Classical Cepheid variable stars ( from hereon : Cepheids ) are high-sensitivity probes of stellar evolution and fundamental tracers of cosmic distances .
While rotational mixing significantly affects the evolution of Cepheid progenitors ( intermediate-mass stars ) , the impact of the resulting changes in stellar structure and composition on Cepheids on their pulsational properties is hitherto unknown .

Here we present the first detailed pulsational instability analysis of stellar evolution models that include the effects of rotation , for both fundamental mode and first overtone pulsation .
We employ Geneva evolution models spanning a three-dimensional grid in mass ( 1.7 - 15 M _ { \odot } ) , metallicity ( Z = 0.014 , 0.006 , 0.002 ) , and rotation ( non-rotating , average & fast rotation ) .
We determine ( 1 ) hot and cool instability strip ( IS ) boundaries taking into account the coupling between convection and pulsation , ( 2 ) pulsation periods , and ( 3 ) rates of period change .
We investigate relations between period and ( a ) luminosity , ( b ) age , ( c ) radius , ( d ) temperature , ( e ) rate of period change , ( f ) mass , ( g ) the flux-weighted gravity-luminosity relation ( FWGLR ) .
We confront all predictions aside from those for age with observations , finding generally excellent agreement .

We tabulate period-luminosity relations ( PLRs ) for several photometric pass-bands and investigate how the finite IS width , different IS crossings , metallicity , and rotation affect PLRs .
We show that a Wesenheit index based on H , V , and I photometry is expected to have the smallest intrinsic PLR dispersion .
We confirm that rotation resolves the Cepheid mass discrepancy .
Period-age relations depend significantly on rotation , with rotation leading to older Cepheids , offering a straightforward explanation for evolved stars in binary systems that can not be matched by conventional isochrones assuming a single age .
We further show that Cepheids obey a tight FWGLR .

Rotation is a fundamental property of stars that has important implications for the study of intermediate-mass stars , intermediate-age clusters , and classical Cepheid variable stars .