First glimpse of string theory in the sky?

We propose a new method for identifying new physics imprints on present observational data in cosmology whereby signatures of string theory are clearly distinguished from imprints of possible features on the inflaton potential. Our method relies on the cross-correlations spectra of cosmic shear from large scale structure (LSS) with the cosmic microwave background (CMB) temperature anisotropies and $E$-mode polarization, by using the following properties: inflationary cosmology provides only one source term for all CMB spectra and LSS which highly constrains any deviations from the standard predictions; string theory can add new noninflationary channels to the source of perturbations as well as modify clustering properties at large scales. Discrepancies in the source terms of correlations and clustering properties provide the evidence for new physics. Models of single-field inflation with a feature are disfavored even with present data. Upcoming Wilkinson microwave anisotropy probe (WMAP) results and future data from weak lensing of LSS will further improve our ability to probe new physics in this manner and could open the first direct window to string theory.

Figure 1

$TT$ spectra of the various models. The full line is the standard $\Lambda \mathrm{CDM}$ model, the dashed line has a modified primordial power spectrum, the dot-dashed a modified perturbation source term [case B]. Finally, the dotted line has a modified Friedman equation and modified source terms [case A]. Normalization is arbitrary.

Figure 2

${\chi }^2$ as a function of $k_c$. The full line is for case A and the dashed for case B.

Figure 3

$TT$ and $TE$ spectra of the various models. The full line is the standard $\Lambda \mathrm{CDM}$ model, the dashed line has a modified primordial power spectrum, the dot-dashed modified perturbation source terms [case A]. Finally, the dotted line has a modified Friedman equation and modified source terms [case B]. The data points are those measured by WMAP. Please note that the “error bars” are simply the diagonal terms in the Fisher matrix. They are not the true error bars for a given $l$, and are only intended as a visual guideline.

Figure 4

$TT$ and $EE$ spectra of models with a modified $\varphi$ according to Eq. (22). The curves are for $\alpha =0$ and various values of $k_c=2\pi /r_c$. The full line is for $k_c=0$, the long-dashed for $k={10}^{-6}h/\mathrm{Mpc}$, the dashed-dotted for $k={10}^{-5}h/\mathrm{Mpc}$, and the dashed for $k={10}^{-4}h/\mathrm{Mpc}$. Normalization is arbitrary.

Figure 5

$TT$ and $EE$ spectra of models with a modified $\varphi$ according to Eq. (22). The curves are for $\alpha =0.5$ and various values of $k_c=2\pi /r_c$. The full line is for $k_c=0$, the long-dashed for $k={10}^{-6}h/\mathrm{Mpc}$, the dashed-dotted for $k={10}^{-5}h/\mathrm{Mpc}$, and the dashed for $k={10}^{-4}h/\mathrm{Mpc}$. Normalization is arbitrary.

Figure 6

$TT$ and $EE$ spectra of models with a modified $\varphi$ according to Eq. (22), but with a negative sign. The curves are for $\alpha =0$ and various values of $k_c=2\pi /r_c$. The full line is for $k_c=0$, the long-dashed for $k={10}^{-6}h/\mathrm{Mpc}$, and the dashed-dotted for $k={10}^{-5}h/\mathrm{Mpc}$. Normalization is arbitrary.

Figure 7

Cross correlation between shear and temperature. The full line is the standard $\Lambda \mathrm{CDM}$ model, the dashed line has a modified primordial power spectrum, the dashed-dotted modified perturbation source terms [case B]. Finally, the dotted line has a modified Friedman equation and modified source terms [case A].