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Cosmology in a Time-Crystal Background
We investigate the effects of a Time Crystal-like Condensate on cosmological
dynamics. It is well known that quadratic gravity reduces to Einstein gravity
along with a decoupled higher derivative dynamical scalar
\cite{Alvarez-Gaume:2015rwa}. According to \cite{Chakraborty:2020ktp}, the
above scalar sector can sustain a Time Crystal-like minimum energy state, with
non-trivial time dependence. In the present work we treat the Time Crystal-like
state as the background (that replaces the classical Minkowski vacuum) and
study cosmic evolution on this ``dynamic'' ground state. In the first part we
re-derive \cite{Chakraborty:2020ktp}, in a covariant and more systematic way,
the frequencies that characterize the oscillator like Time crystalline
condensate and interpret it as a background energy-momentum tensor simulating a
matter-like effect. Importantly, no external matter is introduced here and the
condensate, consists of a combination of the metric field and is
generated due to the -term ( is the Ricci scalar) in quadratic gravity
\cite{Alvarez-Gaume:2015rwa}. In a way the spurious degrees of freedom of
-gravity turns into a useful component. The second part comprises of new
effects where the cosmology in Friedmann-Lem\^{i}atre-Robertson-Walker (FLRW)
universe is studied in presence of the energy-momentum tensor characterizing
the Time Crystal Condensate. Under certain approximations, the scale factor of
the FLRW universe is analytically obtained for any spatial geometry. We also
find that the Time Crystal Condensate contributes as a new matter candidate
having radiation-like behavior in the universe. Additionally, irrespective of
the spatial geometry of the universe, the Time Crystal condensate generates a
decelerating phase before the early acceleration starts. This is an indication
of a contracting phase of the universe before its accelerated expansion.Comment: 11 pages, 4 compound figures. Comments are welcom