Observational tests of Tachyonic and Holographic Models of Inflation
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TIM 20-21 Physics Conference 11 - 13 November 2021, Timisoara, Romania
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Observational tests of Tachyonic and Holographic Models of Inflation
- 1. 11 – 13 November 2021, Timisoara, Romania in collaboration with: N. Bilić (Zagreb), G.S. Djordjević, D.D. Dimitrijević and M. Stojanović (Niš) This work has been supported by the Serbian Ministry for Education, Science and Technological Development under contract No. 451-03-9/2021-14/200124.
- 3. Baumann, D. TASI Lectures on Inflation. (2009), arXiv:0907.5424 [hep-th]
- 4. Baumann, D. TASI Lectures on Inflation. (2009), arXiv:0907.5424 [hep-th]
- 6. 𝑇𝜈 𝜇 = 𝜌𝑐2 0 0 0 0 −𝑝 0 0 0 0 −𝑝 0 0 0 0 −𝑝
- 8. A negative pressure runs inflation 𝜌 ≡ ℋ = 1 2 ሶ 𝜙2 + 𝑉(𝜙) 𝑝 ≡ ℒ = 1 2 ሶ 𝜙2 − 𝑉(𝜙) the canonical Lagrangian
- 9. | | | 3 | | | | | H V
- 10. ሶ 𝜙 = 𝜋 ሶ 𝜋 = −3𝐻𝜋 − 𝑉′ 𝐻2 = 8𝜋𝐺 3 1 2 ሶ 𝜙2 + 𝑉 ሶ 𝐻 = − 8𝜋𝐺 2 ሶ 𝜙2 𝜃,𝜇 = 𝜕ℋ 𝜕𝜋𝜇 𝜋;𝜇 𝜇 = − 𝜕ℋ 𝜕𝜃
- 11. Planck 2018 results. X Constraints on inflation, arXiv:1807.06211 [astro-ph.CO]
- 13. D. Steer, F. Vernizzi, Tachyon inflation: Tests and comparison with single scalar field inflation, Phys. Rev. D. 70 (2004) 43527. M. Milosevic, D.D. Dimitrijevic, G.S. Djordjevic, M.D. Stojanovic, Dynamics of tachyon fields and inflation, Serbian Astronomical Journal. 192 (2016) the non-canonical (DBI) Lagrangian
- 14. 𝜏 = 𝑡/ℓ, 𝜃 = Θ/ℓ, ℎ = ℓ𝐻.
- 16. x 5 x y 0 y = y l = y → Animation: N. Bilic, “Braneworld Universe”, 2nd CERN – SEENET-MTP PhD School, Timisoara, December 2016 0 0 • Observer reside on the brane with negative tension, • Distance to the 2nd brane corresponds to the Netwonian gravitational constant
- 17. 0 y = y → 0 0 Animation: N. Bilic, “Braneworld Universe”, 2nd CERN – SEENET-MTP PhD School, Timisoara, December 2016 x 5 x y • Observer is placed on the positive tension brane • 2nd brane is pushed to infinity
- 18. N. Bilic, G.B. Tupper, AdS braneworld with backreaction, Cent. Eur. J. Phys. 12 (2014) 147–159. N. Bilic, D.D. Dimitrijevic, G.S. Djordjevic, M. Milosevic, Tachyon inflation in an AdS braneworld with back-reaction, IJMPA. 32 (2017) 1750039.
- 19. N. Bilić, S. Domazet, G.S. Djordjevic, Particle Creation and Reheating in a Braneworld Inflationary Scenario, Physical Review D, 96 (2017), 083518 N. Bilić, S. Domazet, and G. S. Djordjevic, Tachyon with an inverse power-law potential in a braneworld cosmology, Class. Quantum Gravity 34, 165006 (2017).
