Emergence of Warm Inflation in Curved Space-Time between Accelerating Branes

It appears that having our own brane to somehow interact with other branes could give rise to quite an interesting system and that
interaction could lead to some observable effects. We consider the question of whether or not these signatures of interaction
between the branes can be observed. To answer this question, we investigate the effect induced by the inflaton in the WMAP7
data using the warm inflationary model. In this model, slow-roll and perturbation parameters are given in terms of the inflaton
thermal distribution. We show that this distribution depends on the orbital radius of the brane motion under the interaction
potential of other branes in extra dimensions. Thus, an enhancement in the brane inflation can be a signature of an orbital
motion in extra dimensions, and consequently, some signals of other branes can be detected by observational data. According to
experimental data, the N ≃ 50 case leads to ns ≃ 0:96, where N and ns are the number of e-folds and the spectral index,
respectively. This standard case may be found in the range 0:01 < Rtensor‐scalar < 0:22, where Rtensor‐scalar is the tensor-scalar ratio.
We find that at this point, the radial distance between our brane and another brane is R = ð1:5 GeVÞ
−1 in intermediate and R =
ð0:02225 GeVÞ
−1 in logamediate inflation.