Constraints from the cosmic microwave background on spacetime noncommutativity and causality violation

We try to constrain the noncommutativity length scale of the theoretical model given in [E. Akofor, A. P. Balachandran, S. G. Jo, A. Joseph, and B. A. Qureshi, J. High Energy Phys. 05 (2008) 092.] using the observational data from ACBAR, CBI and 5 yr WMAP. ACBAR and CBI data restrict the lower bound of the noncommutativity energy scale to be around 10 TeV. We also derive an expression for the amount of noncausality coming from spacetime noncommutativity for the fields of primordial scalar perturbations that are spacelike separated.

Figure 1

Transfer function ${\Delta }_l$ for $l=10$ as a function of $k$. It peaks around $k=0.001{\mathrm{Mpc}}^{-1}$.

Figure 2

Transfer function ${\Delta }_l$ for $l=800$ as a function of $k$. It peaks around $k=0.06{\mathrm{Mpc}}^{-1}$.

Figure 3

CMB power spectrum of $\Lambda \mathrm{CDM}$ model (solid curve) compared to the WMAP data (points with error bars).

Figure 4

The values of $k$ which maximize ${\Delta }_l(k)$, as a function of $l$.

Figure 5

${\chi }^2$ versus $H\theta$ for ACBAR data.