8,263 research outputs found
On cell problems for Hamilton-Jacobi equations with non-coercive Hamiltonians and its application to homogenization problems
We study a cell problem arising in homogenization for a Hamilton-Jacobi
equation whose Hamiltonian is not coercive. We introduce a generalized notion
of effective Hamiltonians by approximating the equation and characterize the
solvability of the cell problem in terms of the generalized effective
Hamiltonian. Under some sufficient conditions, the result is applied to the
associated homogenization problem. We also show that homogenization for
non-coercive equations fails in general
Does the detection of primordial gravitational waves exclude low energy inflation?
We show that a detectable tensor-to-scalar ratio on the CMB
scale can be generated even during extremely low energy inflation which
saturates the BBN bound . The source of
the gravitational waves is not quantum fluctuations of graviton but those of
gauge fields, energetically supported by coupled axion fields. The
curvature perturbation, the backreaction effect and the validity of
perturbative treatment are carefully checked. Our result indicates that
measuring alone does not immediately fix the inflationary energy scale.Comment: 6 pages, 3 figure
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