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Hubble drift in Palatini $f(\mathcal{R})$ f ( R ) theories

Profile image of Marco FerrarisMarco Ferraris

2019, The European Physical Journal Plus

Abstract
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In a Palatini f(R)-model, we define chronodynamical effects due to the choice of atomic clocks as standard reference clocks and develop a formalism to quantitatively separate them from the usual effective dark sources in extended theories obtained by recasting field equations. This formalism is applied to Hubble drift, highlighting the absence of a single physical frame, thereby demonstrating that different frames can yield varying physical interpretations. The Jordan frame is presented as a suitable cosmological framework, albeit with limitations in solar system applications.

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References (51)

  1. F. Melchiorri, B.O. Melchiorri, L. Pietranera, B.O. Melchiorri, Fluctuations in the microwave background at intermediate angular scales, The Astrophysical Journal. 250: L1, (1981).
  2. E. Komatsu et al., Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation, 2009 ApJS 180 330; arXiv:0803.0547 [astro-ph]
  3. Planck Collaboration, Planck 2015 results. XIII. Cosmological parameters, A&A 594, A13 (2016); arXiv:1502.01589 [astro-ph.CO]
  4. The Fermi-LAT Collaboration, The Fermi-LAT high-latitude Survey: Source Count Distributions and the Origin of the Extragalactic Diffuse Background, arXiv:1003.0895 [astro-ph.CO]
  5. The LIGO -Virgo Collaborations, GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral, Phys. Rev. Lett. 119 161101 (2017); arXiv:1710.05832 [gr-qc]
  6. Zwicky, F., Die Rotverschiebung von extragalaktischen Nebeln, Helvetica Phys- ica Acta, 6: (1933) 110-127
  7. Zwicky, F., On the Masses of Nebulae and of Clusters of Nebulae, Astrophysical Journal, 86: (1937) 217
  8. K.C. Freeman, On the Disks of Spiral and S0 Galaxies, Astrophysical Journal 160, 811 (1970)
  9. V.C. Rubin, J.W.K. Ford, Rotation of the Andromeda Nebula from a Spec- troscopic Survey of Emission Regions, The Astrophysical Journal 159, 379 (1970).
  10. V. Trimble, Existence and nature of dark matter in the universe. Annual Re- view of Astronomy and Astrophysics. 25: (1987). 425-472.
  11. A.G. Riess, et al., Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant, In: AJ 116, (1998) 1009-1038; arXiv:astro-ph/9805201
  12. M. Milgrom, A modification of the Newtonian dynamics as a possible alterna- tive to the hidden mass hypothesis, Astrophys. J. 270 (1983) 365.
  13. P. D. Mannheim, D. Kazanas, Exact Vacuum Solution to Conformal Weyl Gravity and Galactic Rotation Curves, Astrophys.J. 342 (1989) 635-638.
  14. M. Campigotto, L. Fatibene, Generally Covariant vs. Gauge Structure for Conformal Field Theories, Annals Phys. 362 (2015) 521?528; arXiv:1506.06071
  15. R. Jackiw, S.-Y. Pi, Fake Conformal Symmetry in Conformal Cosmological Models; arXiv:1407.8545
  16. T.Clifton, P.G.Ferreira, A.Padilla, C.Skordis, Modified Gravity and Cosmology, Phys.Rept. 513 (2012) 1-189; arXiv:1106.2476 [astro-ph.CO]
  17. L.Fatibene, S.Garruto, Extended Gravity, Int. J. Geom. Methods Mod. Phys., 11, 1460018 (2014); arXiv:1403.7036 [gr-qc]
  18. S.Capozziello, M. De Laurentis (2015), F (R) theories of gravitation, Scholar- pedia, 10(2):31422.
  19. L.Fatibene and M.Francaviglia, Extended Theories of Gravitation and the Cur- vature of the Universe -Do We Really Need Dark Matter? in : Open Questions in Cosmology, Edited by Gonzalo J. Olmo, Intech (2012), ISBN 978-953-51- 0880-1; DOI: 10.5772/52041
  20. G.J. Olmo, Palatini Approach to Modified Gravity: f(R) Theories and Beyond, arXiv:1101.3864 [gr-qc]
  21. A.Borowiec, M.Kamionka, A.Kurek, Marek Szyd lowski, Cosmic acceleration from modified gravity with Palatini formalism, arXiv:1109.3420 [gr-qc]
  22. Salvatore Capozziello, Mariafelicia F. De Laurentis, Lorenzo Fatibene, Marco Ferraris and Simon Garruto, Extended Cosmologies, SIGMA 12 (2016), 006, 16 pages; arXiv:1509.08008
  23. G. Magnano, L.M. Sokolowski, On Physical Equivalence between Nonlinear Gravity Theories Phys.Rev. D50 (1994) 5039-5059; gr-qc/9312008
  24. E.Barausse, T.P.Sotiriou, J.C.Miller, A no-go theorem for polytropic spheres in Palatini f (R) gravity, DOI: 10.1088/0264-9381/25/6/062001 (4th March 2008)
  25. G.J.Olmo, Re-examination of polytropic spheres in Palatini f (R) gravity, DOI: 10.1103/PhysRevD.78.104026 (20th October 2008)
