Dark energy as double N-flation - observational predictions

We propose a simple model for dark energy useful for comparison with observations. It is based on the idea that dark energy and inflation should be caused by the same physical process. As motivation, we note that Linde's simple chaotic inflation V = 1/2m(2)phi(2) produces values of n(s) = 0.967 and r = 0.13, which are consistent with the Wilkinson Microwave Anisotropy Probe (WMAP) 1 sigma error bars. We therefore propose V = 1/2m(2)(2)phi(2)(2) + 1/2m(1)(2)phi(2)(1) with m(1) similar to 10(-5) and m(2) <= 10(-60), where c = 1 = h and the reduced Planck mass is set to unity. The field phi(1) drives inflation and has damped by now (phi(1,0) = 0), while phi(2) is currently rolling down its potential to produce dark energy. Using this model, we derive the formula delta w(z) equivalent to w(z) + 1 = delta w(0)(H-0/H(z))(2) via the slow-roll approximation. Our numerical results from exact and self-consistent solution of the equations of motion for phi(2) and the Friedmann equations support this formula, and it should hold for any slow-roll dark energy. Our potential can be easily realized in N-flation models with many fields, and is easily falsifiable by upcoming experiments - for example, if Linde's chaotic inflation is ruled out. But if r values consistent with Linde's chaotic inflation are detected then one should take this model seriously indeed.