382 research outputs found
Born-Infeld gravity with a Brans-Dicke scalar
Recently proposed Born-Infeld (BI) theories of gravity assume a constant BI
parameter (). However, no clear consensus exists on the sign and value
of . Recalling the Brans-Dicke (BD) approach, where a scalar field was
used to generate the gravitational constant , we suggest an extension of
Born-Infeld gravity with a similar Brans-Dicke flavor. Thus, a new action, with
elevated to a spacetime dependent real scalar field, is proposed. We
illustrate this new theory in a cosmological setting with pressureless dust and
radiation as matter. Assuming a functional form of , we numerically
obtain the scale factor evolution and other details of the background
cosmology. It is known that BI gravity differs from general relativity (GR) in
the strong-field regime but reduces to GR for intermediate and weak fields. Our
studies in cosmology demonstrate how, with this new, scalar-tensor BI gravity,
deviations from GR as well as usual BI gravity, may arise in the weak-field
regime too. For example, we note a late-time acceleration without any dark
energy contribution. Apart from such qualitative differences, we note that
fixing the sign and value of is no longer a necessity in this theory,
though the origin of the BD scalar does remain an open question.Comment: 25 pages, 7 figures. Published versio
Alphabet Sizes of Auxiliary Variables in Canonical Inner Bounds
Alphabet size of auxiliary random variables in our canonical description is
derived. Our analysis improves upon estimates known in special cases, and
generalizes to an arbitrary multiterminal setup. The salient steps include
decomposition of constituent rate polytopes into orthants, translation of a
hyperplane till it becomes tangent to the achievable region at an extreme
point, and derivation of minimum auxiliary alphabet sizes based on
Caratheodory's theorem.Comment: 20 pages, no figures, explanation of a part of impending IEEE IT
submissio
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