- 20. 𝜒,𝜃 = 𝜕𝜒 𝜕𝜃 𝜏 = 𝑡/ℓ, 𝜃 = Θ/ℓ, 𝜋𝜃 = ΠΘ/𝜎 and ℎ = ℓ𝐻 ℎ2 = 𝜅2 3 ρ ሶ ℎ = − 𝜅2 2 (𝑝 + ρ) ℎ2 = 𝜅2 3 𝜌 1 + 𝜅2 12 𝜌 ሶ ℎ = − 𝜅2 2 (𝑝 + 𝜌) 1 + 𝜅2 6 𝜌
- 21. time Conformal boundary at z=0 space z x RSII brane at z=zbr N. Bilić, Randall-Sundrum vs Holographic Cosmology, IRB (2015)
- 22. ℎ2 − ℓ2 4 ℎ4 = 𝜅2 3 ℓ4𝜌 ሶ ℎ 1 − ℓ2 2 ℎ2 = − 𝜅2 3 ℓ3 (𝑝 + 𝜌) Standard cosmology: ℎ2 = 𝜅2 3 𝜌 ሶ ℎ = − 𝜅2 2 (𝑝 + 𝜌) Extended RSII cosmology ℎ2 = 𝜅2 3 𝜌 𝜒,𝜑 + 𝜅2 12 𝜌 ሶ ℎ = − 𝜅2 2 (𝜌 + 𝑝) 𝜒,𝜃 + 𝜅2 6 𝜌 + 𝜅2 𝜌 6ℎ 𝜒,𝜃𝜃 ሶ 𝜃 Bilić, N., Dimitrijević, D. D., Djordjevic, G. S., Milošević, M. & Stojanović, M. Tachyon inflation in the holographic braneworld. JCAP 2019, 034–034 (2019).
- 25. Hubble expansion rate at an arbitrarily chosen time At the lowest order in parameters 𝜀1 and 𝜀2 𝜀1 = − ሶ 𝐻 𝐻2 , 𝜀2 = 2𝜀1 + ሷ 𝐻 𝐻 ሶ 𝐻 .
- 27. Bertini, N. R., Bilic, N. & Rodrigues, D. C. Primordial perturbations and inflation in holographic cosmology. arXiv:2007.02332 [gr-qc]
- 28. E. D. Stewart, D. H. Lyth, A more accurate analytic calculation of the spectrum of cosmological perturbations produced during inflation. Physics Letters B 302, 171–175 (1993) S. M. Leach, et al. Cosmological parameter estimation and the inflation cosmology. Physical Review D, 66(2):023515 (2002) D. J. Schwarz, et al. Higher order corrections to primordial spectra from cosmological inflation. Physics Letters B, 517(3-4):243249 (2001)
- 29. J. Garriga, V. F. Mukhanov, Perturbations in k-inflation. Physics Letters B, 458, 219 (2019) Planck Collaboration et al. Planck 2015 results. XX. Constraints on inflation. Astronomy and Astrophysics 594, A20 (2015) Tachyon / RSII models 𝑐𝑠 = 1 − 2𝛼𝜖1 Holography 𝑐𝑠 2 = 1 − 4 2−ℎ2 3 4−ℎ2 𝜖1
- 31. 𝑉 𝜃 = 1/cosh 𝜔 ∙ 𝜃 𝑉 𝜃 = 𝑒−𝜔∙𝜃
- 32. cosh FLRW cosm. Mean SD Median Min Max the 1st order 1.3396E-02 5.5927E-03 1.2097E-02 9.4278E-03 6.9943E-02 SSFI approx. 2.0475E-02 4.7044E-03 1.9572E-02 1.5762E-02 7.0142E-02 DBI approx. 1.2225E-02 5.7737E-03 1.0853E-02 8.3776E-03 6.9909E-02 cosh RSII cosm. Mean SD Median Min Max the 1st order 1.3321E-02 5.3614E-03 1.2100E-02 9.4247E-03 5.2567E-02 SSFI approx. 2.0402E-02 4.5315E-03 1.9560E-02 1.5735E-02 5.3441E-02 DBI approx. 1.2150E-02 5.5342E-03 1.0860E-02 8.3722E-03 5.2419E-02 exp FLRW cosm. Mean SD Median Min Max the 1st order 1.1396E-02 1.3328E-03 1.1241E-02 9.1414E-03 1.4208E-02 SSFI approx. 