Outline Inflationary Cosmology Reconstructing the promodial power spectrum

Outline Ø Inflationary Cosmology Ø Reconstructing the promodial power spectrum Ø Reconstructing the inflationary potential Ø Summary

4 dimensional Inflation predicts No classical inhomogeneities from the past Scale free gaussian fluctuations of all light scalars No vector perturbations Scalar (almost scale free gaussian) metric perturbations Tensor (scale free gaussian) metric perturbations Creation of all SM particles in preheating/thermalization

Inflation in the context of ever changing fundamental theory 1980 -inflation Old Inflation New Inflation Chaotic inflation SUGRA inflation Double Inflation 1990 Extended inflation Hybrid inflation SUSY F-term inflation 2000 Power-law inflation SUSY P-term inflation Racetrack inflation Assisted inflation SUSY D-term inflation Brane inflation Super-natural Inflation K-flation N-flation DBI inflation Tachyon inflation Warped Brane inflation

Reconstruction strategy assuming scalar field is a monotonically varying function of cosmic time Phys. Rev. D. 48. 2529

Perturbative reconstruction During reconstruction, there are three types of expansion being carried out. There is an expansion in terms of observables, an expansion in terms of slow-roll parameters, and an expansion of the potential itself. Rev. Mod. Phys. 69. 373

BICEP 2 V. S. Planck But. . . M. J. Mortonson and U. Seljak, ar. Xiv: 1405. 5857 [astro-ph. CO]. R. Flauger, J. C. Hill and D. N. Spergel, ar. Xiv: 1405. 7351 [astro-ph. CO]

Reconstruction of the primordial power spectra with Planck and BICEP 2 ar. Xiv: 1404. 3690 [astro-ph. CO] Bin Hu , Jian-Wei Hu , Zong-Kuan Guo , Rong-Gen Cai

Reconstruction of the primordial power spectra with Planck and BICEP 2 ar. Xiv: 1403. 7786 [astro-ph. CO] 1403. 5922[astro-ph. CO]

Reconstruction of the primordial power spectra with Planck and BICEP 2 ar. Xiv: 1404. 3690 [astro-ph. CO] Bin Hu , Jian-Wei Hu , Zong-Kuan Guo , Rong-Gen Cai

Reconstruction of the inflation potential with Planck and BICEP 2

Reconstruction of the inflation potential with Planck and BICEP 2

Reconstruction of the inflation potential with Planck and BICEP 2 • Fix k at 0. 05, then we run MCMC. It could output the parameters that we need, including (A , n , α , r) at fix point k = 0. 05, using the formula 0 one can get the values of (A , n , α , r) at any point k, s s s above, s s s • Let ∆ ln k = − 1, using equation (10) or (15), it is easy to calculate the corresponding ∆φ, • For every lnki = lnk 0 +i∆lnk(i = 1, 2, 3, . . . ), we can compute the values of V(ki), V ′′(ki), V ′′′(ki) according to equations (22 -25). Also utilising the relationship between k and φ, one can rewrite the V (φi) and its high derivatives, • to use the interpolate method to reconstruct the inflation potential for a long range.

Reconstructed potential

Summary • we reconstructed the primordial scalar power spectra using the cubic spline interpolation method from recently CMB data, and find that the vanishing scalar index running model is disfavored at more than 3sigma level • the power-low parameterization gives a blut-tilt tensor spectrum, no matter using only the first 5 bandpowers or the full 9 bandpowers of the BICEP 2 data sets • Given that the hint of a large running of the scalar power spectrum, and a nonzero tensor-to-scalar ratio r, we reconstruct the inflationary potential in the perturbative reconstruction framework

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