Role of dissipative effects in the quantum gravitational onset of warm Starobinsky inflation in a closed universe

A problematic feature of low-energy-scale inflationary models, such as Starobinsky inflation, in a spatially closed universe is the occurrence of a recollapse and a big crunch singularity before inflation can even set in. In a recent work, it was shown that this problem can be successfully resolved in loop quantum cosmology for a large class of initial conditions due to a nonsingular cyclic evolution and a hysteresislike phenomenon. However, for certain highly unfavorable initial conditions, the onset of inflation was still difficult to obtain. In this work, we explore the role of dissipative particle production, which is typical in warm inflation scenario, in the above setting. We find that entropy production sourced by such dissipative effects makes hysteresislike phenomena stronger. As a result, the onset of inflation is quick in general, including for highly unfavorable initial conditions where it fails or is significantly delayed in the absence of dissipative effects. We phenomenologically consider three warm inflation scenarios with distinct forms of dissipation coefficient and from dynamical solutions and phase-space portraits find that the phase space of favorable initial conditions turns out to be much larger than in cold inflation.

Figure 1

The evolution of volume for different values of cubic dissipation coefficient. Initial conditions are chosen at the bounce with $v_0=5\times {10}^7$, ${\varphi }_0=-1$, ${\rho }_{r0}={10}^{-12}$, and $g=17$.

Figure 2

The evolution of equation of state for cubic dissipation coefficient and same initial conditions as in Fig. 1.

Figure 3

The evolution of volume for different values of linear dissipation coefficient. Initial conditions are chosen at the bounce with $v_0={10}^7$, ${\varphi }_0=-1.5$, ${\rho }_{r0}={10}^{-11}$, and $g=12.5$.

Figure 4

The evolution of equation of state for linear dissipation coefficient and same initial conditions as in Fig. 3.

Figure 5

The evolution of volume for different values of inverse dissipation coefficient. Initial conditions are chosen at the bounce with $v_0=2.5\times {10}^6$, ${\varphi }_0=-2$, ${\rho }_{r0}={10}^{-9}$, and $g=12.5$.

Figure 6

The evolution of equation of state for inverse dissipation coefficient and same initial conditions as in Fig. 5.

Figure 7

Projection of three-dimensional phase-space portrait on $Z=0$ plane for cubic dissipation coefficient with $m=0.62$, $C_{\mathrm{cub}}=7.5$, $v_0=35$, ${\rho }_{r0}={10}^{-3}$, and seven distinct initial conditions for ${\varphi }_0$.

Figure 8

Evolution of energy components as well as equation of state for cubic dissipation coefficient with $m=0.62$, $C_{\mathrm{cub}}=7.5$, $v_0=35$, ${\rho }_{r0}={10}^{-3}$, and ${\varphi }_0=0.5$ (gray curve in Fig. 7).

Figure 9

Projection of three-dimensional phase-space portrait on the $Z=0$ plane for the linear dissipation coefficient with $m=0.62$, $C_{\mathrm{lin}}=0.8$, $v_0=35$, ${\rho }_{r0}={10}^{-3}$, and seven distinct initial conditions for ${\varphi }_0$.

Figure 10

Evolution of energy components as well as equation of state for linear dissipation coefficient with $m=0.62$, $C_{\mathrm{lin}}=0.8$, $v_0=35$, ${\rho }_{r0}={10}^{-3}$, and ${\varphi }_0=1.55$ (gray curve in Fig. 9).

Figure 11

Projection of three-dimensional phase-space portrait on $Z=0$ plane for inverse dissipation coefficient with $m=0.79$, $C_{\mathrm{inv}}=0.2$, $v_0=30$, ${\rho }_{r0}={10}^{-3}$, and six distinct initial conditions for ${\varphi }_0$.

Figure 12

Evolution of energy components as well as equation of state for inverse dissipation coefficient with $m=0.79$, $C_{\mathrm{inv}}=0.2$, $v_0=30$, ${\rho }_{r0}={10}^{-3}$, and ${\varphi }_0=2.2$ (brown curve in Fig. 11).