Investigating Cosmic Inflation and Dark Energy in blended models of Particle Theory and Modified Gravity

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We aim to study model-building cosmic inflation and dark energy, possibly in a single theoretical framework, employing realistic particle theories beyond the standard model and also modified gravity theories, such as F(R) gravity. We intend to produce concrete predictions regarding the inflationary observables (scalar spectral index, tensor to scalar ratio) as well as characteristics of dark energy beyond CDM, such as the equation of state parameter and its running, to be probed in the near future, e.g. by the EUCLID and Nancy Grace Roman satellites. Contrast with observations will provide insights on the theoretical background. Emphasis will be given on the resolutions of cosmological open questions, such as the Hubble and growth tensions, and on observational signatures of gravitational waves, such as amplified primordial gravitational waves from inflation (or kination) or from primordial black holes (which could be the dark matter), to be probed in the near future directly by LIGO/Virgo of LISA or indirectly by forthcoming CMB observations, e.g. BICEP, SPIDER, Simons.