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The signal strength of primordial gravitational waves experiencing an epoch of early scalar domination is reduced with respect to radiation domination. In this paper, we demonstrate that the specific pattern of this reduction is sensitive to the coupling between the dominant field and gravity. When this coupling is zero, the impact of early matter domination on gravitational waves is solely attributed to the alteration of the Hubble parameter and the scale factor. In the presence of non-zero couplings, on the other hand, the evolution of primordial gravitational waves is directly affected as well, resulting in a distinct step-like feature in the power spectrum of the gravitational wave as a function of frequency. This feature serves as a smoking gun signature of this model. In this paper, we provide an analytical expression of the power spectrum that illustrates the dependence of power spectrum on model parameters and initial conditions. Furthermore, we provide analytical relations that specify the frequency interval in which the step occurs. We compare the analytical estimates with numerical analysis and show they match well., Comment: 19 pages, 7 figures, 1 table, and 2 appendices

In this paper, we explore the evolution of baryon asymmetry as well as the hypermagnetic field in the early universe with an assumption that the flavon of the Froggatt-Nielsen carries an asymmetry. Through the decay of the flavon to Standard Model fermions, this asymmetry is transferred to fermions, where the right-handed electron keeps its asymmetry while its Yukawa interaction is out of thermal equilibrium. Through the existence of the flavon, we can ensure that the freezing-in temperature of the right-handed electron is closer to the electroweak phase transition than the Standard cosmology scenario. With this trick, the asymmetry in the right-handed electron is saved for a longer time. Moreover, the injection of the asymmetry to the right-handed electron is gradual, which helps the preservation of the asymmetry in the right-handed sector significantly. Due to the intimate relationship between fermion number violation and the helicity of the hypermagnetic field, some of the asymmetry is used to amplify the hypermagnetic field which itself helps to preserve the remnant asymmetry through keeping the Yukawa processes out of thermal equilibrium. We find the sweet region of the parameter space that can produce the right asymmetry in the baryons while generating a large hypermagnetic field by the time of the electroweak phase transition., Comment: 18 pages, 9 figures