弦理论与暗能量：沼泽地猜想与真空能的量子效应
Physics Letters B 789 (2019) 639–642
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
The swampland, quintessence and the vacuum energy
M.C. David Marsh
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, United Kingdom
a r t i c l e i n f o a b s t r a c t
Article history:
Received
10 September 2018
Accepted
2 November 2018
Available
online 6 November 2018
Editor:
G.F. Giudice
It has recently been conjectured that string theory does not admit de Sitter vacua, and that quintessence
explains the current epoch of accelerated cosmic expansion. A proposed, key prediction of this scenario
is time-varying couplings in the dark sector, induced by the evolving quintessence field. We note that
cosmological models with varying couplings suffer from severe problems with quantum corrections,
beyond those shared by all quintessence models. The vacuum energy depends on the masses and
couplings of the theory, and even small variations of parameters can lead to overwhelmingly large
corrections to the effective potential. We find that quintessence models with varying parameters can
be realised in consistent quantum theories by either: 1) enforcing exceptional levels of fine-tuning;
2) realising some unknown mechanism that cancels all undesirable contributions to the effective potential
with unprecedented accuracy; or 3) ensuring that the quintessence field couples exclusively to very light
states, and does not backreact on heavy fields.
© 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
An important question in fundamental physics is what distin-
guishes
general effective field theories from those that can be
consistently realised in quantum gravity. Inspired by examples of
compactifications from string theory, the authors of [1] conjectured
that quantum gravity severely restricts the effective scalar poten-
tial,
V , of the low-energy theory:
|∇V |≥cV, (1)
for a positive constant c ∼ O(1) and in units where M
Pl
=
1/
√
8π G = 1.
If true, equation (1) has far-reaching implications [1–7]. Most
notably, equation (1)forbids local de Sitter critical points (see
also [8]) and forces the current period of accelerated expansion
to be realised through particular models of quintessence.
1
Ref-
erence [2]argued
that such models can be naturally realised in
string theory where slowly rolling moduli fields can support the
accelerated expansion.
Some
well-known restrictions on quintessence were discussed
in [2,4,6,7,9]. Very light scalar fields coupled to the Standard Model
can mediate long-range forces, which are severely constrained by
precision tests of the equivalence principle. Moreover, scalar fields
E-mail address: m.c.d.marsh@damtp.cam.ac.uk.
1
The implications for inflation were discussed in [2,36–42].
that modify the masses and couplings of the Standard Model
are constrained by astronomical observations. Finally, models of
quintessence require not only that the value of the scalar poten-
tial
is very small, but so must its gradient.
In
reference [2], the absence of observed variations in the Stan-
dard
Model parameters were interpreted as evidence for compar-
atively
stronger couplings between the quintessence scalar and
some fields in the dark sector. This is not a direct consequence of
equation (1), but is arguably natural as such a scenario can be re-
alised
in string theory through branes, e.g. of type IIB or F-theory.
For example, the quintessence field may control the volume of the
cycle where dark matter originates, so that its evolution leads to
variations in dark matter couplings. In the cosmology literature,
models realising dark energy/dark matter interactions are usually
referred to as ‘interacting dark energy’ [10].
The
purpose of this note is to recall that a cosmic scalar field, φ,
that causes variations in couplings and masses suffers from severe
problems when considered in quantum field theory [11–14](see
also [15–17]). The basic argument (reviewed in detail below) is
that small variations in couplings cause large variations in the vac-
uum
energy. For example, avariation in a fine-structure constant
α(φ) =
¯
α +δα to which matter with large mass M is coupled leads
to a variation of the vacuum energy that is schematically of the
form,
δρ
vac
∼ δα(φ) M
4
. (2)
https://doi.org/10.1016/j.physletb.2018.11.001
0370-2693/
© 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.
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