Understand
In a universe with a cosmological constant, the large-scale gravitational potential varies in time and this is, in principle, observable.
- Using an N-body simulation of a $\Lambda$CDM universe, we show that linear theory is not sufficiently accurate to predict the power spectrum of the time derivative, $\dot{\Phi}$, needed to compute the imprint of large-scale structure on the cosmic microwave background (CMB).
- The linear part of the $\dot{\Phi}$ power spectrum (the integrated Sachs-Wolfe effect or ISW) drops quickly as the relative importance of $\Omega_{\Lambda}$ diminishes at high redshift, while the non-linear part (the Rees-Sciama effect or RS) evolves more slowly with redshift.
- Therefore, the deviation of the total power spectrum from linear theory occurs at larger scales at higher redshifts.