Gravitational wave propagation in a geometric condensate in Starobinsky cosmology

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Abstract In this paper we propose a new paradigm for cosmology: a time dependent scalar condensate background originated from the quadratic $$(R + \alpha R^2)$$ ( R + α R 2 ) Starobinsky model, where R is the Ricci scalar and $$\alpha $$ α the coupling constant. In weak gravity limit the system decouples into a conventional graviton and a higher derivative scalar. It was shown earlier through works from our group (Chakraborty and Ghosh in Phys Dark Universe 35:100976, 2022; Ghosh in Phys. A: Stat. Mech. Appl. 407:245, 2014; Das et al. in Cosmology in R $$^{2}$$ 2 -gravity: effects of a higher derivative scalar condensate background. https://doi.org/10.1016/j.jheap.2024.07.011 ) that the latter can sustain an oscillatory lowest energy configuration or a Geometric Condensate as it consists entirely of metric degrees of freedom. In the present work, we study Gravitational Wave propagation in this condensate background. We show that the explicit time dependent nature of the condensate can generate spatial curvature and radiation-like contributions in the scale factor evolution in FLRW cosmology. Subsequently the condensate leaves its signature on the Gravitational Wave profile as it propagates in the condensate modified FLRW spacetime. The wave profile is calculated analytically in terms of Whittaker functions. The main novelty of the Geometric Condensate scheme is that no external (condensate) matter from outside has been considered.

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