Late-times asymptotic equation of state for a class of nonlocal theories of gravity. (arXiv:1906.10480v1 [gr-qc])

Late-times asymptotic equation of state for a class of nonlocal theories of gravity. (arXiv:1906.10480v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Giani_L/0/1/0/all/0/1">Leonardo Giani</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Piattella_O/0/1/0/all/0/1">Oliver Fabio Piattella</a>

We investigate the behavior of the asymptotic late-times effective equation
of state for nonlocal theories of gravity in which a term involving the inverse
of the d’Alembertian operator acting on the Ricci scalar is added to the
standard Einstein-Hilbert Lagrangian in the action functional. We find that
under general assumptions, imposing vanishing initial conditions for the
auxiliary fields in order to be naturally compatible with the
radiation-dominated epoch implies that in the models that contain terms
proportional to $Box^{-1}R$ the effective equation of state approaches
asymptotically the one given by a cosmological constant,
$omega_{eff}rightarrow -1$. We argue that this behavior is not a coincidence
and discuss under which conditions this is to be expected.

We investigate the behavior of the asymptotic late-times effective equation
of state for nonlocal theories of gravity in which a term involving the inverse
of the d’Alembertian operator acting on the Ricci scalar is added to the
standard Einstein-Hilbert Lagrangian in the action functional. We find that
under general assumptions, imposing vanishing initial conditions for the
auxiliary fields in order to be naturally compatible with the
radiation-dominated epoch implies that in the models that contain terms
proportional to $Box^{-1}R$ the effective equation of state approaches
asymptotically the one given by a cosmological constant,
$omega_{eff}rightarrow -1$. We argue that this behavior is not a coincidence
and discuss under which conditions this is to be expected.

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