo:Obtaining the value of the dark energy from hyperconical universes Contents I. Introduction II. General considerations III. Theoretical features IV. Obtaining parameters V. Conclusions RESULTS & DISCUSSION

  3. Robert Monjo:Obtaining the value of the dark energy from hyperconical universes I. Introduction Motivation The most simple manifold with linear expansion: Similar idea 1/H = t Dirac-Milne model (2012) [k < 0] Proper-time preservation: homogeneous case Local-time preservation: inhomogeneous case

  4. Robert Monjo:Obtaining the value of the dark energy from hyperconical universes Contents I. Introduction II. General considerations III. Theoretical features IV. Obtaining parameters V. Conclusions

  5. Robert Monjo:Obtaining the value of the dark energy from hyperconical universes II. General considerations Equivalence in time The local time of an observer in H4 is the same that in R1,3 Let be x0, x R1,3 two static points, x0 = (t0,0), x =(t,0), with t > t0> 0 Let be x0’, x’ H4 their extension, x0 = (t0,0, nt0), x =(t,0, nt) x0’’ = (t0,0, t/t0·nt0) k :=n– 2 Curvature

  6. Robert Monjo:Obtaining the value of the dark energy from hyperconical universes II. General considerations Hypothesis of local equivalences and projection Spatial projection The local space of an observer in H4 is the same that in R1,3 That is, the spatial distance is given by a locally conformal projection Let be r’ the comoving distance in H4, the spatial distance measured by an observer is: where Distorted stereographic projection Inverse of distorted stereographic projection

  7. Robert Monjo:Obtaining the value of the dark energy from hyperconical universes Contents I. Introduction II. General considerations III. Features of the model IV. Obtaining parameters V. Conclusions • Metric • Redshift-distance relation • Ricci curvature • Arnowitt-Deser-Misner (ADM) equations

  8. Robert Monjo:Obtaining the value of the dark energy from hyperconical universes III. Theoretical features A. Metric tensor Differential line element Metric tensor Change of coordinates

  9. Robert Monjo:Obtaining the value of the dark energy from hyperconical universes III. Theoretical features B. Redshift-distance relation Redshift and comoving distance

  10. Robert Monjo:Obtaining the value of the dark energy from hyperconical universes III. Theoretical features C. Ricci curvature locally k  1 K  0

  11. Robert Monjo:Obtaining the value of the dark energy from hyperconical universes III. Theoretical features D. Arnowitt-Deser-Misner (ADM) equations lapse shift total det spatial ko = k = 1

  12. Robert Monjo:Obtaining the value of the dark energy from hyperconical universes Contents I. Introduction II. General considerations III. Theoretical features IV. Obtaining parameters V. Conclusions

  13. Robert Monjo:Obtaining the value of the dark energy from hyperconical universes IV. Obtaining parameters Equivalent proper distance: Obtaining cosmological parameters

  14. Robert Monjo:Obtaining the value of the dark energy from hyperconical universes IV. Obtaining parameters Equivalent proper distance: Obtaining cosmological parameters

  15. Robert Monjo:Obtaining the value of the dark energy from hyperconical universes IV. Obtaining parameters Equivalent proper distance: Obtaining cosmological parameters

  16. Robert Monjo:Obtaining the value of the dark energy from hyperconical universes Contents I. Introduction II. General considerations III. Theoretical features IV. Obtaining parameters V. Conclusions

  17. Robert Monjo:Obtaining the value of the dark energy from hyperconical universes V. Conclusions • We have considered an inhomogeneous model with linear expansion that does not depends on the matter content. • The Hyperconical model is consistent with k1, and thus freedom for fitting is given by (locally conformal) spatial projections fa. • However, there exists a unique local projection fa(r << t)compatible with the LCDM model (that is, where model provides real values). • Thanks to this compatibility, the Hyperconical model predicts that  L = 0.6937181(2) and m = 0.306192(6) forto 1  k and r = (9.0 ± 0.5) ·10-5, whichis compatible with the Planck Mission results (L= 0.6911 ± 0.0062 and m = 0.3089 ± 0.0062).

  18. Robert Monjo:Obtaining the value of the dark energy from hyperconical universes Questions Thanks to Antonio López-Maroto and RutwigCampoamor for their feedback, and Thanks for your attention email: rmoncho@ucm.es Description of the inhomogeneous model used: R. Monjo, Phys. Rev. D, 96, 103505 (2017). doi:10.1103/PhysRevD.96.103505. arXiv:1710.09697 Geometric interpretation of the dark energy: R. Monjo, Phys. Rev. D, 98, 043508 (2018). doi:10.1103/PhysRevD.98.043508. arXiv:1808.09793

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