  26. A. Mana, L.Fatibene, M.Ferraris A further study on Palatini f (R)-theories for polytropic stars, JCAP 1510 (2015) 040 (2015-10-16) DOI: 10.1088/1475- 7516/2015/10/040; arXiv:1505.06575
  27. A. Wojnar, On stability of a neutron star system in Palatini gravity, Eur. Phys. J. C (2018) 78: 421; arXiv:1712.01943 [gr-qc]
  28. P.Pinto, L.Del Vecchio, L.Fatibene, M.Ferraris, Extended Cosmology in Pala- tini f (R)-theories, (submitted); arXiv:1807.00397 [gr-qc]
  29. S.Nojiri, S.D. Odintsov, Modified gravity with negative and positive powers of the curvature: Unification of the inflation and of the cosmic acceleration, Phys.Rev. D68 (2003) 123512; hep-th/0307288
  30. S.Nojiri, S.D. Odintsov, Introduction to modified gravity and gravita- tional alternative for dark energy, in: eConf C0602061 (2006) 06, Int.J.Geom.Meth.Mod.Phys. 4 (2007) 115-146; hep-th/0601213
  31. S.Nojiri, S.D. Odintsov, Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models, Phys.Rept. 505 (2011) 59-144; arXiv:1011.0544
  32. V.F.Cardone, S.Camera, A.Diaferio, An updated analysis of two classes of f (R) theories of gravity, JCAP12, (2012); arXiv:1201.3272 [astro-ph.CO]
  33. S.Camera, A.Diaferio, V.F.Cardone, Tomography from the Next Generation of Cosmic Shear Experiments for Viable f (R) Models, JCAP07, (2011); arXiv:1104.2740 [astro-ph.CO]
  34. V.F.Cardone, S.Camera, R.Mainini, A.Romano, A.Diaferio, R.Maoli, R.Scaramella, Weak lensing peak count as a probe of f (R) theories, Monthly Notices of the Royal Astronomical Society, Volume 430, Issue 4, 21 (2013); arXiv:1204.3148 [astro-ph.CO]
  35. M.Roshan, F.Shojai, Palatini f (R) gravity and Noether symmetry, Phys.Lett. B668 (2008) 238-240; arXiv:0809.1272 [gr-qc]
  36. J.Ehlers, F.A.E.Pirani, A.Schild, The Geometry of Free Fall and Light Prop- agation, in: General Relativity, ed. L.O.'Raifeartaigh (Clarendon, Oxford, 1972).
  37. M. Di Mauro, L. Fatibene, M.Ferraris, M.Francaviglia, Further Extended The- ories of Gravitation: Part I Int. J. Geom. Methods Mod. Phys. Volume: 7, Issue: 5 (2010), pp. 887-898; gr-qc/0911.2841
  38. L.Fatibene, Relativistic Theories, Gravitational Theories and General Rela- tivity, in preparation, draft version 1.0.1. https://sites.google.com/site/lorenzofatibene/my-links/book-version-1-0-1
  39. V.Perlick, Characterization of Standard Clocks by Means of Light Rays and Freely Falling Particles, Gen. Rel. Grav. 19(11), (1987) 1059-1073
  40. A. Borowiec, M. Ferraris, M. Francaviglia, I. Volovich, Universality of Einstein Equations for the Ricci Squared Lagrangians, Class. Quantum Grav. 15, 43-55, 1998
  41. R. Scaramella et al., Euclid space mission: a cosmological challenge for the next 15 years, in Proceedings IAU Symposium No. 306, 2014, "Statistical Challenges in 21st Century Cosmology", A.F. Heavens, J.-L. Starck & A. Krone-Martins, eds; arXiv:1501.04908
  42. P.-S. Corasaniti, D.Huterer, A. Melchiorri, Exploring the Dark Energy Redshift Desert with the Sandage-Loeb Test, Phys.Rev.D75:062001,2007; arXiv:astro-ph/0701433
  43. EUCLID Collaboration (R. Laureijs (ESTEC, Noordwijk) et al.), Euclid Def- inition Study Report, ESA-SRE(2011)12; arXiv:1110.3193 [astro-ph.CO]
  44. Euclid Theory Working Group (Luca Amendola et al.), Cosmology and funda- mental physics with the Euclid satellite, Living Rev.Rel. 16 (2013) 6; arXiv:1206.1225 [astro-ph.CO]
  45. Luca Amendola et al., Cosmology and fundamental physics with the Euclid satellite, Living Rev.Rel. 21 (2018) no.1, 2; arXiv:1606.00180 [astro-ph.CO]
  46. P. Bull et al., Fundamental Physics with the Square Kilometer Array; arXiv:1810.02680 [astro-ph.CO]
  47. SKA Cosmology SWG Collaboration (Roy Maartens et al.), Overview of Cos- mology with the SKA, PoS AASKA14 (2015) 016 SISSA (2015-05-12); arXiv:1501.04076 [astro-ph.CO]
  48. Hans-Rainer Klckner et al., Real time cosmology -A direct measure of the expansion rate of the Universe with the SKA, PoS AASKA14 (2015) 027 SISSA (2015-05-27); arXiv:1501.03822 [astro-ph.CO]
  49. L.Fatibene, M.Francaviglia, Fluids in Weyl Geometries, IJGMMP, 09(2), 1260003 (2012); arXiv:1109.4115 [math-ph]
  50. G. Magnano, M. Ferraris, M. Francaviglia, Nonlinear gravitational La- grangians, Gen.Rel.Grav. 19(5), 1987, 465-479
  51. L. Fatibene, M.Francaviglia, Mathematical Equivalence versus Physical Equiv- alence between Extended Theories of Gravitation, Int. J. Geom. Methods Mod. Phys. 11(1), 1450008 (2014); arXiv:1302.2938 [gr-qc]

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