Pg-485 of this pdf
Now we shall discuss the role of capacitor in filtering. When the voltage across the capacitor is rising, it gets charged. If there is no external load, it remains charged to the peak voltage of the rectified output. When there is a load, it gets discharged through the load and the voltage across it begins to fall. In the next half-cycle of rectified output it again gets charged to the peak value (Fig. 14.20). The rate of fall of the voltage across the capacitor depends upon the inverse product of capacitor C and the effective resistance RL used in the circuit and is called the time constant. To make the time constant large value of C should be large. So capacitor input filters use large capacitors. The output voltage obtained by using a capacitor input filter is nearer to the peak voltage of the rectified voltage. This type of filter is most widely used in power supplies.
So, as said in the above paragraph, the capacitor after being raised to the peak voltage, discharges to load as rectified voltage supply starts to decrease. The point I am being confused is, if the rectifier's voltage output voltage drops below the capacitor, then wouldn't the capacitor push back current into the rectifier as well? What effect would this have on the rectifier?
Edit: Thank you everyone for the help!