1.9218E-02 2.2846E-03 1.8955E-02 1.5574E-02 2.3888E-02 DBI approx. 1.0103E-02 1.1774E-03 9.9660E-03 8.0761E-03 1.2619E-02 exp RSII cosm. Mean SD Median Min Max the 1st order 1.1365E-02 1.3330E-03 1.1189E-02 9.1555E-03 1.4215E-02 SSFI approx. 1.9163E-02 2.2810E-03 1.8846E-02 1.5602E-02 2.3856E-02 DBI approx. 1.0075E-02 1.1782E-03 9.9210E-03 8.0881E-03 1.2624E-02 Relative distance 𝐷𝑟𝑒𝑙 = 𝑛𝑠 𝑥−𝑛𝑠 𝑛𝑠 2 + 𝑟𝑥−𝑟 𝑟 2
- 33. the 1st order SSFI approx. DBI approx. 1/𝑐𝑜𝑠ℎ 𝑒𝑥𝑝
- 34. 𝑉 𝜃 = 1/cosh 𝜔 ∙ 𝜃 𝑉 𝜃 = 𝑒−𝜔∙𝜃
- 35. cosh Mean SD Median Min Max the 1st order 3.7549E-04 1.8174E-04 3.6010E-04 7.4457E-06 1.2373E-02 SSFI approx. 5.1915E-03 1.9399E-03 5.5239E-03 4.0643E-05 1.6928E-02 DBI approx. 3.7540E-04 1.7579E-04 3.6010E-04 7.4457E-06 1.1617E-02 exp Mean SD Median Min Max the 1st order 4.5297E-04 1.5079E-04 4.3861E-04 6.7424E-07 1.0413E-02 SSFI approx. 7.5232E-03 9.2425E-04 7.4617E-03 5.9833E-03 1.7119E-02 DBI approx. 4.5286E-04 1.4365E-04 4.3861E-04 6.7424E-07 9.3032E-03
- 36. 𝑉 𝜃 = 1/cosh 𝜔 ∙ 𝜃 𝑉 𝜃 = 𝑒−𝜔∙𝜃
- 37. cosh Mean SD Median Min Max the 1st order 8.7564E-04 5.8021E-04 7.5464E-04 4.6819E-05 2.8589E-03 SSFI approx. 3.8238E-03 2.5030E-03 3.4341E-03 1.6676E-04 1.0734E-02 DBI approx. 3.0811E-04 1.5252E-04 3.0213E-04 8.8627E-07 1.6074E-03 exp Mean SD Median Min Max the 1st order 2.1148E-03 2.7486E-04 2.0906E-03 1.4515E-03 3.1080E-03 SSFI approx. 9.5527E-03 1.2652E-03 9.4020E-03 7.4137E-03 1.4797E-02 DBI approx. 3.9348E-04 1.6103E-04 3.7461E-04 1.7968E-06 1.7713E-03
- 38. Model Potential Analytic 1st order SSFI approx. DBI approx. Rel. (1st ord.) Rel. (SSFI) Rel. (DBI) Tachyon FLRW exp 9.165E-01 9.174E-01 9.181E-01 9.173E-01 1.01E-03 6.81E-04 7.94E-04 cosh 9.165E-01 9.174E-01 9.181E-01 9.173E-01 1.01E-03 6.81E-04 7.94E-04 RSII exp 9.163E-01 9.172E-01 9.178E-01 9.171E-01 1.01E-03 6.81E-04 7.94E-04 cosh 8.991E-01 9.001E-01 9.007E-01 9.000E-01 1.11E-03 6.86E-04 8.00E-04 RSII model exp 9.150E-01 9.150E-01 9.157E-01 9.150E-01 1.64E-06 6.83E-04 6.82E-04 cosh 8.686E-01 8.686E-01 8.692E-01 8.686E-01 5.64E-07 6.86E-04 6.85E-04 Holography exp 9.137E-01 9.139E-01 9.145E-01 9.137E-01 1.96E-04 6.83E-04 8.76E-04 cosh 7.933E-01 7.934E-01 7.938E-01 7.933E-01 1.45E-04 5.53E-04 7.00E-04