This lends some support to this idea that two distinct Hubble patches behave for all good purposes classical [145, 171, 283]. But it is still unclear whether the short wavelength modes have any role to play in decohering the long wavelength modes [306]? The density matrix of the fluctuations within the causal horizon, ρ [ δφ ( x ) , δφ ′ ( y )] = 〈 δφ ( x ) | ρ | δφ ′ ( y ) 〉 = Ψ[ δφ ( x )]Ψ ∗ [ δφ ( y )], evolves from pure state to a mixed state, ρ [ δφ ( x ) , δφ ′ ( y )] = P [ δφ ( x )] δ [ δφ ( x ) − δφ ′ ( y )], under the influence of a time dependent in- teraction Hamiltonian arising from (a) time dependent evolution of the inflaton, and (b) the inflaton interactions to matter. It was pointed out in [306] that short wavelength modes can play a role in decohering the long wavelength modes, once reheating takes place. The thermal bath produced from the inflaton decay can act as an environment for the long wave- length modes when these modes re-enter the Hubble patch after the end of inflation. The decoherence effects during inflation are still an open issue [306–308]. 4. Inflaton decay, reheating and thermalization T$_{R}$ = ( 90 π $^{$^{2}$g}$∗ ) 1 / $^{4}$√ Γ$_{φ}$ M$_{P}$ = 0 . 3 ( 200 $^{g}$∗ ) 1 / $^{4}$√ Γ$_{φ}$ M$_{P}$ , (75) Reheating takes place due to the perturbative decay of the inflaton [93–96]. After the end of inflation, when H ≤ m$_{φ}$ , the inflaton field oscillates about the minimum of the potential. Averaging over one oscillation results in pressureless equation of state where 〈 p 〉 = 〈 ˙ φ $^{2}$/ 2 − V ( φ ) 〉 vanishes [93, 94], so that the energy density starts evolving like matter domination (in a quadratic potential) with ρ$_{φ}$ = ρ$_{i}$ ( a$_{i}$/a ) 3 (subscript i denotes the quantities right after the end of inflation) $^{23}$. If Γ$_{φ}$ represents the total decay width of the inflaton to pairs of fermions. This releases the energy into the thermal bath of relativistic particles when H ( a ) = √ (1 / 3 M 2 $_{P}$) ρ$_{i}$ ( a$_{i}$/a ) 3 / 2 ≈ Γ$_{φ}$. The energy density of the thermal bath is determined by the reheat temperature T$_{R}$ , given by: where $^{g}$∗ denotes the effective relativistic degrees of freedom in the plasma. However the inflaton might not decay instantaneously. In such a case there might already exist a thermal plasma of some relativistic species at a temperature higher than the reheat temperature 23 For λφ 4 potential the coherent oscillations yield an effective equation of state similar to that of a radiation epoch. 37