Trajectories 05.11.16

Bond, Contaldi, Frolov, Kofman, Souradeep, Vaudrevange 05

String Theory Landscape & Inflation++ Phenomenology for CMB+LSS

running index as simplest breaking, radically broken scale invariance, 2+-field inflation, isocurvatures, Cosmic strings/defects, compactification & topology, & other baroque add-ons.

subdominant

String/Mtheory-motivated, extra dimensions, brane-ology, reflowering of inflaton/isocon models (includes curvaton), modified kinetic energies, k-

essence, Dirac-Born-Infeld [sqrt(1-momentum**2), “DBI in the Sky” Silverstein etal 2004], etc.

14 std inflation

parameters+ many many

more e.g. “blind”

search for patterns in

the primordial

power spectrum

Potential of the Hybrid D3/D7 Inflation Model

KKLT, KKLMMTany acceleration

trajectory will do??

q (ln Ha)

H(ln a,…)

V(phi,…)

Measure??

anti-baroque prior

Beyond P(k): Inflationary trajectories

[Peiris et al. 2003]

ns

r

H(N) P(k)ï ;ñ:::

ns;nt; r;dn=dlnk;As; :::

Bond, Contaldi, Frolov, Kofman, Souradeep, Vaudrevange 05

HJ + expand about uniform acceleration, 1+q, V and power spectra are derived

HJ + expand about uniform acceleration, 1+q, V and power spectra are derived

7

10

Trajectories cf. WMAP1+B03+CBI+DASI+VSA+Acbar+Maxima + SDSS + 2dF

Chebyshev 7 & 10 H(N) and RG Flow

Trajectories cf. WMAP1+B03+CBI+DASI+VSA+Acbar+Maxima + SDSS + 2dF

Chebyshev 7 & 10 H(N) and RG Flow

H(N) P(k)

ns;nt; r;dn=dlnk;As; :::

ï ;ñ:::

H (ln Ha) / (10-5 mP) inflation trajectory reconstructed from CMB+LSS data using

Chebyshev expansion (order 10) & MCMC.

H (ln Ha) / (10-5 mP) inflation trajectory reconstructed from CMB+LSS data using

Chebyshev expansion (order 10) & MCMC.

Ps,t (ln k) / (10-10) reconstructed from CMB+LSS data using dual

Chebyshev expansions (order 15 scalar & 5 tensor) and Markov Chain Monte Carlo methods. best-fit & mean-fit. No S/T generalized consistency relation is

imposed. Probe of CMB+LSS window only ~ 10 e-folds.

Ps,t (ln k) / (10-10) reconstructed from CMB+LSS data using dual

Chebyshev expansions (order 15 scalar & 5 tensor) and Markov Chain Monte Carlo methods. best-fit & mean-fit. No S/T generalized consistency relation is

imposed. Probe of CMB+LSS window only ~ 10 e-folds.

H (ln a) / (10-5 mP) inflation trajectory reconstructed from CMB+LSS data using

Chebyshev expansion (order 10) & MCMC.

Derived scalar and tensor power spectra Ps,t (ln k) / (10-10) (generalized

consistency relation built in) and derived potential V

H (ln a) / (10-5 mP) inflation trajectory reconstructed from CMB+LSS data using

Chebyshev expansion (order 10) & MCMC.

Derived scalar and tensor power spectra Ps,t (ln k) / (10-10) (generalized

consistency relation built in) and derived potential V

H (ln a) / (10-5 mP) vs ln H (ln a) / (10-5 mP) inflation trajectory reconstructed

from CMB+LSS data using Chebyshev expansion (order 10) & MCMC.

H (ln a) / (10-5 mP) vs ln H (ln a) / (10-5 mP) inflation trajectory reconstructed

from CMB+LSS data using Chebyshev expansion (order 10) & MCMC.

H (ln a) / (10-5 mP) inflation trajectory reconstructed from CMB+LSS data using

Chebyshev expansion (order 10 cf. order 5) & MCMC.

H (ln a) / (10-5 mP) inflation trajectory reconstructed from CMB+LSS data using

Chebyshev expansion (order 10 cf. order 5) & MCMC.

