Rethinking Time at the Big Bang

Transcription

1 Rethinking Time at the Big Bang Elizabeth S. Gould Perimeter Institute for Theoretical Physics and The University of Waterloo PASCOS 2017 June 22, 2017 Elizabeth Gould (PI / UW) Time Big Bang May 27, / 16

2 1 Holographic Cosmology Description Comparison of Models 2 Periodic Time Cosmology Description Results 3 Conclusion Elizabeth Gould (PI / UW) Time Big Bang May 27, / 16

3 1 Holographic Cosmology Description Comparison of Models 2 Periodic Time Cosmology Description Results 3 Conclusion Elizabeth Gould (PI / UW) Time Big Bang May 27, / 16

4 Some References Niayesh Afshordi, Elizabeth Gould, and Kostas Skenderis. Constraining holographic cosmology using Planck data. arxiv: [astro-ph.co]. Niayesh Afshordi, Claudio Corianò, Luigi Delle Rose, Elizabeth Gould, and Kostas Skenderis. From Planck data to Planck era: Observational tests of holographic cosmology. Phys. Rev. Lett., 118:041301, Jan Richard Easther, Raphael Flauger, Paul McFadden, and Kostas Skenderis. Constraining holographic inflation with WMAP. JCAP, 1109:030, Paul McFadden and Kostas Skenderis. The Holographic Universe. J. Phys. Conf. Ser., 222:012007, Elizabeth Gould (PI / UW) Time Big Bang May 27, / 16

5 Model Description domain wall holographic duality dual QFT We are here Wick rotation t iτ analytic continuation QFT (reheating surface) Early Universe t cosmology 'pseudo' QFT (defined operationally) Elizabeth Gould (PI / UW) Time Big Bang May 27, / 16

6 Dual QFT Lagrangian (arxiv ) models are defined by the dual QFT use a superrenormalizable (3D Euclidean) QFT S = 1 ˆ g YM [ 1 d 3 x tr 2 F ijf I Iij + 1 ( Dφ J) 2 1 ( ) + Dχ K 2 + ψ L /Dψ L λ M1 M 2 M 3 M 4 Φ M 1 Φ M 2 Φ M 3 Φ M 4 + µ αβ ML 1 L 2 Φ M ψ L 1 α ψ L 2 β ] dimensions: gym 2, φ, A = 1; ψ = 3 2 SU(N), N 10 4 ; parameters are: number of various fields: N, N φ, N χ, N ψ coupling constants: λ M1M 2M 3M 4, µ αβ ML 1L 2, g YM Elizabeth Gould (PI / UW) Time Big Bang May 27, / 16

7 Modified Spectrum difference between models given by primordial power spectra ( ) ( ) q (ns 1)+ nrun ln q 2 q 1 A = A 0 A = A 0 q 1 + (gq /q) ln (q/βgq ) all parameters are the same except g and ln (β) instead of n s (and n run ) define shape of power spectrum The holographic cosmology perturbation expansion is expected to break down at low l values for large g, when becomes large. gq q Elizabeth Gould (PI / UW) Time Big Bang May 27, / 16

8 Best Fit Parameters HC ΛCDM best fit 68% range best fit 68% range Ω b h ± ± Ω c h ± ± θ ± ± τ ± ± ± ± n s ± α s ± g ln β χ χ 2 = 4.8, difference in likelihood 2.2 σ gq = 2.5, so expansion expected to be invalid when l < 35 q Elizabeth Gould (PI / UW) Time Big Bang May 27, / 16

9 Best Fit Parameters for l > 30 HC ΛCDM best fit 68% range best fit 68% range Ω b h ± ± Ω c h ± ± θ ± ± τ ± ± ± ± n s ± α s ± g ln β χ Here, χ 2 = 0.5, meaning the difference is negligible. Elizabeth Gould (PI / UW) Time Big Bang May 27, / 16

10 1 Holographic Cosmology Description Comparison of Models 2 Periodic Time Cosmology Description Results 3 Conclusion Elizabeth Gould (PI / UW) Time Big Bang May 27, / 16

11 Cyclic Models conception - taking cyclic model and making it exactly periodic will use a conformal matching similar to Penrose s Conformal Cyclic Cosmology (CCC) Elizabeth Gould (PI / UW) Time Big Bang May 27, / 16

12 Transfer Function model matches large scales (with low k) of old spectrum to visible scales in new spectrum x x Bounce Models: expanding universe increases size of comoving scales Conformal Periodic Model: partially conformal sizes are matched to larger scales A 0 2. x x 10-9 ΛCDM Periodic Time Periodic Time with w = k k Penrose s CCC, like other cyclic models and inflation, match in the other direction, taking the portion of the transfer function with no power and reforming or constructing the primordial power spectrum at some time. Elizabeth Gould (PI / UW) Time Big Bang May 27, / 16

13 Description parameter α defines relative conformal rescaling of co-moving scales so k old = αk new P (k) primordial power spectrum, T (k) = ζ k(t= ) ζ k (t=0) transfer function P (k) = A 0 T (αk) 2 T ( α 2 k ) 2... invariant under evolution + rescaling producing repeating pattern, where each cycle shrinks previous and applies low-pass filter: α 1 so for observable k, T (αk) 1 and P (k) is approx. scale invariant with a red tilt Elizabeth Gould (PI / UW) Time Big Bang May 27, / 16

14 Preliminary Minimum χ 2 model run in CosmoMC with present T (k) used to determine P (k) lowteb+highl+lensing+bkp+bao+highp+tau χ 2 for ΛCDM χ 2 for PT χ 2 σ 6 params w w, w a ΛCDM PT Ω b h Ω c h θ τ w n s α Elizabeth Gould (PI / UW) Time Big Bang May 27, / 16

15 1 Holographic Cosmology Description Comparison of Models 2 Periodic Time Cosmology Description Results 3 Conclusion Elizabeth Gould (PI / UW) Time Big Bang May 27, / 16

16 Conclusion Holographic Cosmology By constructing a holographic dual on the "reheating surface", a non-geometric alternative to inflation can be constructed. This model was fit to data using CosmoMC and compared to ΛCDM. Holographic cosmology can match observation as well as ΛCDM. The model becomes non-perturbative for low l values or large angles. Periodic Time model run in CosmoMC which relates cosmic history to initial conditions at the big bang preliminary results indicate model is viable but disfavored 6 parameter model disfavored by 5.1σ best results from w 1, difference of 1.8σ Elizabeth Gould (PI / UW) Time Big Bang May 27, / 16