Moduli fields generically produce strong dark matter – radiation and baryon – radiation isocurvature perturbations through their decay if they remain light during inflation .
We show that existing upper bounds on the magnitude of such fluctuations can thus be translated into stringent constraints on the moduli parameter space m _ { \sigma } ( modulus mass ) – \sigma _ { inf } ( modulus vacuum expectation value at the end of inflation ) .
These constraints are complementary to previously existing bounds so that the moduli problem becomes worse at the perturbative level .
In particular , if the inflationary scale H _ { inf } \sim 10 ^ { 13 } GeV , particle physics scenarios which predict high moduli masses m _ { \sigma } \gtrsim 10 - 100 TeV are plagued by the perturbative moduli problem , even though they evade big-bang nucleosynthesis constraints .