This paper investigates the production of gravitational waves during the reheating phase of inflation, focusing on the minimal production from inflaton scattering in the condensate. The study considers the Starobinsky model and T-models, which are in good agreement with cosmic microwave background (CMB) observations. The gravitational wave spectrum is sensitive to the model parameters, particularly the exponent k in the potential. For k = 2, the spectrum shows a distinct shape compared to k = 4 or higher, allowing for model discrimination. The frequency spectrum can be used to determine the inflaton mass and reheating temperature. The paper computes the gravitational wave spectrum from the inflaton condensate during reheating, showing that the spectrum is redshifted from its initial production to the present day. The results indicate that the gravitational wave spectrum is highly sensitive to the model parameter k, with different behaviors for k = 2, 4, and greater than 4. For k = 2, the spectrum decreases in intensity with increasing frequency, while for k = 4, it is nearly monochromatic. For k > 4, the spectrum increases in frequency, with the maximum intensity at higher frequencies. The paper also discusses the potential for future detectors to observe these gravitational wave signals, highlighting the importance of distinguishing between different inflationary models through their gravitational wave spectra. The results provide a unique signature of the reheating process and the inflaton mass, offering insights into the early universe's dynamics.This paper investigates the production of gravitational waves during the reheating phase of inflation, focusing on the minimal production from inflaton scattering in the condensate. The study considers the Starobinsky model and T-models, which are in good agreement with cosmic microwave background (CMB) observations. The gravitational wave spectrum is sensitive to the model parameters, particularly the exponent k in the potential. For k = 2, the spectrum shows a distinct shape compared to k = 4 or higher, allowing for model discrimination. The frequency spectrum can be used to determine the inflaton mass and reheating temperature. The paper computes the gravitational wave spectrum from the inflaton condensate during reheating, showing that the spectrum is redshifted from its initial production to the present day. The results indicate that the gravitational wave spectrum is highly sensitive to the model parameter k, with different behaviors for k = 2, 4, and greater than 4. For k = 2, the spectrum decreases in intensity with increasing frequency, while for k = 4, it is nearly monochromatic. For k > 4, the spectrum increases in frequency, with the maximum intensity at higher frequencies. The paper also discusses the potential for future detectors to observe these gravitational wave signals, highlighting the importance of distinguishing between different inflationary models through their gravitational wave spectra. The results provide a unique signature of the reheating process and the inflaton mass, offering insights into the early universe's dynamics.