191 research outputs found
Irregular universe in the Nieh-Yan modified teleparallel gravity
The Nieh-Yan modified teleparallel gravity is a model which modifies the
general relativity equivalent teleparallel gravity by a coupling between the
Nieh-Yan density and an axion-like field. This model predicts parity violations
in the gravitational waves if the axion-like field has a non-trivial
background, and more importantly it is ghost free and avoids the pathologies
presented in other parity-violating gravity models. The cosmological dynamics
and perturbations of the Nieh-Yan modified teleparallel gravity have been
investigated in detail, but all these previous investigations rely on the
symmetry requirement that in the background universe both the metric and affine
connection are homogeneous and isotropic. In this paper we relax the symmetry
constraint on the connection and leave it arbitrary at the beginning, after all
the cosmological principle only needs the metric of the background spacetime to
meet the symmetry requirement. We find a new flat universe solution for the
Nieh-Yan modified teleparallel gravity, for which the background dynamics
itself is unchanged but the perturbations around it present a new feature that
the scalar and tensor perturbations are coupled together at the linear level.
The implications of this peculiar feature in primordial perturbations from
inflation are also discussed.Comment: 20 pages, 1 figures, irregular universe, teleparallel gravit
Computing a Basis for an Integer Lattice
The extended gcd problem takes as input two integers, and asks as output an integer linear combination of the integers that are equal to their gcd. The classical extended Euclidean algorithm and fast variants such as the half-gcd algorithm give efficient algorithmic solutions. In this thesis, we give a fast algorithm to solve the simplest — but not trivial — extension of the scalar extended gcd problem on two integers to the case of integer input matrices.
Given a full column rank (n + 1) × n integer matrix A, we present an algorithm that produces a square nonsingular integer matrix B such that the lattice generated by the rows of B — the set of all integer linear combinations of the rows of B — is equal to the lattice generated by the rows of A. The magnitude of entries in the basis B are guaranteed to be not much larger than those of the input matrix A. The cost of our algorithm to produce B is about the same as that required to multiply together two square integer matrices of dimension n and with the size of entries about that of the input matrix. This running time bound improves by about a factor of n on the fastest previously known algorithm
- …