Physics Letters B 793 (2019) 126–129
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
de Sitter Swampland, H
0
tension & observation
Eoin Ó Colgáin
a,∗
, Maurice H.P.M. van Putten
b
, Hossein Yavartanoo
c
a
Asia Pacific Center for Theoretical Physics, Postech, Pohang 37673, Republic of Korea
b
Physics and Astronomy, Sejong University, Seoul, Republic of Korea
c
State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
a r t i c l e i n f o a b s t r a c t
Article history:
Received
13 March 2019
Received
in revised form 5 April 2019
Accepted
12 April 2019
Available
online 17 April 2019
Editor:
M. Cveti
ˇ
c
Realising de Sitter vacua in string theory is challenging. For this reason it has been conjectured that de
Sitter vacua inhabit the Swampland of inconsistent low-energy effective theories coupled to gravity. Since
de Sitter is an attractor for CDM, the conjecture calls CDM into question. Reality appears sympathetic
to this idea as local measurements of the Hubble constant H
0
are also at odds with CDM analysis of
Planck data. This tension suggests that the de Sitter state is unstable, thereby implying a turning point
in the Hubble parameter. We present a model relieving this tension, which predicts a turning at small
positive redshift z
∗
that is dictated by present-day matter density ω
m
. This feature is easily identified by
homogeneous surveys covering redshifts z ≤ 0.1. We comment on the implications for the Swampland
program.
© 2019 The Authors. 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
String theory enjoys a billing as the leading candidate for a
theory of quantum gravity. It is well-documented that the theory
permits a rich landscape of vacua, so much so that de Sitter vacua
may be plentiful. However, the theory appears to secretly abhor
de Sitter and each manifestation is subject to some criticism (see
[1–3]). The lack of acceptable de Sitter vacua has prompted the
conjecture [4] that de Sitter belongs to inconsistent low-energy ef-
fective
theories coupled to gravity, which are deemed to inhabit
the Swampland [5,6]. This conjecture has attracted considerable at-
tention
[7–15].
Concretely,
the conjecture consists of two criteria. The first
states that theories with large scalar field excursions in reduced
Planck units M
p
= (8π G)
−1/2
are inconsistent, while the second
affirms that the gradient of the potential V of a canonically nor-
malised
scalar field in a consistent gravity theory must satisfy the
bound,
M
p
|∇
φ
V |≥Vc, (1)
where c is a constant of order unity, c ∼ O(1). Quintessence mod-
els
naturally satisfy this bound [7].
*
Corresponding author.
E-mail
addresses: ocolgain.eoin@apctp.org (E. Ó Colgáin), mvp@sejong.ac.kr
(M.H.P.M. van Putten),
yavar@itp.ac.cn (H. Yavartanoo).
The constraint (1)is intriguing. First and foremost, it precludes
de Sitter vacua where ∇
φ
V = 0, thus ruling out CDM even when
c 1. Secondly, (1)represents a marriage of the requirements
of early inflationary and late-time dark energy cosmology. In the
wake of Planck, potentials are required to be flat, i.e. ∇
φ
V small,
whereas we also require that any cosmological constant, in other
words, the potential, at late times also be small. In principle, this
requires double fine-tuning, but this can be avoided if the potential
and its gradient are related.
Recalling
that one realisation of de Sitter is an asymptotic fu-
ture
attractor for the CDM cosmological model, and CDM cap-
tures
beautifully measurements of the Cosmic Microwave Back-
ground
(CMB) anisotropies due to Planck [16], one can recognise
that the conjecture is in obvious conflict with CDM. In this note
we assume the conjecture is correct and attempt a reconciliation
with CDM. To this end there are two possibilities: either a devi-
ation
from CDM happens in the past at positive redshift (z > 0),
so that it is observable and of interest to science, or it happens
in the future (z < 0) and is the subject of science fiction. In light
of the recent tension in the Hubble constant H
0
between its local
value H
0
= 73.48 ± 1.66 km s
−1
Mpc
−1
[17] and the Planck result
based on CDM H
0
= 66.93 ±0.62 km s
−1
Mpc
−1
[18], it is natural
to entertain the prospect that some departure happens at positive
redshift. See [19–40]for attempts to explain the tension.
The
question then is how will this deviation from CDM man-
ifest
itself? In this letter, we provide an alternative late-time cos-
mology.
First, note that at low redshift, z < 2, physics is dominated
https://doi.org/10.1016/j.physletb.2019.04.032
0370-2693/
© 2019 The Authors. 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
.