University of Chicago

- Introduction
- Temperature Maps
- Thermal History
- Acoustic Oscillations
- Angular Peaks
- First Peak
- Second Peak
- Higher Peaks
- Damping Tail
- Parameter Estimation
- Polarization
- Summary

- Gravitational waves show a power spectrum with both E and B mode contributions
- Limits on the gravitational wave contribution to the temperature anisotropy imply B-modes < a few tenths of a microKelvin.
- Gravitational waves probe the physics of inflation but will require a thorough understanding of foregrounds and secondary effects for their detection.

If there were only gravitational waves and no density perturbations in the Universe, the CMB temperature, polarization and temperature-polarization cross power spectra would look like:

Notice that the polarization contains power in both the E and B-modes. That we do see acoustic peaks in the spectrum indicates that this scenario cannot actually be true. At most, gravitational waves contribute a fraction of the power in temperature anisotropies. Adding back in the density fluctuations, the power spectrum as a function of the ratio of power in the gravitational wave (tensor, T) versus density (scalar, S) modes becomes:

For realistic values of this ratio or "T/S", the power in the B-mode corresponds to a tenth of a micro Kelvin signal on scales of l~100.

Needless to say, this signal will be very difficult to detect in the presence of foregrounds and secondary anisotropies that also produce B-modes. The rewards of detecting it are however great. The amplitude and spectrum of the gravitational wave contributions are our best probes of the physics of the inflationary epoch.