Author:
Ye Xuan,Zhang Yang,Wang Bo
Abstract
Abstract
We perform the point-splitting regularization
on the vacuum stress tensor of a coupling scalar field in de Sitter space
under the guidance from the adiabatically regularized Green's function.
For the massive scalar field with the minimal coupling ξ = 0,
the 2nd order point-splitting regularization
yields a finite vacuum stress tensor
with a positive, constant energy density,
which can be identified as the cosmological constant
that drives de Sitter inflation.
For the coupling ξ ≠ 0, we find that,
even if the regularized Green's function is continuous, UV and IR convergent,
the point-splitting regularization does not
automatically lead to an appropriate stress tensor.
The coupling ξ R causes log divergent terms,
as well as higher-order finite terms
which depend upon the path of the coincidence limit.
After removing these unwanted terms by extra treatments,
the 2nd-order regularization
for small couplings ξ ∈ (0,1/7.04),
and respectively the 0th-order regularization
for the conformal coupling ξ=1/6,
yield a finite, constant vacuum stress tensor, in analogy to the case ξ=0.
For the massless field with ξ = 0 or ξ = 1/6,
the point-splitting regularization
yields a vanishing vacuum stress tensor,
and there is no conformal trace anomaly for ξ = 1/6.
If the 4th-order regularization were taken,
the regularized energy density for general ξ would be negative,
which is inconsistent with the de Sitter inflation,
and the regularized Green's function would be singular at the zero mass,
which is unphysical.
In all these cases,
the stress tensor from the point-splitting regularization
is equal to that from the adiabatic one. We also discuss the issue of
the adequate order of regularization.
Subject
Astronomy and Astrophysics
Cited by
2 articles.
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