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Modified Amplitude of Gravitational Waves Spectrum

The spectrum of thermal gravitational waves is obtained by including the high frequency thermal gravitons created from extra-dimensional effect and is a new feature of the spectrum. The amplitude and spectral energy density of gravitational waves in thermal vacuum state are found enhanced. The amplitude of the waves get modified in the frequency range (10$^{-16}$ -10 $^{8}$ Hz) but the corresponding spectral energy density is less than the upper bound of various estimated results. With the addition of higher frequency thermal waves, the obtained spectral energy density of the wave in thermal vacuum state does not exceed the upper bound put by nucleosynthesis rate. The existence of cosmologically originated thermal gravitational waves due to extra dimension is not ruled out.