Pre-explosion helium shell flash in type Ia supernovae

I study the possibility that within the frame of the core degenerate (CD) scenario for type Ia supernovae (SNe Ia) the merger process of the core of the asymptotic giant branch (AGB) star and the white dwarf (WD) maintains an envelope mass of ~0.03Mo that causes a later helium shell flash. I estimate the number of pre-explosion helium shell flash events to be less than few per cents of all CD scenario SNe Ia. A helium shell flash while the star moves to the left on the HR diagram as a post-AGB star (late thermal pulse; LTP) or along the WD cooling track (very LTP) causes the star to expand and become a born again AGB star. Merger remnants exploding while still on the AGB form {hydrogen-polluted} peculiar SNe Ia, while an explosion inside an inflated born-again star results in an early flux excess in the light curve of the SN Ia. The fraction of systems that might show an early flux excess due to LTP/VLTP is <(few)x10^{-4} of all SNe Ia, much below the observed fraction. In the frame of the CD scenario SNe Ia with early flux excess result from SN ejecta collision with planetary nebula fallback gas, or from mixing of 56Ni to the outer regions of the SN ejecta. Ongoing sky surveys might find about one case per year where LTP/VLTP influences the SN light curve.