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Physics Letters B 797 (2019) 134904

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Thermodynamic interpretation of the de Sitter swampland conjecture

Min-Seok Seo

Department of Physics Education, Korea National University of Education, Cheongju 28173, Republic of Korea

a r t i c l e i n f o a b s t r a c t

Article history:

Received

15 August 2019

Received

in revised form 28 August 2019

Accepted

28 August 2019

Available

online 3 September 2019

Editor:

M. Cveti

We interpret the de Sitter swampland conjecture in the thermodynamic point of view. When the number

of degrees of freedom is enhanced as the modulus rolls down the potential, the bound on m

∇V /V

equivalent to the condition for the positive temperature phase. The boundary between the positive-

and

the negative temperature phases is preferred by the classical system since the entropy density is

maximized. The distance conjecture imposes that (quasi-)de Sitter spacetime is entirely in the negative

temperature phase and statistically disfavored. By investigating the concave potential, we also justify the

bound on m

∇

V /V .

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

The instability of (quasi-)de Sitter (dS) spacetime has been a

long standing issue. While both primordial inﬂationary paradigm

and CDM model explaining the current accelerating Universe are

well consistent with observations [1], constructing model based

on string theory requires the nontrivial setup [2], as suggested

KKLT [3]or large volume scenario [4]. Once the string theory

solution exists, apart from its naturalness, the anthropic principle

[5]or the string landscape [6]might account for the real world

described by the solution. On the other hand, it was recently pro-

posed

that in any parametrically controllable regime (meta-)stable

de Sitter spacetime is not allowed by quantum gravity [7]. Among

many conjectured effective ﬁeld theory (EFT) properties consis-

tent

with quantum gravity (for reviews, see, [8,9]), this de Sit-

ter

swampland conjecture became controversial. Counter-examples

have been studied through the Higgs and the axion potentials,

from which the role of the curvature, not just the slope of the

potential is emphasized [10–17]. Such a situation calls for the re-

ﬁnement

of the conjecture and also the physically acceptable argu-

ments

supporting it. In [18,19], the reﬁned dS swampland bound

was formulated as

|∇V |

≥c, or

min(∇

∇

V )

≤−c



(1)

E-mail address: minseokseo57@gmail.com.

for some positive order one constants c and c



and more impor-

tantly,

Bousso’s covariant entropy bound [20], as well as the dis-

tance

conjecture [21]were considered to support the conjecture in

[19].

That is, in the presence of some modulus along which the

number of physical degrees of freedom N (hence the entropy) in-

creases

rapidly, the condition that the entropy cannot exceed the

Gibbons-Hawking bound S

(we ignored the numerical

factor of order one) results in the ﬁrst bound in (1)as the Hubble

parameter H is also controlled by the modulus. Meanwhile, the

second bound states the breakdown of the semi-classical picture

for dS spacetime by the tachyonic zero point quantum ﬂuctua-

tion.

this argument, the inequality itself comes from the thermo-

dynamic

property of spacetime, i.e., the entropy bound. On the

other hand, the existence of the modulus with properties given

above as well as order one values of c and c



are results of the dis-

tance

conjecture which claims that as the modulus traverses along

the trans-Planckian geodesic distance towers of light degrees of

freedom rapidly descend from UV. Motivated by these facts, in this

letter we make a more systematic interpretation of the dS swamp-

land

conjecture using the language of thermodynamics. Moreover

we try to specify the role of the distance conjecture which is ir-

relevant

to thermodynamics. For this purpose, we take the ansatz

= N

(H/m

)

for the entropy inside the horizon as considered

in [19]. The nonzero exponent p stands for the effect from the

The dS swampland bound can be written as the condition on the Hubble pa-

rameter

H instead of the potential as given by (1)[22]. This enables us to apply the

dS swampland conjecture to exotic inﬂationary cosmology models, in which quasi-

spacetime is not necessarily a consequence of the almost ﬂat potential (see also

[23–25]).

https://doi.org/10.1016/j.physletb.2019.134904

0370-2693/

SCOAP

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