Phenomenological model for the early universe

We consider the description of cosmological dynamics from the onset of inflation by a perfect fluid whose parameters must be consistent with the strength of the enhanced quantum loop effects that can arise during inflation. The source of these effects must be nonlocal and a simple incarnation of it is studied both analytically and numerically. The resulting evolution stops inflation in a calculable amount of time and leads to an oscillatory universe with a vanishing mean value for the curvature scalar and an oscillation frequency which we compute.

Figure 1

The evolution of the source $X(t)$ over the full range for the exponential model.

Figure 2

The evolution of the source $X(t)$ during the oscillatory regime for the exponential model.

Figure 3

The evolution of the curvature scalar $R(t)$ over the full range for the exponential model.

Figure 4

The evolution of the curvature scalar $R(t)$ during the oscillatory regime for the exponential model.

Figure 5

The evolution of the Hubble parameter $H(t)$ over the full range for the exponential model.

Figure 6

The evolution of the Hubble parameter $H(t)$ during the oscillatory regime for the exponential model.

Figure 7

The evolution of $\dot{H}(t)$ over the full range for the exponential model.

Figure 8

The evolution of $\dot{H}(t)$ during the oscillatory regime for the exponential model.

Figure 9

The evolution of the deceleration parameter $q(t)$ during the oscillatory regime for the exponential model.

Figure 10

The evolution of the deceleration parameter $q(t)$ around the end of inflation for the exponential model.

Figure 11

The evolution of the scale factor ratio $[a(t)/a(150000)]$ during the oscillatory regime for the exponential model versus a linear interpolation.

Figure 12

Determining the critical point $1-8\pi ϵf[-ϵX_i]=0$ for the exponential model.