Forecasts of how ln H(ln Ha) Chebyshev expansions will do with Planck 2.5 year and other CMB datasets using order 10

as an example

CL for H (ln Ha) best-fit inflation trajectory reconstructed from CMB+LSS data

using Chebyshev expansion (order 10) & MCMC cf. dual Chebyshev expansion of scalar (15) & tensor (5) power spectra, unconstrained by T/S consistency / inflation

CL for H (ln Ha) best-fit inflation trajectory reconstructed from CMB+LSS data

using Chebyshev expansion (order 10) & MCMC cf. dual Chebyshev expansion of scalar (15) & tensor (5) power spectra, unconstrained by T/S consistency / inflation

Forecasts of how ln H(ln Ha) Chebyshev expansions will do with Planck 2.5 year datasets using order 10 as an example

cheb used instead of A_s, r_ts, alpha_s, n_s to describe the

inflation dynamics

for planck2.5yr 100 and 143 GHz data,

With a chebyshev expansion of lnH to order 10, with other cosmic parameters fixed: of 10 cheb coeffs, 10 determined to 10%, 5 to 1% accuracy

cheb + 5 cosmic params (4 abundances and the Compton depth): of 15 all to 10%, 10 to 1% (includes one fixed)

9 cosmic params, A_s, r_ts, alpha_s, n_s in place of the Chebyshev coefficients: of 9 all to 10%, 7 to 1%

result of this limited study: omb, omc, omv omnu errors are similar, tauC a little higher. one reason is that there is not much complexity in the cheb in the high L region where omega_b etc are concentrated. Polarization information helps to break degeneracies as well.

Forecasts of how ln H(ln Ha) Chebyshev expansions will do with Planck 2.5 year datasets using order 10 as an example

a series of Delta C_L /C_L figs, comparing simulated data with perturbed chebyshev templates and eigentemplates for TT

Fig: ch1_Planck25_jan04_cosmicvar

magenta error bars are for planck. act and spt will improve the high L end as well. dashed blue +- curves, the higher shows the cosmic variance limit for each multipole, using fsky=0.9, as was used for planck. the lower one shows cosmic variance if the data is banded into log spacings with Delta ln L =0.1.

black error bars are jan04 data, so not including boomerang03, new acbar or combined CBI TT.

dashed black line: best fit to jan04 data relative to lnH10g best fit (which does not have as much freedom at the high L end because thecosmic params were fixed)

Forecasts of how ln H(ln Ha) Chebyshev expansions will do with Planck 2.5 year datasets using order 10 as an example

a series of Delta C_L /C_L figs, comparing simulated data with perturbed chebyshev templates and eigentemplates for TT

Fig: ch1_Planck25_cl5chmodes

CL first 5 templates for the 10 chebyshevs shows that there is not that much complexity in 1 to 5, more for 6 to 10.

Forecasts of how ln H(ln Ha) Chebyshev expansions will do with Planck 2.5 year datasets using order 10 as an example

a series of Delta C_L /C_L figs, comparing simulated data with perturbed chebyshev templates and eigentemplates for TT

Fig: ch1_Planck25_cl10chemodes

CL top 5 eigentemplates for the lnH10 expansion for chebyshev only, with other cosmic parameters fixed

top 5 eigenmodes in CL. the sign of the template patterns is arbitrary. the value of the eigenmode would be determined by shifting the

amplitude of the curve until it fits the data. the templates have been scaled so as to be visible on the figure. some CL modes have been

scaled more than others.

Forecasts of how ln H(ln Ha) Chebyshev expansions will do with Planck 2.5 year datasets using order 10 as an example

a series of Delta C_L /C_L figs, comparing simulated data with perturbed chebyshev templates and eigentemplates for TT

Fig:ch1_Planck25_cl10ch6paremodes

top 5 eigentemplates for the lnH10 expansion for chebyshev + 6

parameters, one of which (omega_k) is frozen (to zero)

Baryonic acoustic oscillations appear in some of the modes

Forecasts of how ln H(ln Ha) Chebyshev expansions will do with Planck 2.5 year datasets using order 10 as an example

a series of Delta C_L /C_L figs, comparing simulated data with perturbed chebyshev templates and eigentemplates for TT

Fig: ch1_Planck25_cl16paremodes

CL top 5 eigentemplates for 10 std cosmo parameters, the usual 6 plus A_s, n_s, alpha_s, r_ts (omega_k is frozen to zero)

Degeneracy of the Potential Reconstruction